| Fully-connected Layer
| ReLU Activation
| Fully-connected Layer
| DIRT
Class Output Head | Fully-connected Layer
Domain Classifier Head | Fully-connected Layer
| ReLU Activation
| Fully-connected Layer
| ReLU Activation
| Fully-connected Layer

###  D.3 Model sequence

Our algorithm, IWA, constructs an ensemble from a sequence of different
classifiers, e.g. obtained from a sequence of possible hyper-parameter
configurations in domain adaptation algorithms. To obtain this sequence of
models, we train multiple models for every domain adaptation task across all
datasets with different hyper-parameter choices. For the experiments on the
language, image and academic dataset, the values of the hyper-parameters are
shown in Table 9. For the time-series datasets we use the best hyper-
parameters in Ragab et al. (2022), and, to obtain a good sequence of values.
For all settings except MiniDomainnet, we multiply each parameter by
$\lambda\in\\{0,0.0001,0.001,0.01,0.05,0.1,0.25,0.5,0.75,1,1.5,2,5,10\\}$. In
this way, we generate a sequence of $14$ hyper-parameter choices. Due to
computational limitations, in MiniDomainNet we use
$\lambda\in\\{0,0.0001,0.001,0.01,0.1,1,5,10\\}$. All values are listed in
Table 9 and Table 10.

Table 9: Domain adaptation hyper-parameter sequences for experiments on the
datasets Transformed Moons, AmazonReviews, and MiniDomainNet. We multiply each
hyper-paramter with a set of scaling factors
$\lambda\in\\{0,0.0001,0.001,0.01,0.05,0.1,0.25,0.5,0.75,1,1.5,2,5,10\\}$ to
obtain a sequence. Due to computational limitations, for MiniDomainNet we use
only $\lambda\in\\{0,0.0001,0.001,0.01,0.1,1,5,10\\}$.

|  | Datasets
---|---|---
Method | Hyper-parameter | Transformed Moons | Amazon Reviews | MiniDomainNet |
DANN | Classification loss weight | $0.9603$ | $0.9603$ | $0.9603$ |
| Domain loss weight | $\lambda\times 0.9238$ | $\lambda\times 0.9238$ | $\lambda\times 0.9238$ |
DeepCoral | Classification loss weight | $0.05931$ | $0.05931$ | $0.05931$ |
| Coral loss weight | $\lambda\times 8.452$ | $\lambda\times 8.452$ | $\lambda\times 8.452$ |
DDC | Classification loss weight | $0.1593$ | $0.1593$ | $0.1593$ |
| MMD loss weight | $\lambda\times 0.2048$ | $\lambda\times 0.2048$ | $\lambda\times 0.2048$ |
CMD | Classification loss weight | $0.96$ | $0.96$ | $0.96$ |
| CMD loss weight | $\lambda\times 5.52$ | $\lambda\times 5.52$ | $\lambda\times 5.52$ |
HoMM | Classification loss weight | $0.2429$ | $0.2429$ | $0.2429$ |
| Higher-order-MMD loss weight | $\lambda\times 0.9824$ | $\lambda\times 0.9824$ | $\lambda\times 0.9824$ |
CoDATS | Classification loss weight | $0.5416$ | $0.5416$ | $0.5416$ |
| Adversarial loss weight | $\lambda\times 0.5582$ | $\lambda\times 0.5582$ | $\lambda\times 0.5582$ |
DSAN | Classification loss weight | $0.4133$ | $0.4133$ | $0.4133$ |
| Local MMD loss weight | $\lambda\times 0.16$ | $\lambda\times 0.16$ | $\lambda\times 0.16$ |
AdvSKM | Classification loss weight | $0.4637$ | $0.4637$ | $0.4637$ |
| Adversarial MMD loss weight | $\lambda\times 0.1511$ | $\lambda\times 0.1511$ | $\lambda\times 0.1511$ |
MMDA | Classification loss weight | $0.9505$ | $0.9505$ | $0.9505$ |
| MMD loss weight | $\lambda\times 0.5476$ | $\lambda\times 0.5476$ | $\lambda\times 0.5476$ |
| Conditional loss weight | $\lambda\times 0.5167$ | $\lambda\times 0.5167$ | $\lambda\times 0.5167$ |
| Coral loss weight | $\lambda\times 0.5838$ | $\lambda\times 0.5838$ | $\lambda\times 0.5838$ |
CDAN | Classification loss weight | $0.6636$ | $0.6636$ | $0.6636$ |
| Adversarial loss weight | $\lambda\times 0.1954$ | $\lambda\times 0.1954$ | $\lambda\times 0.1954$ |
| Conditional loss weight | $\lambda\times 0.0124$ | $\lambda\times 0.0124$ | $\lambda\times 0.0124$ |
DIRT | Classification loss weight | $0.9752$ | $0.9752$ | $0.9752$ |
| Adversarial loss weight | $\lambda\times 0.3892$ | $\lambda\times 0.3892$ | $\lambda\times 0.3892$ |
| Conditional loss weight | $\lambda\times 0.09228$ | $\lambda\times 0.09228$ | $\lambda\times 0.09228$ |
| Virtual adversarial loss weight | $\lambda\times 0.1947$ | $\lambda\times 0.1947$ | $\lambda\times 0.1947$ |

Table 10: Domain adaptation hyper-parameters for experiments on the time-
series data. We multiply each hyper-paramter with a set of scaling factors
$\lambda\in\\{0,0.0001,0.001,0.01,0.05,0.1,0.25,0.5,0.75,1,1.5,2,5,10\\}$ to
obtain a sequence.

|  | Datasets
---|---|---
Method | Hyper-parameter | UCI-HAR | Sleep-EDF | WISDM | HHAR
DANN | Classification loss weight | $9.74$ | $8.3$ | $5.613$ | $0.9603$
| Domain loss weight | $\lambda\times 5.43$ | $\lambda\times 0.324$ | $\lambda\times 1.857$ | $\lambda\times 0.9238$
DeepCoral | Classification loss weight | $8.67$ | $9.39$ | $8.876$ | $0.05931$
| Coral loss weight | $\lambda\times 0.44$ | $\lambda\times 0.19$ | $\lambda\times 5.56$ | $\lambda\times 8.452$
DDC | Classification loss weight | $6.24$ | $2.951$ | $7.01$ | $0.1593$
| MMD loss weight | $\lambda\times 6.36$ | $\lambda\times 8.923$ | $\lambda\times 7.595$ | $\lambda\times 0.2048$
CMD | Classification loss weight | $0.96$ | $0.96$ | $0.96$ | $0.96$
| CMD loss weight | $\lambda\times 5.52$ | $\lambda\times 5.52$ | $\lambda\times 5.52$ | $\lambda\times 5.52$
HoMM | Classification loss weight | $2.15$ | $0.197$ | $0.1913$ | $0.2429$
| Higher-order-MMD loss weight | $\lambda\times 9.13$ | $\lambda\times 1.102$ | $\lambda\times 4.239$ | $\lambda\times 0.9824$
CoDATS | Classification loss weight | $6.21$ | $9.239$ | $7.187$ | $0.5416$
| Adversarial loss weight | $\lambda\times 1.72$ | $\lambda\times 1.342$ | $\lambda\times 6.439$ | $\lambda\times 0.5582$
DSAN | Classification loss weight | $1.76$ | $6.713$ | $0.1$ | $0.4133$
| Local MMD loss weight | $\lambda\times 1.59$ | $\lambda\times 6.708$ | $\lambda\times 0.1$ | $\lambda\times 0.16$
AdvSKM | Classification loss weight | $3.05$ | $2.5$ | $3.05$ | $0.4637$
| Adversarial MMD loss weight | $\lambda\times 2.876$ | $\lambda\times 2.5$ | $\lambda\times 2.876$ | $\lambda\times 0.1511$
MMDA | Classification loss weight | $6.13$ | $4.48$ | $0.1$ | $0.9505$
| MMD loss weight | $\lambda\times 2.37$ | $\lambda\times 5.951$ | $\lambda\times 0.1$ | $\lambda\times 0.5476$
| Conditional loss weight | $\lambda\times 7.16$ | $\lambda\times 6.13$ | $\lambda\times 0.4753$ | $\lambda\times 0.5167$
| Coral loss weight | $\lambda\times 8.63$ | $\lambda\times 3.36$ | $\lambda\times 0.1$ | $\lambda\times 0.5838$
CDAN | Classification loss weight | $5.19$ | $6.803$ | $9.54$ | $0.6636$
| Adversarial loss weight | $\lambda\times 2.91$ | $\lambda\times 4.726$ | $\lambda\times 3.283$ | $\lambda\times 0.1954$
| Conditional loss weight | $\lambda\times 1.73$ | $\lambda\times 1.307$ | $\lambda\times 0.1$ | $\lambda\times 0.0124$
DIRT | Classification loss weight | $7.0$ | $9.183$ | $0.1$ | $0.9752$
| Adversarial loss weight | $\lambda\times 4.51$ | $\lambda\times 7.411$ | $\lambda\times 0.1$ | $\lambda\times 0.3892$
| Conditional loss weight | $\lambda\times 0.79$ | $\lambda\times 2.564$ | $\lambda\times 0.1$ | $\lambda\times 0.09228$
| Virtual adversarial loss weight | $\lambda\times 9.31$ | $\lambda\times 3.583$ | $\lambda\times 0.1$ | $\lambda\times 0.1947$

###  D.4 Matrix Inversion

Matrix inversion is a well-known numerical task, especially in cases of
limited computing precision and ill-conditioned matrices. In our case, similar
models in the given sequence can cause numerical instability due to limited
compute precision. That is, occasionally a tabula rasa inversion of the matrix
$\widetilde{G}$ in Algorithm 1 is numerically unstable. Various standard
approaches can be applied to handle this common issue, including the exclusion
of similar models and various regularization techniques. In our computational
setup, we rely on the Python routine numpy.linalg.pinv, which is based on the
eigendecompostion of $\widetilde{G}$ (coinciding with the singular value
decomposition in our case due to positive-definiteness) and an eigenvalue-
based regularization based on a treshold value rcond for small eigenvalues,
see Strang (1980, pages 138–140) for details. The choice of rcond depends on
the scale of the Gram matrix and can therefore be chosen by source data only.
Based on evaluating our method on source data only (target domain is fixed to
be source domain) on several choices for rcond, we obtain a stable choice for
rcond of $10^{-1}$ for all datasets.

###  D.5 Correlation Analysis: Target Accuracy of Individual Models vs.
Aggregation Weight

Figure 2 in the main paper suggests that there is a positive correlation
between the target accuracy of each individual model (orange dashed line,
Figure 2 top) and the respective aggregation weight (red bars, Figure 2
bottom), if the linear aggregation of the models is computed by our method
IWA. In the following, we analyze whether this trend holds throughout all
other experiments.

More precisely, for a given sequence $f_{1},\ldots,f_{l}$ of models, we
compute the Pearson correlation coefficient between the aggregation weights
$\widetilde{c}_{1},\ldots,\widetilde{c}_{l}$ (see Algorithm 1) and the
corresponding target accuracies
$\frac{1}{t}\sum_{i=1}^{t}\mathbf{1}[y_{i}=f_{1}(x_{i})],\ldots,\frac{1}{t}\sum_{i=1}^{t}\mathbf{1}[y_{i}=f_{l}(x_{i})]$
for the target test data $(x_{1},y_{1}),\ldots,(x_{t},y_{t})$, where
$\mathbf{1}[P]=1$ iff $P$ is true and $\mathbf{1}[P]=0$ otherwise. In this
context, a positive correlation coefficient means that the aggregation
algorithm assigns a higher weight to models performing better on target
samples. We calculate these coefficients for our method IWA and the other
linear regression baselines SOR, TCR, and TMR for all domain adaptation
methods across all datasets and cross-domain scenarios. Note that for this
analysis we cannot compare to the other baseline TMV, as the count-based
aggregation by majority voting does not involve the computation of aggregation
weights.

In Figure 6 and 6 we compare the resulting correlation coefficient
distribution of our method IWA to the ones for the heuristic baselines SOR,
TCR, and TMR. Figure 6 compares the correlation coefficients for IWA on
different datasets.

We find that IWA shows a stronger positive correlation than other methods,
between a model’s target accuracy and its aggregation weight.

Figure 4: Boxplots of the correlation coefficients of IWA and the linear
regression heuristic baselines SOR, TCR, and TMR over all datasets.

Figure 5: Boxplots of the correlation coefficients of IWA for each dataset.

Figure 6: Histogram of the correlation coefficients of IWA and the linear
regression heuristic baselines SOR, TCR and TMR over all datasets (showing the
same data as Figure 6). In comparison to the heuristic baselines, IWA shows a
stronger positive correlation between a model’s target accuracy and its
aggregation weight.

###  D.6 Sensitivity Analysis: Effect of Adding Inaccurate Models

We study the sensitivity of our method with respect to adding inaccurate
models in the given sequence of models. We define an innacurate model as
having a target accuracy lower than $80\%$ of the target accuracy of the model
computed without domain adaptation (SO). In particular, we add $+10,+50$ and
$+100$ inaccurate models to the given sequences of models. One inaccurate
model is constructed as follows: First, a model is chosen uniformly at random
from the given sequence of models. Second, the outputs of the chosen model are
corrupted by adding, to half of the elements of its vector-valued output,
random Gaussian noise with zero-mean and unit variance.

In Figure 7, we show the median performance over all domain adaptation methods
for each dataset. We see, that the performance of our method (IWA) is not very
sensitive w.r.t. an increase in the number of inaccurate models. This is in
contrast to the heuristics (e.g. TMV, TMR or TCR) and model selection method
DEV, which show a high sensitivity concerning adding inaccurate models. SOR
also shows stable results; it is, however, clearly outperformed by our method
in five out of six datasets. We conclude, that IWA is not only overall the
best performing method, but also the most stable choice concerning inaccurate
models in the given sequence.

(a)

(b)

(c)

(d)

(e)

(f)

Figure 7: Sensitivity of methods for parameter choice issues w.r.t. adding
inaccurate models in the given sequence of models; separate for each dataset
(a–f), averaged over all domain adaptation methods, source-target pairs, and
random seeds. Horizontal axes: Number of inaccurate models added to the
initial sequence of models. Vertical axes: Target accuracy. Solid lines
indicate median and shaded area indicate $50\%$ confidence intervals.

###  D.7 Detailed Empirical Results

In this section, we add all result tables for the datasets described in the
main paper. Table 15, Table 16 and Table 17 show all domain adaptation tasks
for the Amazon Review dataset. Table 13 shows all domain adaptation tasks for
the MiniDomainNet experiments. Table 21, Table 22, Table 23, Table 24, Table
25, Table 26, Table 27, and Table 28 show all domain adaptation task results
for the time-series datasets.

##### Baselines

As addressed in the main paper, our method, IWA, is compared to ensemble
learning methods that use linear regression and majority voting as heuristic
for model aggregation, and, model selection methods with theoretical error
guarantees. The heuristic baselines are majority voting on target data (TMV),
source-only regression (SOR), target majority voting regression (TMR), target
confidence average regression (TCR). The model selection methods with
theoretical error guarantees are importance weighted validation (IWV)
(Sugiyama et al., 2007) and deep embedded validation (DEV) (Kouw et al.,
2019). The tables also provide a column for source-only (SO) performance and
target-best (TB) performance. We highlight in bold the performance of the best
performing method with theoretical error guarantees, and in italic the best
performing heuristic.

####  D.7.1 Detailed Summary Results

Table 11: Average target accuracies (and average standard deviations) for all
$7$ datasets (e.g., Sleep-EDF, MiniDomainNet, Amazon Reviews) taken over
several domain adaptation tasks (e.g., $5$ on Sleep-EDF, $5$ on MiniDomainNet,
$12$ on Amazon Reviews), $11$ domain adaptation methods (e.g., DANN, HoMM,
CMD) and $3$ repetitions with different random initialization of model
weights. The input sequences of the approaches (e.g., DEV, IWA) consist of
neural networks computed by runs of the domain adaptation methods with
different hyper-parameters (e.g., $8$ different values of $\lambda$ for DANN).

|  | Heuristic | Theoretical error guarantees |
---|---|---|---|---
Dataset | SO | TMV | TMR | TCR | SOR | IWV | DEV | IWA (ours) | TB
Transformed Moons | $0.989(\pm 0.008)$ | $0.980(\pm 0.006)$ | $0.981(\pm 0.007)$ | ${\it 0.997(\pm 0.002)}$ | $0.989(\pm 0.010)$ | $0.989(\pm 0.008)$ | $0.981(\pm 0.022)$ | ${\bf 0.997(\pm 0.002)}$ | $0.997(\pm 0.005)$
Amazon Reviews | $0.767(\pm 0.011)$ | $0.787(\pm 0.009)$ | $0.786(\pm 0.010)$ | $0.786(\pm 0.010)$ | ${\it 0.789(\pm 0.010)}$ | $0.772(\pm 0.014)$ | $0.764(\pm 0.019)$ | ${\bf 0.788(\pm 0.009)}$ | $0.781(\pm 0.012)$
MiniDomainNet | $0.507(\pm 0.022)$ | ${\it 0.526(\pm 0.011)}$ | $0.525(\pm 0.014)$ | $0.526(\pm 0.013)$ | $0.518(\pm 0.012)$ | $0.513(\pm 0.022)$ | $0.515(\pm 0.028)$ | ${\bf 0.531(\pm 0.011)}$ | $0.534(\pm 0.022)$
Sleep-EDF | $0.655(\pm 0.054)$ | ${\it 0.729(\pm 0.018)}$ | $0.729(\pm 0.024)$ | $0.725(\pm 0.023)$ | $0.717(\pm 0.028)$ | $0.700(\pm 0.052)$ | $0.660(\pm 0.057)$ | ${\bf 0.737(\pm 0.020)}$ | $0.712(\pm 0.045)$
UCI-HAR | $0.770(\pm 0.046)$ | ${\it 0.840(\pm 0.017)}$ | $0.833(\pm 0.023)$ | $0.832(\pm 0.024)$ | $0.769(\pm 0.060)$ | $0.774(\pm 0.070)$ | $0.765(\pm 0.090)$ | ${\bf 0.835(\pm 0.020)}$ | $0.850(\pm 0.029)$
HHAR | $0.732(\pm 0.042)$ | $0.771(\pm 0.015)$ | $0.768(\pm 0.017)$ | ${\it 0.771(\pm 0.018)}$ | $0.722(\pm 0.068)$ | $0.746(\pm 0.037)$ | $0.722(\pm 0.063)$ | ${\bf 0.787(\pm 0.012)}$ | $0.784(\pm 0.028)$
WISDM | $0.736(\pm 0.050)$ | ${\it 0.768(\pm 0.027)}$ | $0.768(\pm 0.036)$ | $0.765(\pm 0.037)$ | $0.737(\pm 0.062)$ | $0.736(\pm 0.052)$ | $0.726(\pm 0.077)$ | ${\bf 0.764(\pm 0.025)}$ | $0.771(\pm 0.046)$

Table 12: Mean and standard deviation (after $\pm$) of target classification
accuracy on Amazon Reviews dataset over three different random initialization
of model weights and 12 domain adaptation tasks.

| Amazon Reviews
---|---
|  | Heuristic | Theoretical error guarantees |
Method | SO | TMV | TMR | TCR | SOR | IWV | DEV | IWA (ours) | TB
HoMM | $0.769(\pm 0.009)$ | $0.777(\pm 0.010)$ | $0.778(\pm 0.010)$ | ${\it 0.778(\pm 0.011)}$ | $0.777(\pm 0.010)$ | $0.765(\pm 0.011)$ | $0.766(\pm 0.011)$ | ${\bf 0.778(\pm 0.010)}$ | $0.769(\pm 0.012)$
AdvSKM | $0.766(\pm 0.012)$ | ${\it 0.780(\pm 0.009)}$ | $0.779(\pm 0.010)$ | $0.779(\pm 0.008)$ | $0.778(\pm 0.011)$ | $0.769(\pm 0.012)$ | $0.766(\pm 0.012)$ | ${\bf 0.780(\pm 0.009)}$ | $0.770(\pm 0.012)$
DIRT | $0.764(\pm 0.009)$ | $0.786(\pm 0.008)$ | $0.786(\pm 0.010)$ | $0.786(\pm 0.008)$ | ${\it 0.800(\pm 0.008)}$ | $0.778(\pm 0.022)$ | $0.773(\pm 0.056)$ | ${\bf 0.787(\pm 0.008)}$ | $0.786(\pm 0.009)$
DDC | $0.766(\pm 0.012)$ | $0.779(\pm 0.010)$ | ${\it 0.780(\pm 0.009)}$ | $0.779(\pm 0.010)$ | $0.778(\pm 0.010)$ | $0.767(\pm 0.017)$ | $0.768(\pm 0.011)$ | ${\bf 0.780(\pm 0.010)}$ | $0.770(\pm 0.013)$
CMD | $0.767(\pm 0.012)$ | $0.791(\pm 0.009)$ | $0.792(\pm 0.009)$ | $0.789(\pm 0.010)$ | ${\it 0.792(\pm 0.010)}$ | $0.765(\pm 0.015)$ | $0.710(\pm 0.015)$ | ${\bf 0.794(\pm 0.009)}$ | $0.785(\pm 0.009)$
MMDA | $0.767(\pm 0.011)$ | $0.787(\pm 0.011)$ | $0.785(\pm 0.010)$ | $0.785(\pm 0.010)$ | ${\it 0.787(\pm 0.012)}$ | $0.769(\pm 0.011)$ | $0.766(\pm 0.010)$ | ${\bf 0.787(\pm 0.011)}$ | $0.782(\pm 0.011)$
CoDATS | $0.766(\pm 0.013)$ | $0.795(\pm 0.009)$ | $0.793(\pm 0.010)$ | $0.794(\pm 0.012)$ | ${\it 0.799(\pm 0.010)}$ | $0.779(\pm 0.016)$ | $0.773(\pm 0.020)$ | ${\bf 0.796(\pm 0.009)}$ | $0.791(\pm 0.015)$
Deep-Coral | $0.766(\pm 0.012)$ | ${\it 0.784(\pm 0.009)}$ | $0.783(\pm 0.009)$ | $0.783(\pm 0.009)$ | $0.782(\pm 0.009)$ | $0.769(\pm 0.016)$ | $0.769(\pm 0.037)$ | ${\bf 0.785(\pm 0.009)}$ | $0.776(\pm 0.013)$
CDAN | $0.767(\pm 0.012)$ | ${\it 0.788(\pm 0.010)}$ | $0.787(\pm 0.009)$ | $0.787(\pm 0.010)$ | $0.787(\pm 0.011)$ | $0.775(\pm 0.011)$ | $0.776(\pm 0.014)$ | ${\bf 0.788(\pm 0.010)}$ | $0.777(\pm 0.011)$
DANN | $0.767(\pm 0.012)$ | $0.796(\pm 0.010)$ | $0.792(\pm 0.010)$ | $0.793(\pm 0.010)$ | ${\it 0.800(\pm 0.011)}$ | $0.776(\pm 0.011)$ | $0.778(\pm 0.012)$ | ${\bf 0.797(\pm 0.009)}$ | $0.798(\pm 0.012)$
DSAN | $0.769(\pm 0.009)$ | $0.796(\pm 0.009)$ | $0.792(\pm 0.009)$ | $0.791(\pm 0.010)$ | ${\it 0.800(\pm 0.010)}$ | $0.779(\pm 0.012)$ | $0.763(\pm 0.017)$ | ${\bf 0.795(\pm 0.009)}$ | $0.789(\pm 0.012)$
Avg. | $0.767(\pm 0.011)$ | $0.787(\pm 0.009)$ | $0.786(\pm 0.010)$ | $0.786(\pm 0.010)$ | ${\it 0.789(\pm 0.010)}$ | $0.772(\pm 0.014)$ | $0.764(\pm 0.019)$ | ${\bf 0.788(\pm 0.009)}$ | $0.781(\pm 0.012)$

Table 13: Mean and standard deviation (after $\pm$) of target classification
accuracy on MiniDomainNet dataset over three different random initialization
of model weights and five domain adaptation tasks.

| MiniDomainNet
---|---
|  | Heuristic | Theoretical error guarantees |
Method | SO | TMV | TMR | TCR | SOR | IWV | DEV | IWA (ours) | TB
HoMM | $0.509(\pm 0.018)$ | ${\it 0.526(\pm 0.009)}$ | $0.524(\pm 0.010)$ | $0.523(\pm 0.010)$ | $0.518(\pm 0.015)$ | $0.511(\pm 0.018)$ | $0.511(\pm 0.018)$ | ${\bf 0.531(\pm 0.007)}$ | $0.537(\pm 0.020)$
AdvSKM | $0.509(\pm 0.015)$ | ${\it 0.516(\pm 0.011)}$ | $0.514(\pm 0.014)$ | $0.514(\pm 0.017)$ | $0.514(\pm 0.009)$ | $0.515(\pm 0.032)$ | $0.512(\pm 0.032)$ | ${\bf 0.516(\pm 0.011)}$ | $0.522(\pm 0.017)$
DIRT | $0.499(\pm 0.022)$ | ${\it 0.517(\pm 0.006)}$ | $0.515(\pm 0.009)$ | $0.508(\pm 0.006)$ | $0.507(\pm 0.018)$ | $0.493(\pm 0.028)$ | $0.498(\pm 0.033)$ | ${\bf 0.519(\pm 0.006)}$ | $0.525(\pm 0.020)$
DDC | $0.510(\pm 0.032)$ | ${\it 0.514(\pm 0.012)}$ | $0.512(\pm 0.018)$ | $0.511(\pm 0.019)$ | $0.514(\pm 0.015)$ | $0.511(\pm 0.028)$ | $0.512(\pm 0.043)$ | ${\bf 0.516(\pm 0.015)}$ | $0.521(\pm 0.019)$
CMD | $0.509(\pm 0.019)$ | $0.528(\pm 0.011)$ | ${\it 0.531(\pm 0.016)}$ | $0.531(\pm 0.016)$ | $0.522(\pm 0.013)$ | $0.518(\pm 0.025)$ | $0.490(\pm 0.037)$ | ${\bf 0.533(\pm 0.009)}$ | $0.533(\pm 0.024)$
MMDA | $0.509(\pm 0.021)$ | ${\it 0.524(\pm 0.004)}$ | $0.522(\pm 0.005)$ | $0.523(\pm 0.007)$ | $0.519(\pm 0.012)$ | $0.517(\pm 0.008)$ | $0.524(\pm 0.006)$ | ${\bf 0.527(\pm 0.009)}$ | $0.531(\pm 0.029)$
CoDATS | $0.502(\pm 0.026)$ | $0.535(\pm 0.026)$ | $0.533(\pm 0.027)$ | ${\it 0.536(\pm 0.028)}$ | $0.525(\pm 0.015)$ | $0.518(\pm 0.031)$ | $0.524(\pm 0.051)$ | ${\bf 0.536(\pm 0.025)}$ | $0.529(\pm 0.042)$
Deep-Coral | $0.505(\pm 0.022)$ | ${\it 0.538(\pm 0.009)}$ | $0.534(\pm 0.013)$ | $0.533(\pm 0.012)$ | $0.520(\pm 0.010)$ | $0.518(\pm 0.022)$ | $0.524(\pm 0.034)$ | ${\bf 0.539(\pm 0.012)}$ | $0.535(\pm 0.024)$
CDAN | $0.514(\pm 0.028)$ | ${\it 0.526(\pm 0.013)}$ | $0.524(\pm 0.011)$ | $0.525(\pm 0.008)$ | $0.517(\pm 0.005)$ | $0.513(\pm 0.011)$ | $0.516(\pm 0.014)$ | ${\bf 0.532(\pm 0.010)}$ | $0.542(\pm 0.017)$
DANN | $0.496(\pm 0.023)$ | $0.530(\pm 0.011)$ | $0.535(\pm 0.011)$ | ${\it 0.538(\pm 0.005)}$ | $0.516(\pm 0.011)$ | $0.519(\pm 0.015)$ | $0.515(\pm 0.013)$ | ${\bf 0.541(\pm 0.006)}$ | $0.532(\pm 0.014)$
DSAN | $0.509(\pm 0.022)$ | $0.537(\pm 0.011)$ | $0.534(\pm 0.013)$ | ${\it 0.543(\pm 0.011)}$ | $0.525(\pm 0.013)$ | $0.513(\pm 0.018)$ | $0.535(\pm 0.023)$ | ${\bf 0.546(\pm 0.007)}$ | $0.563(\pm 0.013)$
Avg. | $0.507(\pm 0.022)$ | ${\it 0.526(\pm 0.011)}$ | $0.525(\pm 0.014)$ | $0.526(\pm 0.013)$ | $0.518(\pm 0.012)$ | $0.513(\pm 0.022)$ | $0.515(\pm 0.028)$ | ${\bf 0.531(\pm 0.011)}$ | $0.534(\pm 0.022)$

Table 14: Mean and standard deviation (after $\pm$) of target classification
accuracy on four time series datasets over three different random
initialization of model weights and five domain adaptation tasks.

| Sleep-EDF
---|---
|  | Heuristic | Theoretical error guarantees |
Method | SO | TMV | TMR | TCR | SOR | IWV | DEV | IWA (ours) | TB
HoMM | $0.676(\pm 0.036)$ | $0.722(\pm 0.017)$ | $0.719(\pm 0.023)$ | $0.718(\pm 0.021)$ | ${\it 0.724(\pm 0.032)}$ | $0.726(\pm 0.046)$ | $0.678(\pm 0.035)$ | ${\bf 0.747(\pm 0.025)}$ | $0.715(\pm 0.047)$
AdvSKM | $0.665(\pm 0.058)$ | $0.708(\pm 0.023)$ | $0.712(\pm 0.027)$ | $0.712(\pm 0.032)$ | ${\it 0.718(\pm 0.030)}$ | $0.703(\pm 0.069)$ | $0.692(\pm 0.038)$ | ${\bf 0.722(\pm 0.025)}$ | $0.706(\pm 0.054)$
DIRT | $0.656(\pm 0.058)$ | $0.743(\pm 0.009)$ | $0.745(\pm 0.012)$ | ${\it 0.748(\pm 0.019)}$ | $0.742(\pm 0.031)$ | $0.679(\pm 0.038)$ | $0.686(\pm 0.066)$ | ${\bf 0.749(\pm 0.010)}$ | $0.728(\pm 0.037)$
DDC | $0.646(\pm 0.035)$ | $0.717(\pm 0.029)$ | ${\it 0.721(\pm 0.037)}$ | $0.712(\pm 0.031)$ | $0.695(\pm 0.020)$ | $0.694(\pm 0.056)$ | $0.666(\pm 0.031)$ | ${\bf 0.724(\pm 0.012)}$ | $0.704(\pm 0.031)$
CMD | $0.653(\pm 0.057)$ | ${\it 0.740(\pm 0.022)}$ | $0.736(\pm 0.016)$ | $0.723(\pm 0.020)$ | $0.709(\pm 0.015)$ | $0.716(\pm 0.052)$ | $0.640(\pm 0.068)$ | ${\bf 0.729(\pm 0.018)}$ | $0.725(\pm 0.053)$
MMDA | $0.650(\pm 0.051)$ | ${\it 0.736(\pm 0.014)}$ | $0.727(\pm 0.021)$ | $0.723(\pm 0.018)$ | $0.714(\pm 0.028)$ | $0.704(\pm 0.033)$ | $0.660(\pm 0.034)$ | ${\bf 0.745(\pm 0.031)}$ | $0.715(\pm 0.042)$
CoDATS | $0.672(\pm 0.084)$ | $0.738(\pm 0.029)$ | ${\it 0.739(\pm 0.036)}$ | $0.736(\pm 0.030)$ | $0.723(\pm 0.039)$ | $0.683(\pm 0.090)$ | $0.690(\pm 0.107)$ | ${\bf 0.744(\pm 0.021)}$ | $0.715(\pm 0.045)$
Deep-Coral | $0.643(\pm 0.049)$ | $0.716(\pm 0.018)$ | ${\it 0.717(\pm 0.028)}$ | $0.712(\pm 0.027)$ | $0.694(\pm 0.032)$ | $0.700(\pm 0.053)$ | $0.675(\pm 0.077)$ | ${\bf 0.713(\pm 0.021)}$ | $0.702(\pm 0.070)$
CDAN | $0.652(\pm 0.056)$ | $0.732(\pm 0.016)$ | $0.739(\pm 0.024)$ | ${\it 0.739(\pm 0.018)}$ | $0.728(\pm 0.029)$ | $0.697(\pm 0.031)$ | $0.642(\pm 0.065)$ | ${\bf 0.748(\pm 0.019)}$ | $0.713(\pm 0.045)$
DANN | $0.641(\pm 0.047)$ | $0.722(\pm 0.017)$ | ${\it 0.723(\pm 0.026)}$ | $0.721(\pm 0.025)$ | $0.714(\pm 0.024)$ | $0.687(\pm 0.034)$ | $0.644(\pm 0.046)$ | ${\bf 0.724(\pm 0.018)}$ | $0.710(\pm 0.035)$
DSAN | $0.653(\pm 0.060)$ | ${\it 0.748(\pm 0.008)}$ | $0.740(\pm 0.016)$ | $0.732(\pm 0.016)$ | $0.728(\pm 0.026)$ | $0.712(\pm 0.070)$ | $0.589(\pm 0.063)$ | ${\bf 0.757(\pm 0.016)}$ | $0.700(\pm 0.033)$
Avg. | $0.655(\pm 0.054)$ | ${\it 0.729(\pm 0.018)}$ | $0.729(\pm 0.024)$ | $0.725(\pm 0.023)$ | $0.717(\pm 0.028)$ | $0.700(\pm 0.052)$ | $0.660(\pm 0.057)$ | ${\bf 0.737(\pm 0.020)}$ | $0.712(\pm 0.045)$

| UCI-HAR
---|---
|  | Heuristic | Theoretical error guarantees |
Method | SO | TMV | TMR | TCR | SOR | IWV | DEV | IWA (ours) | TB
HoMM | $0.782(\pm 0.078)$ | ${\it 0.833(\pm 0.020)}$ | $0.818(\pm 0.023)$ | $0.818(\pm 0.022)$ | $0.783(\pm 0.040)$ | $0.809(\pm 0.095)$ | $0.800(\pm 0.098)$ | ${\bf 0.826(\pm 0.010)}$ | $0.854(\pm 0.039)$
AdvSKM | $0.724(\pm 0.059)$ | $0.791(\pm 0.024)$ | $0.800(\pm 0.022)$ | ${\it 0.810(\pm 0.022)}$ | $0.768(\pm 0.042)$ | $0.707(\pm 0.100)$ | $0.711(\pm 0.167)$ | ${\bf 0.800(\pm 0.022)}$ | $0.811(\pm 0.039)$
DIRT | $0.783(\pm 0.044)$ | ${\it 0.912(\pm 0.013)}$ | $0.907(\pm 0.009)$ | $0.890(\pm 0.016)$ | $0.756(\pm 0.036)$ | $0.807(\pm 0.107)$ | $0.808(\pm 0.112)$ | ${\bf 0.900(\pm 0.015)}$ | $0.928(\pm 0.034)$
DDC | $0.790(\pm 0.061)$ | $0.806(\pm 0.019)$ | $0.807(\pm 0.026)$ | ${\it 0.810(\pm 0.017)}$ | $0.756(\pm 0.108)$ | $0.724(\pm 0.066)$ | $0.734(\pm 0.109)$ | ${\bf 0.804(\pm 0.028)}$ | $0.792(\pm 0.013)$
CMD | $0.788(\pm 0.058)$ | ${\it 0.869(\pm 0.012)}$ | $0.849(\pm 0.014)$ | $0.839(\pm 0.023)$ | $0.731(\pm 0.066)$ | $0.804(\pm 0.064)$ | $0.812(\pm 0.080)$ | ${\bf 0.842(\pm 0.025)}$ | $0.888(\pm 0.037)$
MMDA | $0.785(\pm 0.018)$ | ${\it 0.819(\pm 0.022)}$ | $0.812(\pm 0.028)$ | $0.800(\pm 0.032)$ | $0.759(\pm 0.085)$ | $0.773(\pm 0.073)$ | $0.767(\pm 0.107)$ | ${\bf 0.807(\pm 0.025)}$ | $0.840(\pm 0.055)$
CoDATS | $0.760(\pm 0.037)$ | ${\it 0.854(\pm 0.022)}$ | $0.832(\pm 0.027)$ | $0.832(\pm 0.006)$ | $0.785(\pm 0.057)$ | $0.801(\pm 0.079)$ | $0.794(\pm 0.078)$ | ${\bf 0.846(\pm 0.016)}$ | $0.867(\pm 0.012)$
Deep-Coral | $0.790(\pm 0.035)$ | ${\it 0.810(\pm 0.007)}$ | $0.800(\pm 0.022)$ | $0.808(\pm 0.030)$ | $0.771(\pm 0.023)$ | $0.768(\pm 0.044)$ | $0.773(\pm 0.087)$ | ${\bf 0.808(\pm 0.016)}$ | $0.806(\pm 0.022)$
CDAN | $0.756(\pm 0.055)$ | $0.842(\pm 0.009)$ | ${\it 0.843(\pm 0.020)}$ | $0.840(\pm 0.034)$ | $0.802(\pm 0.080)$ | $0.781(\pm 0.072)$ | $0.687(\pm 0.068)$ | ${\bf 0.846(\pm 0.018)}$ | $0.853(\pm 0.026)$
DANN | $0.756(\pm 0.026)$ | ${\it 0.858(\pm 0.016)}$ | $0.856(\pm 0.033)$ | $0.856(\pm 0.033)$ | $0.800(\pm 0.057)$ | $0.763(\pm 0.032)$ | $0.780(\pm 0.043)$ | ${\bf 0.849(\pm 0.023)}$ | $0.847(\pm 0.007)$
DSAN | $0.762(\pm 0.032)$ | $0.849(\pm 0.023)$ | $0.843(\pm 0.033)$ | ${\it 0.854(\pm 0.025)}$ | $0.749(\pm 0.065)$ | $0.775(\pm 0.043)$ | $0.744(\pm 0.035)$ | ${\bf 0.858(\pm 0.023)}$ | $0.865(\pm 0.038)$
Avg. | $0.770(\pm 0.046)$ | ${\it 0.840(\pm 0.017)}$ | $0.833(\pm 0.023)$ | $0.832(\pm 0.024)$ | $0.769(\pm 0.060)$ | $0.774(\pm 0.070)$ | $0.765(\pm 0.090)$ | ${\bf 0.835(\pm 0.020)}$ | $0.850(\pm 0.029)$

| HHAR
---|---
|  | Heuristic | Theoretical error guarantees |
Method | SO | TMV | TMR | TCR | SOR | IWV | DEV | IWA (ours) | TB
HoMM | $0.739(\pm 0.044)$ | $0.757(\pm 0.014)$ | ${\it 0.759(\pm 0.013)}$ | $0.759(\pm 0.011)$ | $0.700(\pm 0.058)$ | $0.720(\pm 0.027)$ | $0.733(\pm 0.031)$ | ${\bf 0.759(\pm 0.007)}$ | $0.764(\pm 0.023)$
AdvSKM | $0.718(\pm 0.042)$ | ${\it 0.749(\pm 0.027)}$ | $0.742(\pm 0.032)$ | $0.748(\pm 0.034)$ | $0.676(\pm 0.046)$ | $0.730(\pm 0.051)$ | $0.728(\pm 0.051)$ | ${\bf 0.752(\pm 0.031)}$ | $0.749(\pm 0.025)$
DIRT | $0.728(\pm 0.026)$ | ${\it 0.803(\pm 0.011)}$ | $0.792(\pm 0.016)$ | $0.803(\pm 0.017)$ | $0.796(\pm 0.066)$ | $0.743(\pm 0.028)$ | $0.739(\pm 0.075)$ | ${\bf 0.816(\pm 0.008)}$ | $0.820(\pm 0.015)$
DDC | $0.716(\pm 0.063)$ | $0.748(\pm 0.014)$ | ${\it 0.750(\pm 0.009)}$ | $0.748(\pm 0.007)$ | $0.717(\pm 0.075)$ | $0.711(\pm 0.048)$ | $0.705(\pm 0.066)$ | ${\bf 0.748(\pm 0.012)}$ | $0.729(\pm 0.027)$
CMD | $0.748(\pm 0.027)$ | $0.760(\pm 0.014)$ | $0.764(\pm 0.006)$ | ${\it 0.767(\pm 0.007)}$ | $0.737(\pm 0.100)$ | ${\bf 0.775(\pm 0.031)}$ | $0.643(\pm 0.031)$ | $0.766(\pm 0.016)$ | $0.794(\pm 0.023)$
MMDA | $0.738(\pm 0.036)$ | ${\it 0.783(\pm 0.017)}$ | $0.781(\pm 0.016)$ | $0.780(\pm 0.015)$ | $0.698(\pm 0.038)$ | $0.719(\pm 0.036)$ | $0.731(\pm 0.047)$ | ${\bf 0.780(\pm 0.017)}$ | $0.785(\pm 0.035)$
CoDATS | $0.710(\pm 0.030)$ | $0.766(\pm 0.023)$ | $0.772(\pm 0.040)$ | ${\it 0.773(\pm 0.050)}$ | $0.722(\pm 0.064)$ | $0.739(\pm 0.028)$ | $0.739(\pm 0.040)$ | ${\bf 0.812(\pm 0.009)}$ | $0.785(\pm 0.039)$
Deep-Coral | $0.745(\pm 0.046)$ | ${\it 0.766(\pm 0.012)}$ | $0.762(\pm 0.015)$ | $0.766(\pm 0.027)$ | $0.681(\pm 0.073)$ | $0.754(\pm 0.054)$ | $0.758(\pm 0.244)$ | ${\bf 0.764(\pm 0.006)}$ | $0.776(\pm 0.023)$
CDAN | $0.728(\pm 0.039)$ | $0.762(\pm 0.012)$ | $0.758(\pm 0.017)$ | $0.764(\pm 0.016)$ | ${\it 0.765(\pm 0.063)}$ | $0.774(\pm 0.035)$ | $0.775(\pm 0.036)$ | ${\bf 0.816(\pm 0.011)}$ | $0.790(\pm 0.038)$
DANN | $0.757(\pm 0.057)$ | ${\it 0.779(\pm 0.012)}$ | $0.774(\pm 0.009)$ | $0.773(\pm 0.011)$ | $0.722(\pm 0.103)$ | $0.798(\pm 0.041)$ | $0.793(\pm 0.045)$ | ${\bf 0.818(\pm 0.009)}$ | $0.807(\pm 0.020)$
DSAN | $0.721(\pm 0.053)$ | ${\it 0.803(\pm 0.010)}$ | $0.797(\pm 0.014)$ | $0.802(\pm 0.007)$ | $0.724(\pm 0.065)$ | $0.741(\pm 0.033)$ | $0.596(\pm 0.031)$ | ${\bf 0.825(\pm 0.008)}$ | $0.826(\pm 0.046)$
Avg. | $0.732(\pm 0.042)$ | $0.771(\pm 0.015)$ | $0.768(\pm 0.017)$ | ${\it 0.771(\pm 0.018)}$ | $0.722(\pm 0.068)$ | $0.746(\pm 0.037)$ | $0.722(\pm 0.063)$ | ${\bf 0.787(\pm 0.012)}$ | $0.784(\pm 0.028)$

| WISDM
---|---
|  | Heuristic | Theoretical error guarantees |
Method | SO | TMV | TMR | TCR | SOR | IWV | DEV | IWA (ours) | TB
HoMM | $0.753(\pm 0.054)$ | $0.741(\pm 0.026)$ | $0.738(\pm 0.031)$ | $0.739(\pm 0.047)$ | ${\it 0.775(\pm 0.062)}$ | ${\bf 0.753(\pm 0.054)}$ | $0.740(\pm 0.054)$ | $0.728(\pm 0.021)$ | $0.774(\pm 0.037)$
AdvSKM | $0.747(\pm 0.050)$ | $0.771(\pm 0.043)$ | ${\it 0.781(\pm 0.055)}$ | $0.779(\pm 0.035)$ | $0.742(\pm 0.062)$ | $0.747(\pm 0.050)$ | $0.747(\pm 0.135)$ | ${\bf 0.777(\pm 0.031)}$ | $0.779(\pm 0.041)$
DIRT | $0.738(\pm 0.038)$ | $0.792(\pm 0.015)$ | ${\it 0.797(\pm 0.024)}$ | $0.797(\pm 0.037)$ | $0.756(\pm 0.071)$ | $0.738(\pm 0.059)$ | $0.797(\pm 0.059)$ | ${\bf 0.798(\pm 0.018)}$ | $0.816(\pm 0.063)$
DDC | $0.741(\pm 0.071)$ | $0.780(\pm 0.032)$ | $0.779(\pm 0.052)$ | ${\it 0.787(\pm 0.049)}$ | $0.737(\pm 0.071)$ | $0.741(\pm 0.076)$ | $0.741(\pm 0.063)$ | ${\bf 0.782(\pm 0.038)}$ | $0.770(\pm 0.060)$
CMD | $0.710(\pm 0.088)$ | ${\it 0.772(\pm 0.021)}$ | $0.765(\pm 0.032)$ | $0.767(\pm 0.040)$ | $0.728(\pm 0.092)$ | $0.713(\pm 0.084)$ | $0.686(\pm 0.113)$ | ${\bf 0.773(\pm 0.032)}$ | $0.742(\pm 0.071)$
MMDA | $0.759(\pm 0.047)$ | ${\it 0.789(\pm 0.017)}$ | $0.772(\pm 0.030)$ | $0.745(\pm 0.035)$ | $0.754(\pm 0.050)$ | $0.759(\pm 0.047)$ | $0.750(\pm 0.047)$ | ${\bf 0.790(\pm 0.018)}$ | $0.775(\pm 0.030)$
CoDATS | $0.711(\pm 0.039)$ | ${\it 0.775(\pm 0.018)}$ | $0.757(\pm 0.027)$ | $0.751(\pm 0.020)$ | $0.682(\pm 0.057)$ | $0.709(\pm 0.039)$ | $0.735(\pm 0.054)$ | ${\bf 0.764(\pm 0.015)}$ | $0.770(\pm 0.019)$
Deep-Coral | $0.694(\pm 0.030)$ | $0.717(\pm 0.041)$ | ${\it 0.723(\pm 0.037)}$ | $0.713(\pm 0.035)$ | $0.664(\pm 0.055)$ | $0.694(\pm 0.030)$ | $0.670(\pm 0.149)$ | ${\bf 0.723(\pm 0.026)}$ | $0.736(\pm 0.044)$
CDAN | $0.760(\pm 0.057)$ | $0.762(\pm 0.048)$ | $0.762(\pm 0.046)$ | ${\it 0.781(\pm 0.051)}$ | $0.768(\pm 0.074)$ | $0.760(\pm 0.057)$ | $0.750(\pm 0.091)$ | ${\bf 0.765(\pm 0.040)}$ | $0.779(\pm 0.049)$
DANN | $0.724(\pm 0.042)$ | $0.789(\pm 0.018)$ | ${\it 0.802(\pm 0.028)}$ | $0.796(\pm 0.036)$ | $0.745(\pm 0.026)$ | $0.720(\pm 0.042)$ | $0.702(\pm 0.053)$ | ${\bf 0.778(\pm 0.019)}$ | $0.765(\pm 0.044)$
DSAN | $0.759(\pm 0.030)$ | $0.765(\pm 0.024)$ | ${\it 0.769(\pm 0.034)}$ | $0.756(\pm 0.025)$ | $0.757(\pm 0.068)$ | ${\bf 0.759(\pm 0.030)}$ | $0.663(\pm 0.025)$ | $0.722(\pm 0.013)$ | $0.779(\pm 0.044)$
Avg. | $0.736(\pm 0.050)$ | ${\it 0.768(\pm 0.027)}$ | $0.768(\pm 0.036)$ | $0.765(\pm 0.037)$ | $0.737(\pm 0.062)$ | $0.736(\pm 0.052)$ | $0.726(\pm 0.077)$ | ${\bf 0.764(\pm 0.025)}$ | $0.771(\pm 0.046)$

####  D.7.2 Detailed Amazon Reviews Results

Table 15: Mean and standard deviation (after $\pm$) of target classification
accuracy on Amazon Reviews (Part 1) over $3$ repetitions with different random
initialization of model weights.

| HoMM
---|---
|  | Heuristic | Theoretical error guarantees |
Task | SO | TMV | TMR | TCR | SOR | IWV | DEV | IWA (ours) | TB
B $\rightarrow$ D | $0.778(\pm 0.01)$ | $0.793(\pm 0.008)$ | $0.793(\pm 0.008)$ | ${\it 0.795(\pm 0.002)}$ | $0.795(\pm 0.008)$ | $0.782(\pm 0.021)$ | $0.782(\pm 0.021)$ | ${\bf 0.794(\pm 0.007)}$ | $0.789(\pm 0.008)$
B $\rightarrow$ E | $0.745(\pm 0.014)$ | $0.759(\pm 0.013)$ | $0.759(\pm 0.013)$ | $0.761(\pm 0.012)$ | ${\it 0.763(\pm 0.012)}$ | $0.747(\pm 0.005)$ | $0.749(\pm 0.025)$ | ${\bf 0.761(\pm 0.012)}$ | $0.758(\pm 0.012)$
B $\rightarrow$ K | $0.77(\pm 0.018)$ | ${\it 0.782(\pm 0.018)}$ | $0.782(\pm 0.018)$ | $0.782(\pm 0.017)$ | $0.779(\pm 0.013)$ | $0.761(\pm 0.018)$ | $0.767(\pm 0.003)$ | ${\bf 0.781(\pm 0.017)}$ | $0.776(\pm 0.018)$
D $\rightarrow$ B | $0.785(\pm 0.006)$ | ${\it 0.791(\pm 0.004)}$ | $0.791(\pm 0.004)$ | $0.79(\pm 0.002)$ | $0.788(\pm 0.008)$ | $0.778(\pm 0.002)$ | $0.777(\pm 0.015)$ | ${\bf 0.79(\pm 0.003)}$ | $0.787(\pm 0.003)$
D $\rightarrow$ E | $0.772(\pm 0.012)$ | ${\it 0.781(\pm 0.003)}$ | $0.781(\pm 0.003)$ | $0.779(\pm 0.004)$ | $0.778(\pm 0.004)$ | $0.764(\pm 0.017)$ | $0.769(\pm 0.009)$ | ${\bf 0.781(\pm 0.004)}$ | $0.774(\pm 0.003)$
D $\rightarrow$ K | $0.783(\pm 0.015)$ | $0.791(\pm 0.016)$ | $0.791(\pm 0.016)$ | $0.791(\pm 0.016)$ | ${\it 0.791(\pm 0.017)}$ | $0.781(\pm 0.01)$ | $0.782(\pm 0.01)$ | ${\bf 0.789(\pm 0.016)}$ | $0.786(\pm 0.017)$
E $\rightarrow$ B | $0.702(\pm 0.026)$ | $0.7(\pm 0.02)$ | $0.7(\pm 0.02)$ | ${\it 0.701(\pm 0.019)}$ | $0.699(\pm 0.021)$ | $0.69(\pm 0.011)$ | $0.692(\pm 0.014)$ | ${\bf 0.698(\pm 0.011)}$ | $0.703(\pm 0.03)$
E $\rightarrow$ D | $0.733(\pm 0.003)$ | $0.733(\pm 0.006)$ | $0.733(\pm 0.006)$ | ${\it 0.736(\pm 0.011)}$ | $0.733(\pm 0.008)$ | $0.728(\pm 0.011)$ | $0.719(\pm 0.005)$ | ${\bf 0.735(\pm 0.011)}$ | $0.735(\pm 0.011)$
E $\rightarrow$ K | $0.862(\pm 0.009)$ | $0.874(\pm 0.008)$ | $0.874(\pm 0.008)$ | ${\it 0.876(\pm 0.009)}$ | $0.873(\pm 0.008)$ | $0.856(\pm 0.01)$ | $0.858(\pm 0.012)$ | ${\bf 0.873(\pm 0.009)}$ | $0.863(\pm 0.009)$
K $\rightarrow$ B | $0.715(\pm 0.008)$ | ${\it 0.721(\pm 0.004)}$ | $0.721(\pm 0.004)$ | $0.719(\pm 0.004)$ | $0.721(\pm 0.01)$ | $0.714(\pm 0.007)$ | $0.708(\pm 0.003)$ | ${\bf 0.722(\pm 0.007)}$ | $0.717(\pm 0.007)$
K $\rightarrow$ D | $0.745(\pm 0.011)$ | $0.752(\pm 0.01)$ | $0.752(\pm 0.01)$ | $0.747(\pm 0.013)$ | ${\it 0.755(\pm 0.008)}$ | $0.735(\pm 0.018)$ | $0.742(\pm 0.022)$ | ${\bf 0.749(\pm 0.006)}$ | $0.745(\pm 0.008)$
K $\rightarrow$ E | $0.844(\pm 0.009)$ | $0.854(\pm 0.008)$ | $0.854(\pm 0.008)$ | $0.855(\pm 0.005)$ | ${\it 0.857(\pm 0.009)}$ | $0.845(\pm 0.005)$ | $0.844(\pm 0.006)$ | ${\bf 0.856(\pm 0.006)}$ | $0.849(\pm 0.009)$
Avg. | $0.769(\pm 0.012)$ | $0.778(\pm 0.01)$ | $0.778(\pm 0.01)$ | ${\it 0.778(\pm 0.01)}$ | $0.777(\pm 0.011)$ | $0.765(\pm 0.011)$ | $0.766(\pm 0.012)$ | ${\bf 0.778(\pm 0.009)}$ | $0.774(\pm 0.011)$

| AdvSKM
---|---
|  | Heuristic | Theoretical error guarantees |
Task | SO | TMV | TMR | TCR | SOR | IWV | DEV | IWA (ours) | TB
B $\rightarrow$ D | $0.784(\pm 0.004)$ | ${\it 0.79(\pm 0.003)}$ | $0.79(\pm 0.003)$ | $0.789(\pm 0.003)$ | $0.79(\pm 0.003)$ | $0.777(\pm 0.008)$ | $0.778(\pm 0.008)$ | ${\bf 0.794(\pm 0.005)}$ | $0.79(\pm 0.005)$
B $\rightarrow$ E | $0.754(\pm 0.009)$ | $0.761(\pm 0.014)$ | $0.761(\pm 0.014)$ | ${\it 0.763(\pm 0.012)}$ | $0.762(\pm 0.011)$ | $0.754(\pm 0.003)$ | $0.751(\pm 0.007)$ | ${\bf 0.761(\pm 0.012)}$ | $0.756(\pm 0.012)$
B $\rightarrow$ K | $0.769(\pm 0.021)$ | ${\it 0.784(\pm 0.019)}$ | $0.784(\pm 0.019)$ | $0.782(\pm 0.021)$ | $0.78(\pm 0.016)$ | $0.771(\pm 0.012)$ | $0.764(\pm 0.016)$ | ${\bf 0.782(\pm 0.017)}$ | $0.774(\pm 0.019)$
D $\rightarrow$ B | $0.779(\pm 0.004)$ | ${\it 0.795(\pm 0.007)}$ | $0.795(\pm 0.007)$ | $0.794(\pm 0.007)$ | $0.792(\pm 0.003)$ | $0.785(\pm 0.007)$ | $0.78(\pm 0.011)$ | ${\bf 0.796(\pm 0.009)}$ | $0.789(\pm 0.009)$
D $\rightarrow$ E | $0.766(\pm 0.013)$ | ${\it 0.785(\pm 0.006)}$ | $0.785(\pm 0.006)$ | $0.784(\pm 0.008)$ | $0.777(\pm 0.005)$ | $0.773(\pm 0.005)$ | $0.769(\pm 0.009)$ | ${\bf 0.785(\pm 0.005)}$ | $0.776(\pm 0.002)$
D $\rightarrow$ K | $0.777(\pm 0.015)$ | $0.79(\pm 0.015)$ | $0.79(\pm 0.015)$ | $0.79(\pm 0.015)$ | ${\it 0.791(\pm 0.013)}$ | $0.775(\pm 0.014)$ | $0.775(\pm 0.014)$ | ${\bf 0.789(\pm 0.013)}$ | $0.786(\pm 0.013)$
E $\rightarrow$ B | $0.688(\pm 0.015)$ | $0.709(\pm 0.022)$ | $0.709(\pm 0.022)$ | $0.705(\pm 0.024)$ | ${\it 0.709(\pm 0.021)}$ | $0.704(\pm 0.022)$ | $0.695(\pm 0.022)$ | ${\bf 0.712(\pm 0.021)}$ | $0.707(\pm 0.021)$
E $\rightarrow$ D | $0.714(\pm 0.005)$ | $0.734(\pm 0.002)$ | $0.734(\pm 0.002)$ | ${\it 0.737(\pm 0.005)}$ | $0.733(\pm 0.008)$ | $0.725(\pm 0.004)$ | $0.725(\pm 0.004)$ | ${\bf 0.732(\pm 0.006)}$ | $0.737(\pm 0.011)$
E $\rightarrow$ K | $0.858(\pm 0.004)$ | $0.874(\pm 0.01)$ | $0.874(\pm 0.01)$ | $0.874(\pm 0.012)$ | ${\it 0.876(\pm 0.01)}$ | $0.86(\pm 0.012)$ | $0.86(\pm 0.012)$ | ${\bf 0.875(\pm 0.011)}$ | $0.865(\pm 0.01)$
K $\rightarrow$ B | $0.713(\pm 0.002)$ | $0.723(\pm 0.006)$ | $0.723(\pm 0.006)$ | ${\it 0.724(\pm 0.009)}$ | $0.72(\pm 0.004)$ | $0.708(\pm 0.014)$ | $0.705(\pm 0.011)$ | ${\bf 0.726(\pm 0.006)}$ | $0.718(\pm 0.006)$
K $\rightarrow$ D | $0.741(\pm 0.01)$ | ${\it 0.752(\pm 0.012)}$ | $0.752(\pm 0.012)$ | $0.751(\pm 0.013)$ | $0.752(\pm 0.017)$ | ${\bf 0.75(\pm 0.019)}$ | $0.742(\pm 0.008)$ | $0.749(\pm 0.012)$ | $0.756(\pm 0.014)$
K $\rightarrow$ E | $0.848(\pm 0.008)$ | $0.857(\pm 0.007)$ | $0.857(\pm 0.007)$ | ${\it 0.858(\pm 0.008)}$ | $0.856(\pm 0.008)$ | $0.846(\pm 0.012)$ | $0.847(\pm 0.007)$ | ${\bf 0.858(\pm 0.008)}$ | $0.85(\pm 0.008)$
Avg. | $0.766(\pm 0.009)$ | ${\it 0.779(\pm 0.01)}$ | $0.779(\pm 0.01)$ | $0.779(\pm 0.011)$ | $0.778(\pm 0.01)$ | $0.769(\pm 0.011)$ | $0.766(\pm 0.011)$ | ${\bf 0.78(\pm 0.01)}$ | $0.775(\pm 0.011)$

| DIRT
---|---
|  | Heuristic | Theoretical error guarantees |
Task | SO | TMV | TMR | TCR | SOR | IWV | DEV | IWA (ours) | TB
B $\rightarrow$ D | $0.777(\pm 0.01)$ | $0.816(\pm 0.008)$ | $0.816(\pm 0.008)$ | ${\it 0.817(\pm 0.008)}$ | $0.813(\pm 0.007)$ | $0.791(\pm 0.012)$ | $0.787(\pm 0.032)$ | ${\bf 0.813(\pm 0.004)}$ | $0.809(\pm 0.008)$
B $\rightarrow$ E | $0.756(\pm 0.013)$ | $0.792(\pm 0.006)$ | $0.792(\pm 0.006)$ | ${\it 0.792(\pm 0.01)}$ | $0.782(\pm 0.008)$ | $0.758(\pm 0.011)$ | $0.758(\pm 0.011)$ | ${\bf 0.788(\pm 0.008)}$ | $0.804(\pm 0.005)$
B $\rightarrow$ K | $0.77(\pm 0.013)$ | ${\it 0.815(\pm 0.003)}$ | $0.815(\pm 0.003)$ | $0.814(\pm 0.005)$ | $0.813(\pm 0.006)$ | $0.793(\pm 0.009)$ | $0.782(\pm 0.025)$ | ${\bf 0.814(\pm 0.003)}$ | $0.814(\pm 0.003)$
D $\rightarrow$ B | $0.773(\pm 0.008)$ | $0.812(\pm 0.014)$ | $0.812(\pm 0.014)$ | $0.809(\pm 0.019)$ | ${\it 0.814(\pm 0.01)}$ | $0.805(\pm 0.015)$ | $0.808(\pm 0.004)$ | ${\bf 0.81(\pm 0.01)}$ | $0.811(\pm 0.01)$
D $\rightarrow$ E | $0.757(\pm 0.02)$ | $0.813(\pm 0.009)$ | $0.813(\pm 0.009)$ | ${\it 0.814(\pm 0.012)}$ | $0.808(\pm 0.012)$ | $0.787(\pm 0.028)$ | $0.807(\pm 0.024)$ | ${\bf 0.814(\pm 0.009)}$ | $0.812(\pm 0.009)$
D $\rightarrow$ K | $0.775(\pm 0.016)$ | $0.836(\pm 0.009)$ | $0.836(\pm 0.009)$ | $0.835(\pm 0.008)$ | ${\it 0.837(\pm 0.004)}$ | $0.789(\pm 0.025)$ | $0.787(\pm 0.038)$ | ${\bf 0.832(\pm 0.006)}$ | $0.828(\pm 0.004)$
E $\rightarrow$ B | $0.702(\pm 0.018)$ | $0.672(\pm 0.015)$ | $0.672(\pm 0.015)$ | $0.674(\pm 0.015)$ | ${\it 0.714(\pm 0.016)}$ | ${\bf 0.702(\pm 0.018)}$ | $0.675(\pm 0.05)$ | $0.678(\pm 0.015)$ | $0.708(\pm 0.016)$
E $\rightarrow$ D | $0.716(\pm 0.008)$ | $0.689(\pm 0.019)$ | $0.689(\pm 0.019)$ | $0.69(\pm 0.022)$ | ${\it 0.731(\pm 0.029)}$ | ${\bf 0.718(\pm 0.01)}$ | $0.704(\pm 0.027)$ | $0.702(\pm 0.021)$ | $0.73(\pm 0.029)$
E $\rightarrow$ K | $0.855(\pm 0.013)$ | $0.888(\pm 0.01)$ | $0.888(\pm 0.01)$ | $0.885(\pm 0.009)$ | ${\it 0.894(\pm 0.005)}$ | $0.874(\pm 0.008)$ | $0.873(\pm 0.009)$ | ${\bf 0.884(\pm 0.009)}$ | $0.889(\pm 0.005)$
K $\rightarrow$ B | $0.709(\pm 0.012)$ | $0.707(\pm 0.007)$ | $0.707(\pm 0.007)$ | $0.711(\pm 0.003)$ | ${\it 0.749(\pm 0.005)}$ | ${\bf 0.73(\pm 0.02)}$ | $0.715(\pm 0.005)$ | $0.711(\pm 0.008)$ | $0.723(\pm 0.005)$
K $\rightarrow$ D | $0.736(\pm 0.012)$ | $0.721(\pm 0.01)$ | $0.721(\pm 0.01)$ | $0.727(\pm 0.019)$ | ${\it 0.779(\pm 0.003)}$ | ${\bf 0.745(\pm 0.022)}$ | $0.731(\pm 0.007)$ | $0.727(\pm 0.006)$ | $0.756(\pm 0.003)$
K $\rightarrow$ E | $0.842(\pm 0.009)$ | $0.869(\pm 0.01)$ | $0.869(\pm 0.01)$ | $0.868(\pm 0.01)$ | ${\it 0.872(\pm 0.009)}$ | $0.848(\pm 0.012)$ | $0.848(\pm 0.008)$ | ${\bf 0.868(\pm 0.01)}$ | $0.863(\pm 0.009)$
Avg. | $0.764(\pm 0.013)$ | $0.786(\pm 0.01)$ | $0.786(\pm 0.01)$ | $0.786(\pm 0.012)$ | ${\it 0.8(\pm 0.01)}$ | $0.778(\pm 0.016)$ | $0.773(\pm 0.02)$ | ${\bf 0.787(\pm 0.009)}$ | $0.795(\pm 0.009)$

| DDC
---|---
|  | Heuristic | Theoretical error guarantees |
Task | SO | TMV | TMR | TCR | SOR | IWV | DEV | IWA (ours) | TB
B $\rightarrow$ D | $0.781(\pm 0.016)$ | ${\it 0.796(\pm 0.008)}$ | $0.796(\pm 0.008)$ | $0.793(\pm 0.013)$ | $0.794(\pm 0.002)$ | $0.775(\pm 0.017)$ | $0.778(\pm 0.02)$ | ${\bf 0.789(\pm 0.009)}$ | $0.786(\pm 0.008)$
B $\rightarrow$ E | $0.752(\pm 0.007)$ | $0.762(\pm 0.014)$ | $0.762(\pm 0.014)$ | $0.762(\pm 0.013)$ | ${\it 0.766(\pm 0.01)}$ | $0.752(\pm 0.013)$ | $0.749(\pm 0.006)$ | ${\bf 0.763(\pm 0.014)}$ | $0.756(\pm 0.01)$
B $\rightarrow$ K | $0.766(\pm 0.015)$ | $0.781(\pm 0.015)$ | $0.781(\pm 0.015)$ | ${\it 0.782(\pm 0.017)}$ | $0.778(\pm 0.02)$ | $0.776(\pm 0.016)$ | $0.774(\pm 0.008)$ | ${\bf 0.783(\pm 0.014)}$ | $0.78(\pm 0.014)$
D $\rightarrow$ B | $0.781(\pm 0.008)$ | ${\it 0.793(\pm 0.007)}$ | $0.793(\pm 0.007)$ | $0.791(\pm 0.006)$ | $0.789(\pm 0.012)$ | $0.787(\pm 0.009)$ | $0.783(\pm 0.005)$ | ${\bf 0.796(\pm 0.006)}$ | $0.788(\pm 0.006)$
D $\rightarrow$ E | $0.767(\pm 0.015)$ | $0.782(\pm 0.004)$ | $0.782(\pm 0.004)$ | $0.78(\pm 0.004)$ | ${\it 0.783(\pm 0.008)}$ | $0.778(\pm 0.002)$ | $0.776(\pm 0.004)$ | ${\bf 0.784(\pm 0.004)}$ | $0.778(\pm 0.004)$
D $\rightarrow$ K | $0.782(\pm 0.013)$ | $0.792(\pm 0.015)$ | $0.792(\pm 0.015)$ | ${\it 0.793(\pm 0.015)}$ | $0.792(\pm 0.018)$ | $0.782(\pm 0.014)$ | $0.783(\pm 0.014)$ | ${\bf 0.793(\pm 0.017)}$ | $0.788(\pm 0.017)$
E $\rightarrow$ B | $0.693(\pm 0.019)$ | $0.703(\pm 0.023)$ | $0.703(\pm 0.023)$ | ${\it 0.706(\pm 0.021)}$ | $0.7(\pm 0.023)$ | $0.696(\pm 0.011)$ | $0.689(\pm 0.021)$ | ${\bf 0.705(\pm 0.025)}$ | $0.704(\pm 0.021)$
E $\rightarrow$ D | $0.725(\pm 0.006)$ | ${\it 0.736(\pm 0.004)}$ | $0.736(\pm 0.004)$ | $0.731(\pm 0.006)$ | $0.735(\pm 0.012)$ | $0.711(\pm 0.009)$ | $0.736(\pm 0.004)$ | ${\bf 0.736(\pm 0.008)}$ | $0.736(\pm 0.007)$
E $\rightarrow$ K | $0.857(\pm 0.011)$ | ${\it 0.874(\pm 0.009)}$ | $0.874(\pm 0.009)$ | $0.872(\pm 0.007)$ | $0.874(\pm 0.006)$ | $0.857(\pm 0.014)$ | $0.853(\pm 0.009)$ | ${\bf 0.877(\pm 0.011)}$ | $0.864(\pm 0.011)$
K $\rightarrow$ B | $0.713(\pm 0.002)$ | ${\it 0.728(\pm 0.002)}$ | $0.728(\pm 0.002)$ | $0.727(\pm 0.005)$ | $0.721(\pm 0.003)$ | $0.709(\pm 0.015)$ | $0.708(\pm 0.007)$ | ${\bf 0.726(\pm 0.003)}$ | $0.719(\pm 0.002)$
K $\rightarrow$ D | $0.741(\pm 0.018)$ | $0.752(\pm 0.011)$ | $0.752(\pm 0.011)$ | ${\it 0.753(\pm 0.01)}$ | $0.752(\pm 0.016)$ | $0.743(\pm 0.012)$ | $0.748(\pm 0.01)$ | ${\bf 0.755(\pm 0.013)}$ | $0.748(\pm 0.012)$
K $\rightarrow$ E | $0.841(\pm 0.001)$ | $0.855(\pm 0.011)$ | $0.855(\pm 0.011)$ | $0.856(\pm 0.008)$ | ${\it 0.858(\pm 0.008)}$ | $0.84(\pm 0.003)$ | $0.84(\pm 0.01)$ | ${\bf 0.856(\pm 0.008)}$ | $0.849(\pm 0.008)$
Avg. | $0.766(\pm 0.011)$ | ${\it 0.78(\pm 0.01)}$ | $0.78(\pm 0.01)$ | $0.779(\pm 0.01)$ | $0.778(\pm 0.012)$ | $0.767(\pm 0.011)$ | $0.768(\pm 0.01)$ | ${\bf 0.78(\pm 0.011)}$ | $0.775(\pm 0.01)$

Table 16: Mean and standard deviation (after $\pm$) of target classification
accuracy on Amazon Reviews (Part 2) over $3$ repetitions with different random
initialization of model weights.

| CMD
---|---
|  | Heuristic | Theoretical error guarantees |
Task | SO | TMV | TMR | TCR | SOR | IWV | DEV | IWA (ours) | TB
B $\rightarrow$ D | $0.772(\pm 0.009)$ | $0.794(\pm 0.008)$ | $0.794(\pm 0.008)$ | $0.794(\pm 0.004)$ | ${\it 0.798(\pm 0.003)}$ | $0.779(\pm 0.018)$ | $0.748(\pm 0.036)$ | ${\bf 0.8(\pm 0.003)}$ | $0.789(\pm 0.003)$
B $\rightarrow$ E | $0.745(\pm 0.012)$ | ${\it 0.785(\pm 0.014)}$ | $0.785(\pm 0.014)$ | $0.779(\pm 0.011)$ | $0.779(\pm 0.011)$ | $0.746(\pm 0.032)$ | $0.651(\pm 0.077)$ | ${\bf 0.782(\pm 0.01)}$ | $0.78(\pm 0.014)$
B $\rightarrow$ K | $0.763(\pm 0.015)$ | ${\it 0.796(\pm 0.01)}$ | $0.796(\pm 0.01)$ | $0.79(\pm 0.007)$ | $0.794(\pm 0.013)$ | $0.787(\pm 0.011)$ | $0.749(\pm 0.028)$ | ${\bf 0.797(\pm 0.007)}$ | $0.793(\pm 0.008)$
D $\rightarrow$ B | $0.788(\pm 0.01)$ | $0.801(\pm 0.007)$ | $0.801(\pm 0.007)$ | $0.798(\pm 0.003)$ | ${\it 0.804(\pm 0.002)}$ | $0.785(\pm 0.011)$ | $0.754(\pm 0.022)$ | ${\bf 0.803(\pm 0.008)}$ | $0.794(\pm 0.002)$
D $\rightarrow$ E | $0.768(\pm 0.003)$ | ${\it 0.804(\pm 0.006)}$ | $0.804(\pm 0.006)$ | $0.798(\pm 0.003)$ | $0.801(\pm 0.013)$ | $0.777(\pm 0.031)$ | $0.744(\pm 0.095)$ | ${\bf 0.802(\pm 0.004)}$ | $0.798(\pm 0.007)$
D $\rightarrow$ K | $0.777(\pm 0.012)$ | $0.803(\pm 0.009)$ | $0.803(\pm 0.009)$ | $0.797(\pm 0.014)$ | ${\it 0.804(\pm 0.009)}$ | $0.773(\pm 0.006)$ | $0.673(\pm 0.094)$ | ${\bf 0.801(\pm 0.011)}$ | $0.811(\pm 0.007)$
E $\rightarrow$ B | $0.699(\pm 0.014)$ | $0.72(\pm 0.013)$ | $0.72(\pm 0.013)$ | $0.717(\pm 0.014)$ | ${\it 0.724(\pm 0.013)}$ | $0.71(\pm 0.016)$ | $0.68(\pm 0.039)$ | ${\bf 0.719(\pm 0.013)}$ | $0.712(\pm 0.013)$
E $\rightarrow$ D | $0.722(\pm 0.008)$ | $0.752(\pm 0.006)$ | $0.752(\pm 0.006)$ | ${\it 0.752(\pm 0.004)}$ | $0.751(\pm 0.005)$ | $0.693(\pm 0.041)$ | $0.573(\pm 0.01)$ | ${\bf 0.755(\pm 0.003)}$ | $0.738(\pm 0.003)$
E $\rightarrow$ K | $0.86(\pm 0.012)$ | $0.874(\pm 0.013)$ | $0.874(\pm 0.013)$ | $0.872(\pm 0.007)$ | ${\it 0.875(\pm 0.008)}$ | $0.822(\pm 0.058)$ | $0.807(\pm 0.054)$ | ${\bf 0.876(\pm 0.009)}$ | $0.871(\pm 0.009)$
K $\rightarrow$ B | $0.718(\pm 0.005)$ | ${\it 0.749(\pm 0.007)}$ | $0.749(\pm 0.007)$ | $0.738(\pm 0.003)$ | $0.74(\pm 0.003)$ | $0.716(\pm 0.022)$ | $0.679(\pm 0.056)$ | ${\bf 0.746(\pm 0.004)}$ | $0.74(\pm 0.007)$
K $\rightarrow$ D | $0.748(\pm 0.003)$ | $0.761(\pm 0.016)$ | $0.761(\pm 0.016)$ | $0.766(\pm 0.022)$ | ${\it 0.77(\pm 0.017)}$ | $0.746(\pm 0.011)$ | $0.655(\pm 0.119)$ | ${\bf 0.775(\pm 0.016)}$ | $0.761(\pm 0.016)$
K $\rightarrow$ E | $0.842(\pm 0.005)$ | $0.864(\pm 0.006)$ | $0.864(\pm 0.006)$ | $0.862(\pm 0.002)$ | ${\it 0.869(\pm 0.004)}$ | $0.85(\pm 0.011)$ | $0.806(\pm 0.041)$ | ${\bf 0.867(\pm 0.008)}$ | $0.858(\pm 0.004)$
Avg. | $0.767(\pm 0.009)$ | $0.792(\pm 0.01)$ | $0.792(\pm 0.01)$ | $0.789(\pm 0.008)$ | ${\it 0.792(\pm 0.008)}$ | $0.765(\pm 0.022)$ | $0.71(\pm 0.056)$ | ${\bf 0.794(\pm 0.008)}$ | $0.787(\pm 0.008)$

| MMDA
---|---
|  | Heuristic | Theoretical error guarantees |
Task | SO | TMV | TMR | TCR | SOR | IWV | DEV | IWA (ours) | TB
B $\rightarrow$ D | $0.775(\pm 0.005)$ | $0.796(\pm 0.005)$ | $0.796(\pm 0.005)$ | ${\it 0.797(\pm 0.009)}$ | $0.794(\pm 0.015)$ | $0.783(\pm 0.004)$ | $0.786(\pm 0.006)$ | ${\bf 0.797(\pm 0.003)}$ | $0.792(\pm 0.004)$
B $\rightarrow$ E | $0.752(\pm 0.006)$ | $0.775(\pm 0.01)$ | $0.775(\pm 0.01)$ | ${\it 0.776(\pm 0.008)}$ | $0.771(\pm 0.014)$ | $0.766(\pm 0.022)$ | $0.756(\pm 0.012)$ | ${\bf 0.779(\pm 0.012)}$ | $0.781(\pm 0.006)$
B $\rightarrow$ K | $0.765(\pm 0.009)$ | $0.793(\pm 0.016)$ | $0.793(\pm 0.016)$ | $0.792(\pm 0.017)$ | ${\it 0.803(\pm 0.019)}$ | $0.763(\pm 0.009)$ | $0.767(\pm 0.024)$ | ${\bf 0.795(\pm 0.017)}$ | $0.802(\pm 0.019)$
D $\rightarrow$ B | $0.783(\pm 0.007)$ | ${\it 0.796(\pm 0.007)}$ | $0.796(\pm 0.007)$ | $0.795(\pm 0.008)$ | $0.796(\pm 0.006)$ | $0.789(\pm 0.013)$ | $0.789(\pm 0.012)$ | ${\bf 0.798(\pm 0.009)}$ | $0.79(\pm 0.009)$
D $\rightarrow$ E | $0.764(\pm 0.003)$ | ${\it 0.792(\pm 0.005)}$ | $0.792(\pm 0.005)$ | $0.792(\pm 0.005)$ | $0.788(\pm 0.005)$ | $0.775(\pm 0.009)$ | $0.773(\pm 0.009)$ | ${\bf 0.795(\pm 0.006)}$ | $0.799(\pm 0.006)$
D $\rightarrow$ K | $0.775(\pm 0.012)$ | $0.797(\pm 0.014)$ | $0.797(\pm 0.014)$ | $0.796(\pm 0.013)$ | ${\it 0.811(\pm 0.008)}$ | $0.791(\pm 0.018)$ | $0.79(\pm 0.019)$ | ${\bf 0.8(\pm 0.012)}$ | $0.8(\pm 0.008)$
E $\rightarrow$ B | $0.701(\pm 0.015)$ | $0.707(\pm 0.017)$ | $0.707(\pm 0.017)$ | $0.707(\pm 0.021)$ | ${\it 0.713(\pm 0.014)}$ | $0.688(\pm 0.022)$ | $0.699(\pm 0.004)$ | ${\bf 0.709(\pm 0.016)}$ | $0.707(\pm 0.014)$
E $\rightarrow$ D | $0.738(\pm 0.01)$ | $0.741(\pm 0.004)$ | $0.741(\pm 0.004)$ | ${\it 0.744(\pm 0.004)}$ | $0.738(\pm 0.001)$ | $0.732(\pm 0.007)$ | $0.703(\pm 0.026)$ | ${\bf 0.749(\pm 0.001)}$ | $0.738(\pm 0.001)$
E $\rightarrow$ K | $0.855(\pm 0.015)$ | $0.875(\pm 0.007)$ | $0.875(\pm 0.007)$ | $0.875(\pm 0.007)$ | ${\it 0.878(\pm 0.008)}$ | $0.852(\pm 0.01)$ | $0.856(\pm 0.014)$ | ${\bf 0.878(\pm 0.009)}$ | $0.867(\pm 0.009)$
K $\rightarrow$ B | $0.715(\pm 0.008)$ | $0.73(\pm 0.003)$ | $0.73(\pm 0.003)$ | $0.726(\pm 0.002)$ | ${\it 0.739(\pm 0.006)}$ | $0.72(\pm 0.009)$ | $0.716(\pm 0.015)$ | ${\bf 0.732(\pm 0.004)}$ | $0.73(\pm 0.006)$
K $\rightarrow$ D | $0.736(\pm 0.014)$ | $0.761(\pm 0.013)$ | $0.761(\pm 0.013)$ | $0.755(\pm 0.011)$ | ${\it 0.764(\pm 0.018)}$ | $0.734(\pm 0.012)$ | $0.728(\pm 0.045)$ | ${\bf 0.758(\pm 0.017)}$ | $0.75(\pm 0.018)$
K $\rightarrow$ E | $0.842(\pm 0.008)$ | $0.856(\pm 0.009)$ | $0.856(\pm 0.009)$ | ${\it 0.858(\pm 0.009)}$ | $0.855(\pm 0.012)$ | $0.835(\pm 0.01)$ | $0.832(\pm 0.014)$ | ${\bf 0.858(\pm 0.005)}$ | $0.847(\pm 0.009)$
Avg. | $0.767(\pm 0.009)$ | $0.785(\pm 0.009)$ | $0.785(\pm 0.009)$ | $0.785(\pm 0.01)$ | ${\it 0.787(\pm 0.01)}$ | $0.769(\pm 0.012)$ | $0.766(\pm 0.017)$ | ${\bf 0.787(\pm 0.009)}$ | $0.784(\pm 0.009)$

| CoDATS
---|---
|  | Heuristic | Theoretical error guarantees |
Task | SO | TMV | TMR | TCR | SOR | IWV | DEV | IWA (ours) | TB
B $\rightarrow$ D | $0.783(\pm 0.013)$ | $0.8(\pm 0.002)$ | $0.8(\pm 0.002)$ | $0.8(\pm 0.004)$ | ${\it 0.803(\pm 0.003)}$ | $0.788(\pm 0.008)$ | $0.792(\pm 0.001)$ | ${\bf 0.805(\pm 0.009)}$ | $0.801(\pm 0.008)$
B $\rightarrow$ E | $0.755(\pm 0.005)$ | $0.788(\pm 0.004)$ | $0.788(\pm 0.004)$ | $0.787(\pm 0.005)$ | ${\it 0.792(\pm 0.008)}$ | $0.771(\pm 0.011)$ | $0.771(\pm 0.011)$ | ${\bf 0.788(\pm 0.006)}$ | $0.802(\pm 0.009)$
B $\rightarrow$ K | $0.771(\pm 0.022)$ | ${\it 0.808(\pm 0.007)}$ | $0.808(\pm 0.007)$ | $0.808(\pm 0.008)$ | $0.807(\pm 0.008)$ | $0.775(\pm 0.022)$ | $0.793(\pm 0.023)$ | ${\bf 0.806(\pm 0.009)}$ | $0.817(\pm 0.007)$
D $\rightarrow$ B | $0.774(\pm 0.001)$ | $0.796(\pm 0.005)$ | $0.796(\pm 0.005)$ | $0.795(\pm 0.005)$ | ${\it 0.807(\pm 0.007)}$ | $0.791(\pm 0.007)$ | $0.792(\pm 0.007)$ | ${\bf 0.802(\pm 0.004)}$ | $0.8(\pm 0.007)$
D $\rightarrow$ E | $0.769(\pm 0.003)$ | $0.808(\pm 0.009)$ | $0.808(\pm 0.009)$ | ${\it 0.81(\pm 0.009)}$ | $0.808(\pm 0.008)$ | $0.789(\pm 0.02)$ | $0.777(\pm 0.008)$ | ${\bf 0.811(\pm 0.009)}$ | $0.817(\pm 0.011)$
D $\rightarrow$ K | $0.782(\pm 0.021)$ | $0.819(\pm 0.011)$ | $0.819(\pm 0.011)$ | $0.82(\pm 0.01)$ | ${\it 0.824(\pm 0.01)}$ | $0.796(\pm 0.021)$ | $0.789(\pm 0.011)$ | ${\bf 0.82(\pm 0.01)}$ | $0.828(\pm 0.01)$
E $\rightarrow$ B | $0.687(\pm 0.013)$ | $0.714(\pm 0.019)$ | $0.714(\pm 0.019)$ | $0.713(\pm 0.015)$ | ${\it 0.725(\pm 0.021)}$ | $0.7(\pm 0.027)$ | $0.688(\pm 0.01)$ | ${\bf 0.717(\pm 0.018)}$ | $0.723(\pm 0.021)$
E $\rightarrow$ D | $0.72(\pm 0.013)$ | $0.745(\pm 0.023)$ | $0.745(\pm 0.023)$ | $0.744(\pm 0.026)$ | ${\it 0.756(\pm 0.017)}$ | $0.738(\pm 0.025)$ | $0.731(\pm 0.027)$ | ${\bf 0.747(\pm 0.025)}$ | $0.736(\pm 0.017)$
E $\rightarrow$ K | $0.859(\pm 0.016)$ | ${\it 0.883(\pm 0.009)}$ | $0.883(\pm 0.009)$ | $0.882(\pm 0.008)$ | $0.879(\pm 0.007)$ | $0.867(\pm 0.01)$ | $0.866(\pm 0.01)$ | ${\bf 0.883(\pm 0.012)}$ | $0.87(\pm 0.012)$
K $\rightarrow$ B | $0.712(\pm 0.012)$ | $0.732(\pm 0.004)$ | $0.732(\pm 0.004)$ | $0.732(\pm 0.009)$ | ${\it 0.747(\pm 0.012)}$ | $0.726(\pm 0.037)$ | $0.694(\pm 0.008)$ | ${\bf 0.737(\pm 0.006)}$ | $0.751(\pm 0.016)$
K $\rightarrow$ D | $0.73(\pm 0.022)$ | $0.759(\pm 0.006)$ | $0.759(\pm 0.006)$ | $0.766(\pm 0.009)$ | ${\it 0.775(\pm 0.016)}$ | $0.752(\pm 0.015)$ | $0.738(\pm 0.007)$ | ${\bf 0.766(\pm 0.004)}$ | $0.764(\pm 0.016)$
K $\rightarrow$ E | $0.845(\pm 0.0)$ | $0.867(\pm 0.01)$ | $0.867(\pm 0.01)$ | $0.866(\pm 0.011)$ | ${\it 0.868(\pm 0.007)}$ | $0.853(\pm 0.003)$ | $0.851(\pm 0.011)$ | ${\bf 0.867(\pm 0.007)}$ | $0.856(\pm 0.007)$
Avg. | $0.766(\pm 0.012)$ | $0.793(\pm 0.009)$ | $0.793(\pm 0.009)$ | $0.794(\pm 0.01)$ | ${\it 0.799(\pm 0.01)}$ | $0.779(\pm 0.017)$ | $0.773(\pm 0.011)$ | ${\bf 0.796(\pm 0.01)}$ | $0.797(\pm 0.012)$

| Deep-Coral
---|---
|  | Heuristic | Theoretical error guarantees |
Task | SO | TMV | TMR | TCR | SOR | IWV | DEV | IWA (ours) | TB
B $\rightarrow$ D | $0.778(\pm 0.018)$ | ${\it 0.799(\pm 0.011)}$ | $0.799(\pm 0.011)$ | $0.799(\pm 0.006)$ | $0.794(\pm 0.011)$ | $0.792(\pm 0.023)$ | $0.789(\pm 0.025)$ | ${\bf 0.801(\pm 0.01)}$ | $0.794(\pm 0.012)$
B $\rightarrow$ E | $0.749(\pm 0.013)$ | $0.771(\pm 0.01)$ | $0.771(\pm 0.01)$ | ${\it 0.771(\pm 0.008)}$ | $0.764(\pm 0.018)$ | $0.759(\pm 0.002)$ | $0.752(\pm 0.011)$ | ${\bf 0.773(\pm 0.008)}$ | $0.767(\pm 0.008)$
B $\rightarrow$ K | $0.769(\pm 0.011)$ | ${\it 0.785(\pm 0.013)}$ | $0.785(\pm 0.013)$ | $0.784(\pm 0.016)$ | $0.783(\pm 0.015)$ | $0.762(\pm 0.013)$ | $0.77(\pm 0.014)$ | ${\bf 0.785(\pm 0.017)}$ | $0.779(\pm 0.017)$
D $\rightarrow$ B | $0.783(\pm 0.009)$ | ${\it 0.796(\pm 0.003)}$ | $0.796(\pm 0.003)$ | $0.796(\pm 0.006)$ | $0.792(\pm 0.006)$ | $0.78(\pm 0.005)$ | $0.773(\pm 0.005)$ | ${\bf 0.797(\pm 0.004)}$ | $0.786(\pm 0.004)$
D $\rightarrow$ E | $0.76(\pm 0.013)$ | $0.785(\pm 0.002)$ | $0.785(\pm 0.002)$ | ${\it 0.785(\pm 0.002)}$ | $0.778(\pm 0.006)$ | $0.762(\pm 0.006)$ | $0.764(\pm 0.008)$ | ${\bf 0.784(\pm 0.003)}$ | $0.785(\pm 0.005)$
D $\rightarrow$ K | $0.78(\pm 0.016)$ | $0.794(\pm 0.011)$ | $0.794(\pm 0.011)$ | $0.793(\pm 0.012)$ | ${\it 0.795(\pm 0.014)}$ | $0.787(\pm 0.007)$ | $0.783(\pm 0.019)$ | ${\bf 0.795(\pm 0.013)}$ | $0.789(\pm 0.013)$
E $\rightarrow$ B | $0.696(\pm 0.009)$ | $0.708(\pm 0.022)$ | $0.708(\pm 0.022)$ | ${\it 0.709(\pm 0.024)}$ | $0.708(\pm 0.024)$ | $0.688(\pm 0.016)$ | $0.698(\pm 0.018)$ | ${\bf 0.71(\pm 0.024)}$ | $0.708(\pm 0.027)$
E $\rightarrow$ D | $0.722(\pm 0.009)$ | $0.738(\pm 0.005)$ | $0.738(\pm 0.005)$ | $0.741(\pm 0.005)$ | ${\it 0.741(\pm 0.001)}$ | $0.73(\pm 0.016)$ | $0.72(\pm 0.017)$ | ${\bf 0.74(\pm 0.004)}$ | $0.739(\pm 0.001)$
E $\rightarrow$ K | $0.859(\pm 0.01)$ | ${\it 0.879(\pm 0.005)}$ | $0.879(\pm 0.005)$ | $0.878(\pm 0.007)$ | $0.877(\pm 0.007)$ | $0.857(\pm 0.007)$ | $0.858(\pm 0.009)$ | ${\bf 0.878(\pm 0.007)}$ | $0.864(\pm 0.005)$
K $\rightarrow$ B | $0.72(\pm 0.01)$ | $0.733(\pm 0.009)$ | $0.733(\pm 0.009)$ | ${\it 0.736(\pm 0.009)}$ | $0.733(\pm 0.009)$ | $0.719(\pm 0.011)$ | $0.722(\pm 0.022)$ | ${\bf 0.739(\pm 0.01)}$ | $0.74(\pm 0.005)$
K $\rightarrow$ D | $0.733(\pm 0.011)$ | $0.755(\pm 0.012)$ | $0.755(\pm 0.012)$ | $0.751(\pm 0.009)$ | ${\it 0.759(\pm 0.009)}$ | $0.75(\pm 0.009)$ | $0.752(\pm 0.013)$ | ${\bf 0.755(\pm 0.015)}$ | $0.751(\pm 0.009)$
K $\rightarrow$ E | $0.841(\pm 0.01)$ | $0.858(\pm 0.009)$ | $0.858(\pm 0.009)$ | ${\it 0.858(\pm 0.011)}$ | $0.857(\pm 0.008)$ | $0.844(\pm 0.011)$ | $0.849(\pm 0.005)$ | ${\bf 0.857(\pm 0.01)}$ | $0.849(\pm 0.011)$
Avg. | $0.766(\pm 0.012)$ | ${\it 0.783(\pm 0.009)}$ | $0.783(\pm 0.009)$ | $0.783(\pm 0.01)$ | $0.782(\pm 0.011)$ | $0.769(\pm 0.011)$ | $0.769(\pm 0.014)$ | ${\bf 0.785(\pm 0.01)}$ | $0.779(\pm 0.01)$

Table 17: Mean and standard deviation (after $\pm$) of target classification
accuracy on Amazon Reviews (Part 3) over $3$ repetitions with different random
initialization of model weights.

| CDAN
---|---
|  | Heuristic | Theoretical error guarantees |
Task | SO | TMV | TMR | TCR | SOR | IWV | DEV | IWA (ours) | TB
B $\rightarrow$ D | $0.784(\pm 0.022)$ | ${\it 0.803(\pm 0.007)}$ | $0.803(\pm 0.007)$ | $0.803(\pm 0.004)$ | $0.795(\pm 0.009)$ | $0.795(\pm 0.009)$ | $0.792(\pm 0.006)$ | ${\bf 0.804(\pm 0.009)}$ | $0.797(\pm 0.006)$
B $\rightarrow$ E | $0.758(\pm 0.013)$ | ${\it 0.776(\pm 0.009)}$ | $0.776(\pm 0.009)$ | $0.774(\pm 0.009)$ | $0.776(\pm 0.012)$ | $0.764(\pm 0.012)$ | $0.764(\pm 0.012)$ | ${\bf 0.778(\pm 0.009)}$ | $0.775(\pm 0.009)$
B $\rightarrow$ K | $0.769(\pm 0.019)$ | $0.796(\pm 0.008)$ | $0.796(\pm 0.008)$ | ${\it 0.796(\pm 0.008)}$ | $0.792(\pm 0.014)$ | $0.78(\pm 0.006)$ | $0.791(\pm 0.007)$ | ${\bf 0.796(\pm 0.01)}$ | $0.796(\pm 0.01)$
D $\rightarrow$ B | $0.786(\pm 0.01)$ | ${\it 0.797(\pm 0.007)}$ | $0.797(\pm 0.007)$ | $0.795(\pm 0.004)$ | $0.79(\pm 0.004)$ | $0.793(\pm 0.01)$ | $0.782(\pm 0.01)$ | ${\bf 0.798(\pm 0.007)}$ | $0.794(\pm 0.008)$
D $\rightarrow$ E | $0.761(\pm 0.003)$ | $0.8(\pm 0.004)$ | $0.8(\pm 0.004)$ | ${\it 0.8(\pm 0.006)}$ | $0.8(\pm 0.005)$ | $0.775(\pm 0.007)$ | $0.77(\pm 0.009)$ | ${\bf 0.799(\pm 0.004)}$ | $0.794(\pm 0.006)$
D $\rightarrow$ K | $0.778(\pm 0.018)$ | $0.797(\pm 0.012)$ | $0.797(\pm 0.012)$ | $0.797(\pm 0.01)$ | ${\it 0.804(\pm 0.015)}$ | $0.792(\pm 0.02)$ | $0.793(\pm 0.015)$ | ${\bf 0.801(\pm 0.013)}$ | $0.801(\pm 0.015)$
E $\rightarrow$ B | $0.692(\pm 0.014)$ | $0.707(\pm 0.015)$ | $0.707(\pm 0.015)$ | $0.707(\pm 0.015)$ | ${\it 0.713(\pm 0.024)}$ | $0.695(\pm 0.012)$ | $0.707(\pm 0.021)$ | ${\bf 0.71(\pm 0.018)}$ | $0.711(\pm 0.024)$
E $\rightarrow$ D | $0.72(\pm 0.018)$ | $0.741(\pm 0.021)$ | $0.741(\pm 0.021)$ | $0.738(\pm 0.011)$ | ${\it 0.741(\pm 0.005)}$ | $0.722(\pm 0.017)$ | $0.723(\pm 0.028)$ | ${\bf 0.741(\pm 0.006)}$ | $0.735(\pm 0.009)$
E $\rightarrow$ K | $0.86(\pm 0.006)$ | ${\it 0.879(\pm 0.011)}$ | $0.879(\pm 0.011)$ | $0.878(\pm 0.01)$ | $0.874(\pm 0.012)$ | $0.861(\pm 0.018)$ | $0.861(\pm 0.018)$ | ${\bf 0.879(\pm 0.011)}$ | $0.865(\pm 0.011)$
K $\rightarrow$ B | $0.706(\pm 0.004)$ | $0.727(\pm 0.003)$ | $0.727(\pm 0.003)$ | $0.728(\pm 0.001)$ | ${\it 0.732(\pm 0.005)}$ | $0.724(\pm 0.011)$ | $0.722(\pm 0.004)$ | ${\bf 0.733(\pm 0.004)}$ | $0.724(\pm 0.004)$
K $\rightarrow$ D | $0.748(\pm 0.013)$ | $0.765(\pm 0.013)$ | $0.765(\pm 0.013)$ | $0.764(\pm 0.011)$ | ${\it 0.766(\pm 0.021)}$ | $0.752(\pm 0.021)$ | $0.755(\pm 0.005)$ | ${\bf 0.762(\pm 0.01)}$ | $0.752(\pm 0.021)$
K $\rightarrow$ E | $0.845(\pm 0.007)$ | $0.86(\pm 0.005)$ | $0.86(\pm 0.005)$ | $0.861(\pm 0.007)$ | ${\it 0.863(\pm 0.003)}$ | $0.848(\pm 0.005)$ | $0.849(\pm 0.007)$ | ${\bf 0.861(\pm 0.006)}$ | $0.85(\pm 0.003)$
Avg. | $0.767(\pm 0.012)$ | ${\it 0.787(\pm 0.01)}$ | $0.787(\pm 0.01)$ | $0.787(\pm 0.008)$ | $0.787(\pm 0.011)$ | $0.775(\pm 0.012)$ | $0.776(\pm 0.012)$ | ${\bf 0.788(\pm 0.009)}$ | $0.783(\pm 0.01)$

| DANN
---|---
|  | Heuristic | Theoretical error guarantees |
Task | SO | TMV | TMR | TCR | SOR | IWV | DEV | IWA (ours) | TB
B $\rightarrow$ D | $0.783(\pm 0.004)$ | $0.794(\pm 0.003)$ | $0.794(\pm 0.003)$ | $0.794(\pm 0.008)$ | ${\it 0.803(\pm 0.007)}$ | $0.782(\pm 0.005)$ | $0.782(\pm 0.005)$ | ${\bf 0.804(\pm 0.008)}$ | $0.813(\pm 0.017)$
B $\rightarrow$ E | $0.752(\pm 0.011)$ | $0.787(\pm 0.009)$ | $0.787(\pm 0.009)$ | $0.787(\pm 0.013)$ | ${\it 0.796(\pm 0.006)}$ | $0.783(\pm 0.013)$ | $0.782(\pm 0.013)$ | ${\bf 0.789(\pm 0.008)}$ | $0.8(\pm 0.005)$
B $\rightarrow$ K | $0.767(\pm 0.022)$ | $0.804(\pm 0.007)$ | $0.804(\pm 0.007)$ | $0.804(\pm 0.008)$ | ${\it 0.805(\pm 0.004)}$ | $0.796(\pm 0.003)$ | ${\bf 0.806(\pm 0.015)}$ | $0.804(\pm 0.008)$ | $0.82(\pm 0.004)$
D $\rightarrow$ B | $0.779(\pm 0.002)$ | $0.8(\pm 0.007)$ | $0.8(\pm 0.007)$ | $0.799(\pm 0.006)$ | ${\it 0.802(\pm 0.003)}$ | $0.796(\pm 0.004)$ | $0.778(\pm 0.014)$ | ${\bf 0.804(\pm 0.004)}$ | $0.799(\pm 0.004)$
D $\rightarrow$ E | $0.767(\pm 0.016)$ | $0.805(\pm 0.006)$ | $0.805(\pm 0.006)$ | $0.807(\pm 0.009)$ | ${\it 0.808(\pm 0.012)}$ | $0.775(\pm 0.023)$ | $0.78(\pm 0.035)$ | ${\bf 0.81(\pm 0.007)}$ | $0.815(\pm 0.007)$
D $\rightarrow$ K | $0.784(\pm 0.013)$ | $0.815(\pm 0.008)$ | $0.815(\pm 0.008)$ | $0.817(\pm 0.011)$ | ${\it 0.829(\pm 0.014)}$ | $0.788(\pm 0.007)$ | $0.779(\pm 0.012)$ | ${\bf 0.816(\pm 0.011)}$ | $0.827(\pm 0.014)$
E $\rightarrow$ B | $0.701(\pm 0.019)$ | $0.712(\pm 0.014)$ | $0.712(\pm 0.014)$ | $0.712(\pm 0.015)$ | ${\it 0.724(\pm 0.014)}$ | $0.69(\pm 0.03)$ | $0.702(\pm 0.022)$ | ${\bf 0.712(\pm 0.012)}$ | $0.721(\pm 0.014)$
E $\rightarrow$ D | $0.736(\pm 0.005)$ | $0.743(\pm 0.014)$ | $0.743(\pm 0.014)$ | $0.747(\pm 0.012)$ | ${\it 0.758(\pm 0.012)}$ | $0.735(\pm 0.053)$ | $0.738(\pm 0.019)$ | ${\bf 0.751(\pm 0.008)}$ | $0.757(\pm 0.012)$
E $\rightarrow$ K | $0.854(\pm 0.016)$ | $0.877(\pm 0.011)$ | $0.877(\pm 0.011)$ | $0.878(\pm 0.012)$ | ${\it 0.879(\pm 0.014)}$ | $0.86(\pm 0.009)$ | $0.858(\pm 0.007)$ | ${\bf 0.88(\pm 0.013)}$ | $0.875(\pm 0.012)$
K $\rightarrow$ B | $0.711(\pm 0.014)$ | $0.741(\pm 0.004)$ | $0.741(\pm 0.004)$ | $0.74(\pm 0.004)$ | ${\it 0.759(\pm 0.007)}$ | $0.718(\pm 0.012)$ | $0.729(\pm 0.003)$ | ${\bf 0.75(\pm 0.004)}$ | $0.747(\pm 0.007)$
K $\rightarrow$ D | $0.738(\pm 0.006)$ | $0.768(\pm 0.011)$ | $0.768(\pm 0.011)$ | $0.765(\pm 0.011)$ | ${\it 0.778(\pm 0.013)}$ | $0.733(\pm 0.013)$ | $0.758(\pm 0.019)$ | ${\bf 0.778(\pm 0.012)}$ | $0.762(\pm 0.012)$
K $\rightarrow$ E | $0.837(\pm 0.013)$ | $0.864(\pm 0.008)$ | $0.864(\pm 0.008)$ | $0.864(\pm 0.007)$ | ${\it 0.865(\pm 0.009)}$ | $0.86(\pm 0.013)$ | $0.851(\pm 0.008)$ | ${\bf 0.866(\pm 0.011)}$ | $0.859(\pm 0.011)$
Avg. | $0.767(\pm 0.012)$ | $0.792(\pm 0.009)$ | $0.792(\pm 0.009)$ | $0.793(\pm 0.01)$ | ${\it 0.8(\pm 0.01)}$ | $0.776(\pm 0.015)$ | $0.778(\pm 0.015)$ | ${\bf 0.797(\pm 0.009)}$ | $0.8(\pm 0.01)$

| DSAN
---|---
|  | Heuristic | Theoretical error guarantees |
Task | SO | TMV | TMR | TCR | SOR | IWV | DEV | IWA (ours) | TB
B $\rightarrow$ D | $0.779(\pm 0.013)$ | $0.801(\pm 0.014)$ | $0.801(\pm 0.014)$ | $0.803(\pm 0.015)$ | ${\it 0.807(\pm 0.01)}$ | $0.79(\pm 0.02)$ | $0.689(\pm 0.108)$ | ${\bf 0.805(\pm 0.014)}$ | $0.805(\pm 0.01)$
B $\rightarrow$ E | $0.752(\pm 0.005)$ | $0.788(\pm 0.005)$ | $0.788(\pm 0.005)$ | $0.783(\pm 0.005)$ | ${\it 0.798(\pm 0.002)}$ | $0.775(\pm 0.022)$ | $0.764(\pm 0.02)$ | ${\bf 0.787(\pm 0.006)}$ | $0.796(\pm 0.002)$
B $\rightarrow$ K | $0.768(\pm 0.012)$ | $0.799(\pm 0.008)$ | $0.799(\pm 0.008)$ | $0.799(\pm 0.01)$ | ${\it 0.815(\pm 0.007)}$ | $0.786(\pm 0.036)$ | $0.798(\pm 0.031)$ | ${\bf 0.801(\pm 0.011)}$ | $0.816(\pm 0.005)$
D $\rightarrow$ B | $0.782(\pm 0.008)$ | $0.795(\pm 0.004)$ | $0.795(\pm 0.004)$ | $0.795(\pm 0.002)$ | ${\it 0.799(\pm 0.007)}$ | $0.797(\pm 0.01)$ | $0.729(\pm 0.111)$ | ${\bf 0.801(\pm 0.005)}$ | $0.802(\pm 0.007)$
D $\rightarrow$ E | $0.771(\pm 0.002)$ | $0.804(\pm 0.008)$ | $0.804(\pm 0.008)$ | $0.804(\pm 0.008)$ | ${\it 0.816(\pm 0.012)}$ | $0.79(\pm 0.02)$ | $0.792(\pm 0.02)$ | ${\bf 0.808(\pm 0.003)}$ | $0.813(\pm 0.012)$
D $\rightarrow$ K | $0.786(\pm 0.013)$ | $0.804(\pm 0.01)$ | $0.804(\pm 0.01)$ | $0.802(\pm 0.012)$ | ${\it 0.821(\pm 0.014)}$ | $0.789(\pm 0.013)$ | $0.801(\pm 0.025)$ | ${\bf 0.807(\pm 0.012)}$ | $0.83(\pm 0.016)$
E $\rightarrow$ B | $0.702(\pm 0.021)$ | $0.716(\pm 0.017)$ | $0.716(\pm 0.017)$ | $0.718(\pm 0.021)$ | ${\it 0.718(\pm 0.018)}$ | $0.71(\pm 0.021)$ | $0.707(\pm 0.018)$ | ${\bf 0.721(\pm 0.02)}$ | $0.711(\pm 0.02)$
E $\rightarrow$ D | $0.725(\pm 0.007)$ | $0.743(\pm 0.008)$ | $0.743(\pm 0.008)$ | $0.741(\pm 0.005)$ | ${\it 0.744(\pm 0.008)}$ | $0.723(\pm 0.021)$ | $0.735(\pm 0.012)$ | ${\bf 0.749(\pm 0.005)}$ | $0.732(\pm 0.005)$
E $\rightarrow$ K | $0.865(\pm 0.013)$ | $0.883(\pm 0.009)$ | $0.883(\pm 0.009)$ | $0.882(\pm 0.008)$ | ${\it 0.886(\pm 0.009)}$ | $0.874(\pm 0.003)$ | $0.876(\pm 0.006)$ | ${\bf 0.883(\pm 0.01)}$ | $0.876(\pm 0.009)$
K $\rightarrow$ B | $0.716(\pm 0.016)$ | $0.741(\pm 0.01)$ | $0.741(\pm 0.01)$ | $0.736(\pm 0.007)$ | ${\it 0.746(\pm 0.011)}$ | $0.712(\pm 0.014)$ | $0.707(\pm 0.016)$ | ${\bf 0.742(\pm 0.008)}$ | $0.739(\pm 0.011)$
K $\rightarrow$ D | $0.739(\pm 0.023)$ | $0.773(\pm 0.006)$ | $0.773(\pm 0.006)$ | $0.768(\pm 0.003)$ | ${\it 0.777(\pm 0.01)}$ | $0.746(\pm 0.016)$ | $0.726(\pm 0.035)$ | ${\bf 0.776(\pm 0.005)}$ | $0.763(\pm 0.012)$
K $\rightarrow$ E | $0.84(\pm 0.01)$ | $0.86(\pm 0.005)$ | $0.86(\pm 0.005)$ | $0.858(\pm 0.007)$ | ${\it 0.868(\pm 0.005)}$ | $0.854(\pm 0.001)$ | $0.835(\pm 0.04)$ | ${\bf 0.865(\pm 0.008)}$ | $0.857(\pm 0.005)$
Avg. | $0.769(\pm 0.012)$ | $0.792(\pm 0.009)$ | $0.792(\pm 0.009)$ | $0.791(\pm 0.009)$ | ${\it 0.8(\pm 0.009)}$ | $0.779(\pm 0.016)$ | $0.763(\pm 0.037)$ | ${\bf 0.795(\pm 0.009)}$ | $0.795(\pm 0.009)$

####  D.7.3 Detailed MiniDomainNet Results

Table 18: Mean and standard deviation (after $\pm$) of target classification
accuracy on MiniDomainNet dataset over three different random initialization
of model weights and five domain adaptation tasks.

| MiniDomainNet
---|---
|  | Heuristic | Theoretical error guarantees |
Method | SO | TMV | TMR | TCR | SOR | IWV | DEV | IWA (ours) | TB
HoMM | $0.509(\pm 0.018)$ | ${\it 0.526(\pm 0.009)}$ | $0.524(\pm 0.010)$ | $0.523(\pm 0.010)$ | $0.518(\pm 0.015)$ | $0.511(\pm 0.018)$ | $0.511(\pm 0.018)$ | ${\bf 0.531(\pm 0.007)}$ | $0.537(\pm 0.020)$
AdvSKM | $0.509(\pm 0.015)$ | ${\it 0.516(\pm 0.011)}$ | $0.514(\pm 0.014)$ | $0.514(\pm 0.017)$ | $0.514(\pm 0.009)$ | $0.515(\pm 0.032)$ | $0.512(\pm 0.032)$ | ${\bf 0.516(\pm 0.011)}$ | $0.522(\pm 0.017)$
DIRT | $0.499(\pm 0.022)$ | ${\it 0.517(\pm 0.006)}$ | $0.515(\pm 0.009)$ | $0.508(\pm 0.006)$ | $0.507(\pm 0.018)$ | $0.493(\pm 0.028)$ | $0.498(\pm 0.033)$ | ${\bf 0.519(\pm 0.006)}$ | $0.525(\pm 0.020)$
DDC | $0.510(\pm 0.032)$ | ${\it 0.514(\pm 0.012)}$ | $0.512(\pm 0.018)$ | $0.511(\pm 0.019)$ | $0.514(\pm 0.015)$ | $0.511(\pm 0.028)$ | $0.512(\pm 0.043)$ | ${\bf 0.516(\pm 0.015)}$ | $0.521(\pm 0.019)$
CMD | $0.509(\pm 0.019)$ | $0.528(\pm 0.011)$ | ${\it 0.531(\pm 0.016)}$ | $0.531(\pm 0.016)$ | $0.522(\pm 0.013)$ | $0.518(\pm 0.025)$ | $0.490(\pm 0.037)$ | ${\bf 0.533(\pm 0.009)}$ | $0.533(\pm 0.024)$
MMDA | $0.509(\pm 0.021)$ | ${\it 0.524(\pm 0.004)}$ | $0.522(\pm 0.005)$ | $0.523(\pm 0.007)$ | $0.519(\pm 0.012)$ | $0.517(\pm 0.008)$ | $0.524(\pm 0.006)$ | ${\bf 0.527(\pm 0.009)}$ | $0.531(\pm 0.029)$
CoDATS | $0.502(\pm 0.026)$ | $0.535(\pm 0.026)$ | $0.533(\pm 0.027)$ | ${\it 0.536(\pm 0.028)}$ | $0.525(\pm 0.015)$ | $0.518(\pm 0.031)$ | $0.524(\pm 0.051)$ | ${\bf 0.536(\pm 0.025)}$ | $0.529(\pm 0.042)$
Deep-Coral | $0.505(\pm 0.022)$ | ${\it 0.538(\pm 0.009)}$ | $0.534(\pm 0.013)$ | $0.533(\pm 0.012)$ | $0.520(\pm 0.010)$ | $0.518(\pm 0.022)$ | $0.524(\pm 0.034)$ | ${\bf 0.539(\pm 0.012)}$ | $0.535(\pm 0.024)$
CDAN | $0.514(\pm 0.028)$ | ${\it 0.526(\pm 0.013)}$ | $0.524(\pm 0.011)$ | $0.525(\pm 0.008)$ | $0.517(\pm 0.005)$ | $0.513(\pm 0.011)$ | $0.516(\pm 0.014)$ | ${\bf 0.532(\pm 0.010)}$ | $0.542(\pm 0.017)$
DANN | $0.496(\pm 0.023)$ | $0.530(\pm 0.011)$ | $0.535(\pm 0.011)$ | ${\it 0.538(\pm 0.005)}$ | $0.516(\pm 0.011)$ | $0.519(\pm 0.015)$ | $0.515(\pm 0.013)$ | ${\bf 0.541(\pm 0.006)}$ | $0.532(\pm 0.014)$
DSAN | $0.509(\pm 0.022)$ | $0.537(\pm 0.011)$ | $0.534(\pm 0.013)$ | ${\it 0.543(\pm 0.011)}$ | $0.525(\pm 0.013)$ | $0.513(\pm 0.018)$ | $0.535(\pm 0.023)$ | ${\bf 0.546(\pm 0.007)}$ | $0.563(\pm 0.013)$
Avg. | $0.507(\pm 0.022)$ | ${\it 0.526(\pm 0.011)}$ | $0.525(\pm 0.014)$ | $0.526(\pm 0.013)$ | $0.518(\pm 0.012)$ | $0.513(\pm 0.022)$ | $0.515(\pm 0.028)$ | ${\bf 0.531(\pm 0.011)}$ | $0.534(\pm 0.022)$

Table 19: Mean and standard deviation (after $\pm$) of target classification
accuracy on MiniDomainNet (Part 1) over $3$ repetitions with different random
initialization of model weights.

| HoMM
---|---
|  | Heuristic | Theoretical error guarantees |
Task | SO | TMV | TMR | TCR | SOR | IWV | DEV | IWA (ours) | TB
R $\rightarrow$ C | $0.552(\pm 0.041)$ | ${\it 0.587(\pm 0.017)}$ | $0.587(\pm 0.017)$ | $0.587(\pm 0.005)$ | $0.557(\pm 0.008)$ | $0.538(\pm 0.029)$ | $0.56(\pm 0.017)$ | ${\bf 0.596(\pm 0.009)}$ | $0.607(\pm 0.022)$
R $\rightarrow$ I | $0.373(\pm 0.014)$ | $0.376(\pm 0.012)$ | $0.376(\pm 0.012)$ | $0.373(\pm 0.005)$ | ${\it 0.386(\pm 0.007)}$ | $0.37(\pm 0.01)$ | $0.37(\pm 0.01)$ | ${\bf 0.392(\pm 0.007)}$ | $0.413(\pm 0.041)$
R $\rightarrow$ P | $0.709(\pm 0.026)$ | ${\it 0.722(\pm 0.01)}$ | $0.722(\pm 0.01)$ | $0.718(\pm 0.006)$ | $0.709(\pm 0.011)$ | $0.704(\pm 0.013)$ | $0.705(\pm 0.014)$ | ${\bf 0.73(\pm 0.003)}$ | $0.721(\pm 0.003)$
R $\rightarrow$ Q | $0.332(\pm 0.009)$ | $0.35(\pm 0.006)$ | $0.35(\pm 0.006)$ | $0.353(\pm 0.008)$ | ${\it 0.356(\pm 0.02)}$ | ${\bf 0.367(\pm 0.019)}$ | $0.342(\pm 0.018)$ | $0.353(\pm 0.003)$ | $0.37(\pm 0.013)$
R $\rightarrow$ S | $0.579(\pm 0.022)$ | ${\it 0.587(\pm 0.012)}$ | $0.587(\pm 0.012)$ | $0.586(\pm 0.003)$ | $0.582(\pm 0.01)$ | $0.577(\pm 0.004)$ | $0.577(\pm 0.004)$ | ${\bf 0.586(\pm 0.008)}$ | $0.609(\pm 0.011)$
Avg. | $0.509(\pm 0.023)$ | ${\it 0.524(\pm 0.011)}$ | $0.524(\pm 0.011)$ | $0.523(\pm 0.005)$ | $0.518(\pm 0.011)$ | $0.511(\pm 0.015)$ | $0.511(\pm 0.013)$ | ${\bf 0.531(\pm 0.006)}$ | $0.544(\pm 0.018)$

| AdvSKM
---|---
|  | Heuristic | Theoretical error guarantees |
Task | SO | TMV | TMR | TCR | SOR | IWV | DEV | IWA (ours) | TB
R $\rightarrow$ C | $0.544(\pm 0.017)$ | $0.56(\pm 0.025)$ | $0.56(\pm 0.025)$ | ${\it 0.566(\pm 0.03)}$ | $0.544(\pm 0.024)$ | $0.549(\pm 0.022)$ | $0.549(\pm 0.022)$ | ${\bf 0.568(\pm 0.009)}$ | $0.582(\pm 0.046)$
R $\rightarrow$ I | $0.38(\pm 0.018)$ | $0.373(\pm 0.016)$ | $0.373(\pm 0.016)$ | $0.371(\pm 0.009)$ | ${\it 0.394(\pm 0.037)}$ | $0.394(\pm 0.021)$ | ${\bf 0.394(\pm 0.021)}$ | $0.377(\pm 0.013)$ | $0.395(\pm 0.02)$
R $\rightarrow$ P | $0.723(\pm 0.009)$ | ${\it 0.721(\pm 0.004)}$ | $0.721(\pm 0.004)$ | $0.719(\pm 0.003)$ | $0.712(\pm 0.006)$ | $0.706(\pm 0.041)$ | $0.695(\pm 0.034)$ | ${\bf 0.721(\pm 0.003)}$ | $0.723(\pm 0.009)$
R $\rightarrow$ Q | $0.322(\pm 0.027)$ | $0.332(\pm 0.006)$ | $0.332(\pm 0.006)$ | $0.328(\pm 0.005)$ | ${\it 0.335(\pm 0.002)}$ | ${\bf 0.335(\pm 0.002)}$ | $0.332(\pm 0.006)$ | $0.333(\pm 0.005)$ | $0.335(\pm 0.004)$
R $\rightarrow$ S | $0.579(\pm 0.017)$ | ${\it 0.586(\pm 0.001)}$ | $0.586(\pm 0.001)$ | $0.584(\pm 0.003)$ | $0.586(\pm 0.005)$ | $0.589(\pm 0.007)$ | ${\bf 0.589(\pm 0.007)}$ | $0.582(\pm 0.004)$ | $0.592(\pm 0.009)$
Avg. | $0.509(\pm 0.018)$ | ${\it 0.514(\pm 0.01)}$ | $0.514(\pm 0.01)$ | $0.514(\pm 0.01)$ | $0.514(\pm 0.015)$ | $0.515(\pm 0.018)$ | $0.512(\pm 0.018)$ | ${\bf 0.516(\pm 0.007)}$ | $0.525(\pm 0.018)$

| DIRT
---|---
|  | Heuristic | Theoretical error guarantees |
Task | SO | TMV | TMR | TCR | SOR | IWV | DEV | IWA (ours) | TB
R $\rightarrow$ C | $0.53(\pm 0.013)$ | ${\it 0.577(\pm 0.033)}$ | $0.577(\pm 0.033)$ | $0.546(\pm 0.031)$ | $0.571(\pm 0.017)$ | $0.541(\pm 0.025)$ | $0.544(\pm 0.025)$ | ${\bf 0.577(\pm 0.025)}$ | $0.587(\pm 0.037)$
R $\rightarrow$ I | $0.373(\pm 0.038)$ | $0.365(\pm 0.041)$ | $0.365(\pm 0.041)$ | ${\it 0.374(\pm 0.037)}$ | $0.37(\pm 0.007)$ | $0.36(\pm 0.011)$ | ${\bf 0.385(\pm 0.062)}$ | $0.38(\pm 0.031)$ | $0.431(\pm 0.045)$
R $\rightarrow$ P | $0.704(\pm 0.031)$ | ${\it 0.708(\pm 0.026)}$ | $0.708(\pm 0.026)$ | $0.706(\pm 0.02)$ | $0.689(\pm 0.015)$ | $0.663(\pm 0.03)$ | $0.67(\pm 0.042)$ | ${\bf 0.713(\pm 0.03)}$ | $0.715(\pm 0.028)$
R $\rightarrow$ Q | $0.34(\pm 0.02)$ | ${\it 0.345(\pm 0.031)}$ | $0.345(\pm 0.031)$ | $0.34(\pm 0.046)$ | $0.336(\pm 0.024)$ | $0.326(\pm 0.086)$ | ${\bf 0.365(\pm 0.038)}$ | $0.342(\pm 0.022)$ | $0.382(\pm 0.027)$
R $\rightarrow$ S | $0.55(\pm 0.028)$ | ${\it 0.578(\pm 0.006)}$ | $0.578(\pm 0.006)$ | $0.571(\pm 0.006)$ | $0.571(\pm 0.012)$ | $0.572(\pm 0.005)$ | $0.525(\pm 0.088)$ | ${\bf 0.583(\pm 0.016)}$ | $0.588(\pm 0.033)$
Avg. | $0.499(\pm 0.026)$ | ${\it 0.515(\pm 0.027)}$ | $0.515(\pm 0.027)$ | $0.508(\pm 0.028)$ | $0.507(\pm 0.015)$ | $0.493(\pm 0.031)$ | $0.498(\pm 0.051)$ | ${\bf 0.519(\pm 0.025)}$ | $0.541(\pm 0.034)$

| DDC
---|---
|  | Heuristic | Theoretical error guarantees |
Task | SO | TMV | TMR | TCR | SOR | IWV | DEV | IWA (ours) | TB
R $\rightarrow$ C | $0.555(\pm 0.045)$ | ${\it 0.555(\pm 0.013)}$ | $0.555(\pm 0.013)$ | $0.549(\pm 0.008)$ | $0.552(\pm 0.009)$ | $0.546(\pm 0.013)$ | $0.546(\pm 0.013)$ | ${\bf 0.568(\pm 0.025)}$ | $0.585(\pm 0.076)$
R $\rightarrow$ I | $0.374(\pm 0.014)$ | $0.391(\pm 0.003)$ | $0.391(\pm 0.003)$ | $0.38(\pm 0.014)$ | ${\it 0.398(\pm 0.024)}$ | $0.379(\pm 0.009)$ | $0.379(\pm 0.009)$ | ${\bf 0.385(\pm 0.008)}$ | $0.416(\pm 0.014)$
R $\rightarrow$ P | $0.709(\pm 0.025)$ | ${\it 0.714(\pm 0.0)}$ | $0.714(\pm 0.0)$ | $0.712(\pm 0.004)$ | $0.709(\pm 0.004)$ | $0.713(\pm 0.006)$ | ${\bf 0.718(\pm 0.003)}$ | $0.715(\pm 0.002)$ | $0.717(\pm 0.004)$
R $\rightarrow$ Q | $0.334(\pm 0.002)$ | $0.331(\pm 0.003)$ | $0.331(\pm 0.003)$ | ${\it 0.333(\pm 0.0)}$ | $0.327(\pm 0.018)$ | $0.333(\pm 0.005)$ | ${\bf 0.335(\pm 0.002)}$ | $0.335(\pm 0.003)$ | $0.337(\pm 0.004)$
R $\rightarrow$ S | $0.576(\pm 0.022)$ | $0.571(\pm 0.01)$ | $0.571(\pm 0.01)$ | $0.578(\pm 0.008)$ | ${\it 0.582(\pm 0.005)}$ | $0.582(\pm 0.005)$ | ${\bf 0.582(\pm 0.005)}$ | $0.579(\pm 0.007)$ | $0.585(\pm 0.021)$
Avg. | $0.51(\pm 0.021)$ | $0.512(\pm 0.005)$ | $0.512(\pm 0.005)$ | $0.511(\pm 0.007)$ | ${\it 0.514(\pm 0.012)}$ | $0.511(\pm 0.008)$ | $0.512(\pm 0.006)$ | ${\bf 0.516(\pm 0.009)}$ | $0.528(\pm 0.024)$

| CMD
---|---
|  | Heuristic | Theoretical error guarantees |
Task | SO | TMV | TMR | TCR | SOR | IWV | DEV | IWA (ours) | TB
R $\rightarrow$ C | $0.555(\pm 0.042)$ | ${\it 0.598(\pm 0.008)}$ | $0.598(\pm 0.008)$ | $0.59(\pm 0.008)$ | $0.544(\pm 0.021)$ | $0.552(\pm 0.031)$ | $0.443(\pm 0.067)$ | ${\bf 0.593(\pm 0.009)}$ | $0.617(\pm 0.025)$
R $\rightarrow$ I | $0.377(\pm 0.009)$ | $0.368(\pm 0.007)$ | $0.368(\pm 0.007)$ | $0.371(\pm 0.005)$ | ${\it 0.395(\pm 0.007)}$ | $0.379(\pm 0.011)$ | $0.379(\pm 0.011)$ | ${\bf 0.379(\pm 0.007)}$ | $0.389(\pm 0.007)$
R $\rightarrow$ P | $0.704(\pm 0.02)$ | ${\it 0.741(\pm 0.015)}$ | $0.741(\pm 0.015)$ | $0.733(\pm 0.01)$ | $0.723(\pm 0.02)$ | $0.732(\pm 0.019)$ | $0.736(\pm 0.013)$ | ${\bf 0.74(\pm 0.004)}$ | $0.734(\pm 0.015)$
R $\rightarrow$ Q | $0.332(\pm 0.015)$ | $0.365(\pm 0.005)$ | $0.365(\pm 0.005)$ | ${\it 0.374(\pm 0.003)}$ | $0.361(\pm 0.036)$ | $0.338(\pm 0.059)$ | $0.303(\pm 0.061)$ | ${\bf 0.364(\pm 0.007)}$ | $0.378(\pm 0.008)$
R $\rightarrow$ S | $0.578(\pm 0.022)$ | $0.582(\pm 0.01)$ | $0.582(\pm 0.01)$ | $0.587(\pm 0.005)$ | ${\it 0.589(\pm 0.005)}$ | $0.588(\pm 0.019)$ | $0.591(\pm 0.015)$ | ${\bf 0.592(\pm 0.003)}$ | $0.59(\pm 0.003)$
Avg. | $0.509(\pm 0.022)$ | ${\it 0.531(\pm 0.009)}$ | $0.531(\pm 0.009)$ | $0.531(\pm 0.006)$ | $0.522(\pm 0.018)$ | $0.518(\pm 0.028)$ | $0.49(\pm 0.033)$ | ${\bf 0.533(\pm 0.006)}$ | $0.542(\pm 0.012)$

| MMDA
---|---
|  | Heuristic | Theoretical error guarantees |
Task | SO | TMV | TMR | TCR | SOR | IWV | DEV | IWA (ours) | TB
R $\rightarrow$ C | $0.555(\pm 0.042)$ | ${\it 0.587(\pm 0.009)}$ | $0.587(\pm 0.009)$ | $0.571(\pm 0.013)$ | $0.56(\pm 0.019)$ | $0.544(\pm 0.033)$ | $0.544(\pm 0.033)$ | ${\bf 0.585(\pm 0.009)}$ | $0.585(\pm 0.009)$
R $\rightarrow$ I | $0.377(\pm 0.009)$ | $0.379(\pm 0.007)$ | $0.379(\pm 0.007)$ | $0.376(\pm 0.012)$ | ${\it 0.389(\pm 0.008)}$ | $0.389(\pm 0.021)$ | ${\bf 0.389(\pm 0.021)}$ | $0.373(\pm 0.003)$ | $0.415(\pm 0.016)$
R $\rightarrow$ P | $0.704(\pm 0.02)$ | $0.714(\pm 0.014)$ | $0.714(\pm 0.014)$ | $0.714(\pm 0.011)$ | ${\it 0.717(\pm 0.014)}$ | $0.713(\pm 0.003)$ | $0.721(\pm 0.015)$ | ${\bf 0.723(\pm 0.004)}$ | $0.735(\pm 0.007)$
R $\rightarrow$ Q | $0.332(\pm 0.015)$ | $0.352(\pm 0.023)$ | $0.352(\pm 0.023)$ | ${\it 0.372(\pm 0.006)}$ | $0.335(\pm 0.018)$ | $0.353(\pm 0.025)$ | ${\bf 0.38(\pm 0.035)}$ | $0.362(\pm 0.009)$ | $0.392(\pm 0.018)$
R $\rightarrow$ S | $0.578(\pm 0.022)$ | $0.581(\pm 0.011)$ | $0.581(\pm 0.011)$ | $0.583(\pm 0.013)$ | ${\it 0.592(\pm 0.004)}$ | $0.587(\pm 0.01)$ | $0.587(\pm 0.01)$ | ${\bf 0.593(\pm 0.009)}$ | $0.605(\pm 0.008)$
Avg. | $0.509(\pm 0.022)$ | $0.522(\pm 0.013)$ | $0.522(\pm 0.013)$ | ${\it 0.523(\pm 0.011)}$ | $0.519(\pm 0.013)$ | $0.517(\pm 0.018)$ | $0.524(\pm 0.023)$ | ${\bf 0.527(\pm 0.007)}$ | $0.546(\pm 0.012)$

Table 20: Mean and standard deviation (after $\pm$) of target classification
accuracy on MiniDomainNet (Part 2) over $3$ repetitions with different random
initialization of model weights.

| CoDATS
---|---
|  | Heuristic | Theoretical error guarantees |
Task | SO | TMV | TMR | TCR | SOR | IWV | DEV | IWA (ours) | TB
R $\rightarrow$ C | $0.538(\pm 0.072)$ | $0.585(\pm 0.025)$ | $0.585(\pm 0.025)$ | ${\it 0.607(\pm 0.028)}$ | $0.585(\pm 0.013)$ | $0.555(\pm 0.031)$ | ${\bf 0.626(\pm 0.058)}$ | $0.577(\pm 0.026)$ | $0.617(\pm 0.058)$
R $\rightarrow$ I | $0.365(\pm 0.037)$ | $0.371(\pm 0.024)$ | $0.371(\pm 0.024)$ | $0.367(\pm 0.016)$ | ${\it 0.38(\pm 0.02)}$ | ${\bf 0.373(\pm 0.041)}$ | $0.363(\pm 0.056)$ | $0.371(\pm 0.012)$ | $0.406(\pm 0.021)$
R $\rightarrow$ P | $0.689(\pm 0.024)$ | ${\it 0.735(\pm 0.01)}$ | $0.735(\pm 0.01)$ | $0.734(\pm 0.015)$ | $0.726(\pm 0.014)$ | $0.689(\pm 0.043)$ | $0.689(\pm 0.043)$ | ${\bf 0.743(\pm 0.016)}$ | $0.732(\pm 0.016)$
R $\rightarrow$ Q | $0.322(\pm 0.022)$ | $0.356(\pm 0.02)$ | $0.356(\pm 0.02)$ | ${\it 0.358(\pm 0.017)}$ | $0.34(\pm 0.017)$ | ${\bf 0.384(\pm 0.012)}$ | $0.348(\pm 0.044)$ | $0.364(\pm 0.012)$ | $0.417(\pm 0.025)$
R $\rightarrow$ S | $0.597(\pm 0.004)$ | ${\it 0.619(\pm 0.013)}$ | $0.619(\pm 0.013)$ | $0.616(\pm 0.018)$ | $0.593(\pm 0.01)$ | $0.592(\pm 0.013)$ | $0.592(\pm 0.013)$ | ${\bf 0.622(\pm 0.009)}$ | $0.627(\pm 0.008)$
Avg. | $0.502(\pm 0.032)$ | $0.533(\pm 0.018)$ | $0.533(\pm 0.018)$ | ${\it 0.536(\pm 0.019)}$ | $0.525(\pm 0.015)$ | $0.518(\pm 0.028)$ | $0.524(\pm 0.043)$ | ${\bf 0.536(\pm 0.015)}$ | $0.56(\pm 0.026)$

| Deep-Coral
---|---
|  | Heuristic | Theoretical error guarantees |
Task | SO | TMV | TMR | TCR | SOR | IWV | DEV | IWA (ours) | TB
R $\rightarrow$ C | $0.555(\pm 0.045)$ | ${\it 0.585(\pm 0.017)}$ | $0.585(\pm 0.017)$ | $0.582(\pm 0.014)$ | $0.557(\pm 0.0)$ | $0.536(\pm 0.025)$ | $0.568(\pm 0.013)$ | ${\bf 0.59(\pm 0.022)}$ | $0.601(\pm 0.056)$
R $\rightarrow$ I | $0.376(\pm 0.012)$ | $0.37(\pm 0.01)$ | $0.37(\pm 0.01)$ | $0.368(\pm 0.01)$ | ${\it 0.38(\pm 0.005)}$ | $0.368(\pm 0.003)$ | ${\bf 0.368(\pm 0.003)}$ | $0.367(\pm 0.012)$ | $0.386(\pm 0.007)$
R $\rightarrow$ P | $0.711(\pm 0.021)$ | ${\it 0.726(\pm 0.015)}$ | $0.726(\pm 0.015)$ | $0.723(\pm 0.007)$ | $0.714(\pm 0.007)$ | $0.722(\pm 0.007)$ | $0.722(\pm 0.012)$ | ${\bf 0.738(\pm 0.012)}$ | $0.734(\pm 0.012)$
R $\rightarrow$ Q | $0.316(\pm 0.041)$ | $0.383(\pm 0.003)$ | $0.383(\pm 0.003)$ | ${\it 0.386(\pm 0.004)}$ | $0.365(\pm 0.008)$ | $0.378(\pm 0.011)$ | $0.375(\pm 0.033)$ | ${\bf 0.38(\pm 0.002)}$ | $0.388(\pm 0.002)$
R $\rightarrow$ S | $0.569(\pm 0.02)$ | ${\it 0.606(\pm 0.009)}$ | $0.606(\pm 0.009)$ | $0.606(\pm 0.005)$ | $0.581(\pm 0.007)$ | $0.588(\pm 0.008)$ | $0.588(\pm 0.008)$ | ${\bf 0.622(\pm 0.001)}$ | $0.658(\pm 0.035)$
Avg. | $0.505(\pm 0.028)$ | ${\it 0.534(\pm 0.011)}$ | $0.534(\pm 0.011)$ | $0.533(\pm 0.008)$ | $0.52(\pm 0.005)$ | $0.518(\pm 0.011)$ | $0.524(\pm 0.014)$ | ${\bf 0.539(\pm 0.01)}$ | $0.554(\pm 0.022)$

| CDAN
---|---
|  | Heuristic | Theoretical error guarantees |
Task | SO | TMV | TMR | TCR | SOR | IWV | DEV | IWA (ours) | TB
R $\rightarrow$ C | $0.557(\pm 0.008)$ | $0.587(\pm 0.013)$ | $0.587(\pm 0.013)$ | ${\it 0.593(\pm 0.026)}$ | $0.563(\pm 0.009)$ | $0.552(\pm 0.025)$ | $0.574(\pm 0.05)$ | ${\bf 0.598(\pm 0.022)}$ | $0.615(\pm 0.008)$
R $\rightarrow$ I | $0.386(\pm 0.01)$ | $0.359(\pm 0.005)$ | $0.359(\pm 0.005)$ | $0.357(\pm 0.009)$ | ${\it 0.368(\pm 0.005)}$ | ${\bf 0.363(\pm 0.04)}$ | $0.335(\pm 0.016)$ | $0.357(\pm 0.009)$ | $0.386(\pm 0.01)$
R $\rightarrow$ P | $0.709(\pm 0.022)$ | $0.732(\pm 0.02)$ | $0.732(\pm 0.02)$ | ${\it 0.734(\pm 0.023)}$ | $0.71(\pm 0.006)$ | $0.72(\pm 0.039)$ | $0.723(\pm 0.036)$ | ${\bf 0.731(\pm 0.004)}$ | $0.716(\pm 0.023)$
R $\rightarrow$ Q | $0.342(\pm 0.006)$ | ${\it 0.352(\pm 0.024)}$ | $0.352(\pm 0.024)$ | $0.349(\pm 0.02)$ | $0.347(\pm 0.016)$ | $0.356(\pm 0.034)$ | ${\bf 0.38(\pm 0.028)}$ | $0.364(\pm 0.013)$ | $0.442(\pm 0.114)$
R $\rightarrow$ S | $0.576(\pm 0.027)$ | $0.588(\pm 0.01)$ | $0.588(\pm 0.01)$ | $0.593(\pm 0.005)$ | ${\it 0.596(\pm 0.01)}$ | $0.574(\pm 0.022)$ | $0.568(\pm 0.03)$ | ${\bf 0.61(\pm 0.008)}$ | $0.651(\pm 0.056)$
Avg. | $0.514(\pm 0.015)$ | $0.524(\pm 0.014)$ | $0.524(\pm 0.014)$ | ${\it 0.525(\pm 0.017)}$ | $0.517(\pm 0.009)$ | $0.513(\pm 0.032)$ | $0.516(\pm 0.032)$ | ${\bf 0.532(\pm 0.011)}$ | $0.562(\pm 0.042)$

| DANN
---|---
|  | Heuristic | Theoretical error guarantees |
Task | SO | TMV | TMR | TCR | SOR | IWV | DEV | IWA (ours) | TB
R $\rightarrow$ C | $0.519(\pm 0.013)$ | ${\it 0.626(\pm 0.021)}$ | $0.626(\pm 0.021)$ | $0.623(\pm 0.036)$ | $0.557(\pm 0.014)$ | $0.582(\pm 0.022)$ | $0.56(\pm 0.07)$ | ${\bf 0.607(\pm 0.008)}$ | $0.631(\pm 0.038)$
R $\rightarrow$ I | $0.376(\pm 0.016)$ | $0.37(\pm 0.013)$ | $0.37(\pm 0.013)$ | $0.377(\pm 0.013)$ | ${\it 0.389(\pm 0.032)}$ | $0.379(\pm 0.036)$ | $0.379(\pm 0.036)$ | ${\bf 0.388(\pm 0.019)}$ | $0.4(\pm 0.025)$
R $\rightarrow$ P | $0.705(\pm 0.011)$ | ${\it 0.704(\pm 0.013)}$ | $0.704(\pm 0.013)$ | $0.704(\pm 0.011)$ | $0.696(\pm 0.006)$ | $0.699(\pm 0.006)$ | $0.697(\pm 0.014)$ | ${\bf 0.721(\pm 0.008)}$ | $0.713(\pm 0.008)$
R $\rightarrow$ Q | $0.3(\pm 0.043)$ | $0.377(\pm 0.008)$ | $0.377(\pm 0.008)$ | ${\it 0.38(\pm 0.006)}$ | $0.343(\pm 0.004)$ | $0.351(\pm 0.048)$ | $0.351(\pm 0.048)$ | ${\bf 0.374(\pm 0.003)}$ | $0.392(\pm 0.005)$
R $\rightarrow$ S | $0.581(\pm 0.014)$ | $0.598(\pm 0.023)$ | $0.598(\pm 0.023)$ | ${\it 0.607(\pm 0.016)}$ | $0.596(\pm 0.01)$ | $0.586(\pm 0.015)$ | $0.586(\pm 0.015)$ | ${\bf 0.617(\pm 0.005)}$ | $0.657(\pm 0.015)$
Avg. | $0.496(\pm 0.019)$ | $0.535(\pm 0.016)$ | $0.535(\pm 0.016)$ | ${\it 0.538(\pm 0.016)}$ | $0.516(\pm 0.013)$ | $0.519(\pm 0.025)$ | $0.515(\pm 0.037)$ | ${\bf 0.541(\pm 0.009)}$ | $0.559(\pm 0.018)$

| DSAN
---|---
|  | Heuristic | Theoretical error guarantees |
Task | SO | TMV | TMR | TCR | SOR | IWV | DEV | IWA (ours) | TB
R $\rightarrow$ C | $0.555(\pm 0.042)$ | $0.637(\pm 0.021)$ | $0.637(\pm 0.021)$ | ${\it 0.639(\pm 0.022)}$ | $0.566(\pm 0.016)$ | $0.557(\pm 0.059)$ | $0.571(\pm 0.045)$ | ${\bf 0.639(\pm 0.008)}$ | $0.648(\pm 0.014)$
R $\rightarrow$ I | $0.377(\pm 0.009)$ | $0.363(\pm 0.01)$ | $0.363(\pm 0.01)$ | $0.374(\pm 0.015)$ | ${\it 0.406(\pm 0.005)}$ | $0.362(\pm 0.034)$ | $0.362(\pm 0.034)$ | ${\bf 0.377(\pm 0.016)}$ | $0.404(\pm 0.005)$
R $\rightarrow$ P | $0.705(\pm 0.021)$ | $0.712(\pm 0.009)$ | $0.712(\pm 0.009)$ | $0.714(\pm 0.005)$ | ${\it 0.72(\pm 0.008)}$ | $0.716(\pm 0.003)$ | $0.719(\pm 0.003)$ | ${\bf 0.719(\pm 0.007)}$ | $0.716(\pm 0.008)$
R $\rightarrow$ Q | $0.332(\pm 0.012)$ | $0.364(\pm 0.021)$ | $0.364(\pm 0.021)$ | ${\it 0.38(\pm 0.012)}$ | $0.34(\pm 0.016)$ | $0.342(\pm 0.009)$ | ${\bf 0.437(\pm 0.083)}$ | $0.372(\pm 0.011)$ | $0.478(\pm 0.013)$
R $\rightarrow$ S | $0.577(\pm 0.026)$ | $0.594(\pm 0.004)$ | $0.594(\pm 0.004)$ | ${\it 0.607(\pm 0.005)}$ | $0.594(\pm 0.003)$ | $0.585(\pm 0.004)$ | $0.585(\pm 0.004)$ | ${\bf 0.625(\pm 0.016)}$ | $0.639(\pm 0.052)$
Avg. | $0.509(\pm 0.022)$ | $0.534(\pm 0.013)$ | $0.534(\pm 0.013)$ | ${\it 0.543(\pm 0.012)}$ | $0.525(\pm 0.01)$ | $0.513(\pm 0.022)$ | $0.535(\pm 0.034)$ | ${\bf 0.546(\pm 0.012)}$ | $0.577(\pm 0.018)$

####  D.7.4 Detailed Time-Series Results

Table 21: Mean and standard deviation (after $\pm$) of target classification
accuracy on Sleep-EDF (Part 1) over $3$ repetitions with different random
initialization of model weights.

| HoMM
---|---
|  | Heuristic | Theoretical error guarantees |
Task | SO | TMV | TMR | TCR | SOR | IWV | DEV | IWA (ours) | TB
0 $\rightarrow$ 11 | $0.565(\pm 0.033)$ | $0.557(\pm 0.066)$ | $0.557(\pm 0.066)$ | $0.553(\pm 0.068)$ | ${\it 0.72(\pm 0.052)}$ | $0.694(\pm 0.075)$ | $0.488(\pm 0.09)$ | ${\bf 0.719(\pm 0.04)}$ | $0.654(\pm 0.052)$
12 $\rightarrow$ 5 | $0.698(\pm 0.081)$ | $0.771(\pm 0.014)$ | $0.771(\pm 0.014)$ | $0.768(\pm 0.008)$ | ${\it 0.788(\pm 0.022)}$ | $0.776(\pm 0.026)$ | ${\bf 0.776(\pm 0.026)}$ | $0.762(\pm 0.022)$ | $0.811(\pm 0.013)$
16 $\rightarrow$ 1 | $0.664(\pm 0.068)$ | ${\it 0.702(\pm 0.02)}$ | $0.702(\pm 0.02)$ | $0.698(\pm 0.025)$ | $0.616(\pm 0.017)$ | $0.628(\pm 0.017)$ | $0.628(\pm 0.017)$ | ${\bf 0.682(\pm 0.008)}$ | $0.729(\pm 0.025)$
7 $\rightarrow$ 18 | $0.712(\pm 0.024)$ | $0.734(\pm 0.021)$ | $0.734(\pm 0.021)$ | ${\it 0.736(\pm 0.012)}$ | $0.678(\pm 0.006)$ | $0.729(\pm 0.025)$ | $0.734(\pm 0.028)$ | ${\bf 0.74(\pm 0.008)}$ | $0.755(\pm 0.02)$
9 $\rightarrow$ 14 | $0.741(\pm 0.031)$ | $0.832(\pm 0.008)$ | $0.832(\pm 0.008)$ | ${\it 0.833(\pm 0.01)}$ | $0.82(\pm 0.024)$ | $0.802(\pm 0.025)$ | $0.764(\pm 0.07)$ | ${\bf 0.832(\pm 0.01)}$ | $0.814(\pm 0.01)$
Avg. | $0.676(\pm 0.047)$ | $0.719(\pm 0.026)$ | $0.719(\pm 0.026)$ | $0.718(\pm 0.025)$ | ${\it 0.724(\pm 0.024)}$ | $0.726(\pm 0.034)$ | $0.678(\pm 0.046)$ | ${\bf 0.747(\pm 0.018)}$ | $0.753(\pm 0.024)$

| AdvSKM
---|---
|  | Heuristic | Theoretical error guarantees |
Task | SO | TMV | TMR | TCR | SOR | IWV | DEV | IWA (ours) | TB
0 $\rightarrow$ 11 | $0.611(\pm 0.005)$ | $0.59(\pm 0.02)$ | $0.59(\pm 0.02)$ | $0.589(\pm 0.025)$ | ${\it 0.706(\pm 0.043)}$ | $0.645(\pm 0.038)$ | $0.595(\pm 0.035)$ | ${\bf 0.664(\pm 0.05)}$ | $0.611(\pm 0.043)$
12 $\rightarrow$ 5 | $0.723(\pm 0.061)$ | $0.75(\pm 0.02)$ | $0.75(\pm 0.02)$ | $0.747(\pm 0.011)$ | ${\it 0.777(\pm 0.024)}$ | $0.753(\pm 0.015)$ | $0.753(\pm 0.015)$ | ${\bf 0.754(\pm 0.027)}$ | $0.777(\pm 0.051)$
16 $\rightarrow$ 1 | $0.558(\pm 0.035)$ | $0.667(\pm 0.037)$ | $0.667(\pm 0.037)$ | ${\it 0.671(\pm 0.035)}$ | $0.619(\pm 0.043)$ | $0.65(\pm 0.076)$ | $0.65(\pm 0.076)$ | ${\bf 0.658(\pm 0.03)}$ | $0.73(\pm 0.033)$
7 $\rightarrow$ 18 | $0.651(\pm 0.053)$ | ${\it 0.72(\pm 0.022)}$ | $0.72(\pm 0.022)$ | $0.72(\pm 0.018)$ | $0.669(\pm 0.018)$ | $0.706(\pm 0.041)$ | $0.681(\pm 0.023)$ | ${\bf 0.707(\pm 0.004)}$ | $0.723(\pm 0.033)$
9 $\rightarrow$ 14 | $0.78(\pm 0.027)$ | ${\it 0.835(\pm 0.016)}$ | $0.835(\pm 0.016)$ | $0.835(\pm 0.016)$ | $0.819(\pm 0.032)$ | $0.76(\pm 0.059)$ | $0.78(\pm 0.027)$ | ${\bf 0.824(\pm 0.014)}$ | $0.789(\pm 0.016)$
Avg. | $0.665(\pm 0.036)$ | $0.712(\pm 0.023)$ | $0.712(\pm 0.023)$ | $0.712(\pm 0.021)$ | ${\it 0.718(\pm 0.032)}$ | $0.703(\pm 0.046)$ | $0.692(\pm 0.035)$ | ${\bf 0.722(\pm 0.025)}$ | $0.726(\pm 0.035)$

| DIRT
---|---
|  | Heuristic | Theoretical error guarantees |
Task | SO | TMV | TMR | TCR | SOR | IWV | DEV | IWA (ours) | TB
0 $\rightarrow$ 11 | $0.582(\pm 0.041)$ | $0.493(\pm 0.106)$ | $0.493(\pm 0.106)$ | $0.509(\pm 0.094)$ | ${\it 0.625(\pm 0.031)}$ | $0.447(\pm 0.123)$ | $0.487(\pm 0.188)$ | ${\bf 0.54(\pm 0.043)}$ | $0.582(\pm 0.031)$
12 $\rightarrow$ 5 | $0.712(\pm 0.08)$ | $0.835(\pm 0.015)$ | $0.835(\pm 0.015)$ | $0.832(\pm 0.017)$ | ${\it 0.87(\pm 0.019)}$ | $0.805(\pm 0.061)$ | $0.789(\pm 0.105)$ | ${\bf 0.829(\pm 0.02)}$ | $0.857(\pm 0.019)$
16 $\rightarrow$ 1 | $0.526(\pm 0.162)$ | ${\it 0.757(\pm 0.025)}$ | $0.757(\pm 0.025)$ | $0.755(\pm 0.021)$ | $0.671(\pm 0.071)$ | $0.618(\pm 0.124)$ | $0.618(\pm 0.124)$ | ${\bf 0.746(\pm 0.03)}$ | $0.797(\pm 0.02)$
7 $\rightarrow$ 18 | $0.749(\pm 0.041)$ | ${\it 0.777(\pm 0.018)}$ | $0.777(\pm 0.018)$ | $0.775(\pm 0.005)$ | $0.717(\pm 0.044)$ | $0.74(\pm 0.069)$ | $0.719(\pm 0.072)$ | ${\bf 0.762(\pm 0.0)}$ | $0.789(\pm 0.02)$
9 $\rightarrow$ 14 | $0.711(\pm 0.098)$ | $0.862(\pm 0.016)$ | $0.862(\pm 0.016)$ | ${\it 0.871(\pm 0.014)}$ | $0.826(\pm 0.027)$ | $0.786(\pm 0.071)$ | $0.818(\pm 0.045)$ | ${\bf 0.868(\pm 0.012)}$ | $0.874(\pm 0.022)$
Avg. | $0.656(\pm 0.084)$ | $0.745(\pm 0.036)$ | $0.745(\pm 0.036)$ | ${\it 0.748(\pm 0.03)}$ | $0.742(\pm 0.039)$ | $0.679(\pm 0.09)$ | $0.686(\pm 0.107)$ | ${\bf 0.749(\pm 0.021)}$ | $0.78(\pm 0.023)$

| DDC
---|---
|  | Heuristic | Theoretical error guarantees |
Task | SO | TMV | TMR | TCR | SOR | IWV | DEV | IWA (ours) | TB
0 $\rightarrow$ 11 | $0.546(\pm 0.033)$ | $0.603(\pm 0.029)$ | $0.603(\pm 0.029)$ | $0.598(\pm 0.027)$ | ${\it 0.658(\pm 0.06)}$ | $0.629(\pm 0.059)$ | $0.492(\pm 0.032)$ | ${\bf 0.645(\pm 0.095)}$ | $0.641(\pm 0.06)$
12 $\rightarrow$ 5 | $0.695(\pm 0.075)$ | $0.751(\pm 0.01)$ | $0.751(\pm 0.01)$ | $0.749(\pm 0.012)$ | ${\it 0.779(\pm 0.029)}$ | $0.716(\pm 0.046)$ | $0.716(\pm 0.046)$ | ${\bf 0.755(\pm 0.015)}$ | $0.783(\pm 0.013)$
16 $\rightarrow$ 1 | $0.551(\pm 0.091)$ | ${\it 0.683(\pm 0.013)}$ | $0.683(\pm 0.013)$ | $0.672(\pm 0.005)$ | $0.56(\pm 0.028)$ | $0.618(\pm 0.021)$ | $0.623(\pm 0.012)$ | ${\bf 0.666(\pm 0.017)}$ | $0.728(\pm 0.051)$
7 $\rightarrow$ 18 | $0.699(\pm 0.022)$ | ${\it 0.729(\pm 0.038)}$ | $0.729(\pm 0.038)$ | $0.717(\pm 0.018)$ | $0.674(\pm 0.009)$ | $0.724(\pm 0.029)$ | $0.712(\pm 0.036)$ | ${\bf 0.733(\pm 0.013)}$ | $0.743(\pm 0.033)$
9 $\rightarrow$ 14 | $0.737(\pm 0.035)$ | ${\it 0.84(\pm 0.014)}$ | $0.84(\pm 0.014)$ | $0.827(\pm 0.025)$ | $0.802(\pm 0.014)$ | $0.784(\pm 0.01)$ | $0.788(\pm 0.042)$ | ${\bf 0.823(\pm 0.016)}$ | $0.792(\pm 0.014)$
Avg. | $0.646(\pm 0.051)$ | ${\it 0.721(\pm 0.021)}$ | $0.721(\pm 0.021)$ | $0.712(\pm 0.018)$ | $0.695(\pm 0.028)$ | $0.694(\pm 0.033)$ | $0.666(\pm 0.034)$ | ${\bf 0.724(\pm 0.031)}$ | $0.737(\pm 0.034)$

| CMD
---|---
|  | Heuristic | Theoretical error guarantees |
Task | SO | TMV | TMR | TCR | SOR | IWV | DEV | IWA (ours) | TB
0 $\rightarrow$ 11 | $0.536(\pm 0.041)$ | $0.564(\pm 0.01)$ | $0.564(\pm 0.01)$ | $0.551(\pm 0.027)$ | ${\it 0.655(\pm 0.079)}$ | ${\bf 0.607(\pm 0.087)}$ | $0.505(\pm 0.016)$ | $0.581(\pm 0.009)$ | $0.611(\pm 0.079)$
12 $\rightarrow$ 5 | $0.751(\pm 0.032)$ | ${\it 0.805(\pm 0.012)}$ | $0.805(\pm 0.012)$ | $0.79(\pm 0.016)$ | $0.798(\pm 0.016)$ | $0.784(\pm 0.03)$ | $0.629(\pm 0.044)$ | ${\bf 0.793(\pm 0.014)}$ | $0.835(\pm 0.02)$
16 $\rightarrow$ 1 | $0.557(\pm 0.099)$ | ${\it 0.747(\pm 0.011)}$ | $0.747(\pm 0.011)$ | $0.701(\pm 0.034)$ | $0.624(\pm 0.018)$ | $0.678(\pm 0.005)$ | $0.665(\pm 0.018)$ | ${\bf 0.69(\pm 0.015)}$ | $0.749(\pm 0.019)$
7 $\rightarrow$ 18 | $0.681(\pm 0.047)$ | $0.715(\pm 0.017)$ | $0.715(\pm 0.017)$ | ${\it 0.727(\pm 0.004)}$ | $0.669(\pm 0.019)$ | ${\bf 0.741(\pm 0.005)}$ | $0.728(\pm 0.025)$ | $0.738(\pm 0.004)$ | $0.75(\pm 0.026)$
9 $\rightarrow$ 14 | $0.74(\pm 0.07)$ | ${\it 0.85(\pm 0.008)}$ | $0.85(\pm 0.008)$ | $0.848(\pm 0.014)$ | $0.797(\pm 0.021)$ | $0.772(\pm 0.064)$ | $0.672(\pm 0.229)$ | ${\bf 0.841(\pm 0.006)}$ | $0.841(\pm 0.008)$
Avg. | $0.653(\pm 0.058)$ | ${\it 0.736(\pm 0.012)}$ | $0.736(\pm 0.012)$ | $0.723(\pm 0.019)$ | $0.709(\pm 0.031)$ | $0.716(\pm 0.038)$ | $0.64(\pm 0.066)$ | ${\bf 0.729(\pm 0.01)}$ | $0.757(\pm 0.03)$

| MMDA
---|---
|  | Heuristic | Theoretical error guarantees |
Task | SO | TMV | TMR | TCR | SOR | IWV | DEV | IWA (ours) | TB
0 $\rightarrow$ 11 | $0.538(\pm 0.032)$ | $0.52(\pm 0.01)$ | $0.52(\pm 0.01)$ | $0.523(\pm 0.007)$ | ${\it 0.654(\pm 0.025)}$ | $0.596(\pm 0.086)$ | $0.405(\pm 0.099)$ | ${\bf 0.612(\pm 0.037)}$ | $0.615(\pm 0.025)$
12 $\rightarrow$ 5 | $0.749(\pm 0.034)$ | $0.797(\pm 0.016)$ | $0.797(\pm 0.016)$ | $0.79(\pm 0.025)$ | ${\it 0.798(\pm 0.006)}$ | $0.698(\pm 0.079)$ | $0.747(\pm 0.076)$ | ${\bf 0.793(\pm 0.01)}$ | $0.823(\pm 0.025)$
16 $\rightarrow$ 1 | $0.544(\pm 0.116)$ | ${\it 0.705(\pm 0.015)}$ | $0.705(\pm 0.015)$ | $0.7(\pm 0.022)$ | $0.645(\pm 0.032)$ | ${\bf 0.703(\pm 0.02)}$ | $0.692(\pm 0.008)$ | $0.7(\pm 0.014)$ | $0.739(\pm 0.061)$
7 $\rightarrow$ 18 | $0.678(\pm 0.046)$ | ${\it 0.773(\pm 0.01)}$ | $0.773(\pm 0.01)$ | $0.762(\pm 0.0)$ | $0.68(\pm 0.051)$ | $0.729(\pm 0.094)$ | $0.702(\pm 0.082)$ | ${\bf 0.772(\pm 0.005)}$ | $0.797(\pm 0.004)$
9 $\rightarrow$ 14 | $0.742(\pm 0.071)$ | ${\it 0.84(\pm 0.029)}$ | $0.84(\pm 0.029)$ | $0.839(\pm 0.027)$ | $0.793(\pm 0.014)$ | $0.792(\pm 0.073)$ | $0.755(\pm 0.051)$ | ${\bf 0.85(\pm 0.012)}$ | $0.835(\pm 0.012)$
Avg. | $0.65(\pm 0.06)$ | ${\it 0.727(\pm 0.016)}$ | $0.727(\pm 0.016)$ | $0.723(\pm 0.016)$ | $0.714(\pm 0.026)$ | $0.704(\pm 0.07)$ | $0.66(\pm 0.063)$ | ${\bf 0.745(\pm 0.016)}$ | $0.762(\pm 0.025)$

Table 22: Mean and standard deviation (after $\pm$) of target classification
accuracy on Sleep-EDF (Part 2) over $3$ repetitions with different random
initialization of model weights.

| CoDATS
---|---
|  | Heuristic | Theoretical error guarantees |
Task | SO | TMV | TMR | TCR | SOR | IWV | DEV | IWA (ours) | TB
0 $\rightarrow$ 11 | $0.568(\pm 0.027)$ | $0.565(\pm 0.118)$ | $0.565(\pm 0.118)$ | $0.556(\pm 0.107)$ | ${\it 0.625(\pm 0.023)}$ | $0.539(\pm 0.155)$ | $0.564(\pm 0.008)$ | ${\bf 0.602(\pm 0.027)}$ | $0.6(\pm 0.023)$
12 $\rightarrow$ 5 | $0.682(\pm 0.043)$ | $0.812(\pm 0.014)$ | $0.812(\pm 0.014)$ | $0.805(\pm 0.014)$ | ${\it 0.827(\pm 0.012)}$ | $0.75(\pm 0.024)$ | $0.728(\pm 0.018)$ | ${\bf 0.809(\pm 0.007)}$ | $0.798(\pm 0.012)$
16 $\rightarrow$ 1 | $0.574(\pm 0.026)$ | ${\it 0.732(\pm 0.016)}$ | $0.732(\pm 0.016)$ | $0.729(\pm 0.007)$ | $0.642(\pm 0.042)$ | $0.633(\pm 0.066)$ | $0.676(\pm 0.031)$ | ${\bf 0.729(\pm 0.004)}$ | $0.735(\pm 0.082)$
7 $\rightarrow$ 18 | $0.759(\pm 0.039)$ | $0.749(\pm 0.023)$ | $0.749(\pm 0.023)$ | ${\it 0.75(\pm 0.02)}$ | $0.715(\pm 0.014)$ | $0.724(\pm 0.008)$ | $0.717(\pm 0.092)$ | ${\bf 0.742(\pm 0.01)}$ | $0.771(\pm 0.02)$
9 $\rightarrow$ 14 | $0.779(\pm 0.038)$ | $0.837(\pm 0.013)$ | $0.837(\pm 0.013)$ | ${\it 0.839(\pm 0.008)}$ | $0.805(\pm 0.01)$ | $0.771(\pm 0.026)$ | $0.763(\pm 0.006)$ | ${\bf 0.84(\pm 0.014)}$ | $0.811(\pm 0.014)$
Avg. | $0.672(\pm 0.035)$ | ${\it 0.739(\pm 0.037)}$ | $0.739(\pm 0.037)$ | $0.736(\pm 0.031)$ | $0.723(\pm 0.02)$ | $0.683(\pm 0.056)$ | $0.69(\pm 0.031)$ | ${\bf 0.744(\pm 0.012)}$ | $0.743(\pm 0.03)$

| Deep-Coral
---|---
|  | Heuristic | Theoretical error guarantees |
Task | SO | TMV | TMR | TCR | SOR | IWV | DEV | IWA (ours) | TB
0 $\rightarrow$ 11 | $0.547(\pm 0.032)$ | $0.586(\pm 0.028)$ | $0.586(\pm 0.028)$ | $0.6(\pm 0.029)$ | ${\it 0.652(\pm 0.058)}$ | ${\bf 0.629(\pm 0.063)}$ | $0.569(\pm 0.11)$ | $0.592(\pm 0.028)$ | $0.637(\pm 0.058)$
12 $\rightarrow$ 5 | $0.694(\pm 0.084)$ | $0.75(\pm 0.02)$ | $0.75(\pm 0.02)$ | $0.745(\pm 0.016)$ | ${\it 0.781(\pm 0.028)}$ | $0.758(\pm 0.036)$ | ${\bf 0.758(\pm 0.036)}$ | $0.755(\pm 0.018)$ | $0.776(\pm 0.028)$
16 $\rightarrow$ 1 | $0.545(\pm 0.097)$ | ${\it 0.68(\pm 0.015)}$ | $0.68(\pm 0.015)$ | $0.671(\pm 0.007)$ | $0.564(\pm 0.034)$ | $0.605(\pm 0.018)$ | $0.553(\pm 0.104)$ | ${\bf 0.662(\pm 0.017)}$ | $0.728(\pm 0.036)$
7 $\rightarrow$ 18 | $0.698(\pm 0.022)$ | ${\it 0.73(\pm 0.042)}$ | $0.73(\pm 0.042)$ | $0.716(\pm 0.02)$ | $0.673(\pm 0.006)$ | $0.723(\pm 0.027)$ | $0.711(\pm 0.034)$ | ${\bf 0.733(\pm 0.013)}$ | $0.741(\pm 0.016)$
9 $\rightarrow$ 14 | $0.733(\pm 0.047)$ | ${\it 0.836(\pm 0.016)}$ | $0.836(\pm 0.016)$ | $0.826(\pm 0.02)$ | $0.802(\pm 0.018)$ | $0.786(\pm 0.014)$ | $0.784(\pm 0.043)$ | ${\bf 0.82(\pm 0.02)}$ | $0.792(\pm 0.016)$
Avg. | $0.643(\pm 0.056)$ | ${\it 0.717(\pm 0.024)}$ | $0.717(\pm 0.024)$ | $0.712(\pm 0.018)$ | $0.694(\pm 0.029)$ | $0.7(\pm 0.031)$ | $0.675(\pm 0.065)$ | ${\bf 0.713(\pm 0.019)}$ | $0.735(\pm 0.031)$

| CDAN
---|---
|  | Heuristic | Theoretical error guarantees |
Task | SO | TMV | TMR | TCR | SOR | IWV | DEV | IWA (ours) | TB
0 $\rightarrow$ 11 | $0.553(\pm 0.024)$ | $0.499(\pm 0.065)$ | $0.499(\pm 0.065)$ | $0.507(\pm 0.079)$ | ${\it 0.643(\pm 0.053)}$ | $0.529(\pm 0.111)$ | $0.342(\pm 0.024)$ | ${\bf 0.565(\pm 0.078)}$ | $0.553(\pm 0.053)$
12 $\rightarrow$ 5 | $0.658(\pm 0.101)$ | ${\it 0.844(\pm 0.01)}$ | $0.844(\pm 0.01)$ | $0.84(\pm 0.007)$ | $0.829(\pm 0.01)$ | $0.792(\pm 0.06)$ | $0.671(\pm 0.055)$ | ${\bf 0.835(\pm 0.002)}$ | $0.85(\pm 0.016)$
16 $\rightarrow$ 1 | $0.699(\pm 0.077)$ | ${\it 0.729(\pm 0.023)}$ | $0.729(\pm 0.023)$ | $0.726(\pm 0.028)$ | $0.659(\pm 0.05)$ | $0.626(\pm 0.117)$ | $0.682(\pm 0.029)$ | ${\bf 0.706(\pm 0.017)}$ | $0.764(\pm 0.084)$
7 $\rightarrow$ 18 | $0.647(\pm 0.045)$ | $0.758(\pm 0.017)$ | $0.758(\pm 0.017)$ | ${\it 0.76(\pm 0.016)}$ | $0.704(\pm 0.005)$ | $0.73(\pm 0.004)$ | $0.754(\pm 0.041)$ | ${\bf 0.773(\pm 0.012)}$ | $0.794(\pm 0.035)$
9 $\rightarrow$ 14 | $0.703(\pm 0.041)$ | ${\it 0.865(\pm 0.018)}$ | $0.865(\pm 0.018)$ | $0.862(\pm 0.028)$ | $0.806(\pm 0.032)$ | $0.81(\pm 0.053)$ | $0.759(\pm 0.041)$ | ${\bf 0.862(\pm 0.018)}$ | $0.832(\pm 0.018)$
Avg. | $0.652(\pm 0.058)$ | $0.739(\pm 0.027)$ | $0.739(\pm 0.027)$ | ${\it 0.739(\pm 0.032)}$ | $0.728(\pm 0.03)$ | $0.697(\pm 0.069)$ | $0.642(\pm 0.038)$ | ${\bf 0.748(\pm 0.025)}$ | $0.759(\pm 0.041)$

| DANN
---|---
|  | Heuristic | Theoretical error guarantees |
Task | SO | TMV | TMR | TCR | SOR | IWV | DEV | IWA (ours) | TB
0 $\rightarrow$ 11 | $0.551(\pm 0.018)$ | $0.602(\pm 0.058)$ | $0.602(\pm 0.058)$ | $0.602(\pm 0.052)$ | ${\it 0.672(\pm 0.008)}$ | $0.594(\pm 0.081)$ | $0.495(\pm 0.114)$ | ${\bf 0.622(\pm 0.04)}$ | $0.574(\pm 0.008)$
12 $\rightarrow$ 5 | $0.645(\pm 0.075)$ | ${\it 0.801(\pm 0.014)}$ | $0.801(\pm 0.014)$ | $0.792(\pm 0.014)$ | $0.798(\pm 0.018)$ | $0.686(\pm 0.051)$ | $0.686(\pm 0.051)$ | ${\bf 0.784(\pm 0.02)}$ | $0.819(\pm 0.054)$
16 $\rightarrow$ 1 | $0.57(\pm 0.136)$ | ${\it 0.676(\pm 0.002)}$ | $0.676(\pm 0.002)$ | $0.67(\pm 0.008)$ | $0.593(\pm 0.025)$ | $0.651(\pm 0.055)$ | $0.651(\pm 0.055)$ | ${\bf 0.661(\pm 0.008)}$ | $0.747(\pm 0.049)$
7 $\rightarrow$ 18 | $0.695(\pm 0.037)$ | ${\it 0.725(\pm 0.006)}$ | $0.725(\pm 0.006)$ | $0.725(\pm 0.014)$ | $0.686(\pm 0.013)$ | $0.703(\pm 0.034)$ | $0.703(\pm 0.034)$ | ${\bf 0.732(\pm 0.011)}$ | $0.738(\pm 0.018)$
9 $\rightarrow$ 14 | $0.746(\pm 0.021)$ | $0.814(\pm 0.002)$ | $0.814(\pm 0.002)$ | $0.815(\pm 0.015)$ | ${\it 0.822(\pm 0.012)}$ | $0.799(\pm 0.039)$ | $0.686(\pm 0.085)$ | ${\bf 0.822(\pm 0.01)}$ | $0.81(\pm 0.01)$
Avg. | $0.641(\pm 0.057)$ | ${\it 0.723(\pm 0.016)}$ | $0.723(\pm 0.016)$ | $0.721(\pm 0.02)$ | $0.714(\pm 0.015)$ | $0.687(\pm 0.052)$ | $0.644(\pm 0.068)$ | ${\bf 0.724(\pm 0.018)}$ | $0.738(\pm 0.028)$

| DSAN
---|---
|  | Heuristic | Theoretical error guarantees |
Task | SO | TMV | TMR | TCR | SOR | IWV | DEV | IWA (ours) | TB
0 $\rightarrow$ 11 | $0.547(\pm 0.012)$ | $0.539(\pm 0.035)$ | $0.539(\pm 0.035)$ | $0.527(\pm 0.063)$ | ${\it 0.668(\pm 0.024)}$ | $0.59(\pm 0.055)$ | $0.311(\pm 0.026)$ | ${\bf 0.629(\pm 0.051)}$ | $0.603(\pm 0.024)$
12 $\rightarrow$ 5 | $0.717(\pm 0.086)$ | $0.84(\pm 0.02)$ | $0.84(\pm 0.02)$ | ${\it 0.841(\pm 0.022)}$ | $0.837(\pm 0.026)$ | $0.822(\pm 0.028)$ | $0.699(\pm 0.061)$ | ${\bf 0.842(\pm 0.018)}$ | $0.855(\pm 0.007)$
16 $\rightarrow$ 1 | $0.697(\pm 0.06)$ | ${\it 0.755(\pm 0.031)}$ | $0.755(\pm 0.031)$ | $0.722(\pm 0.02)$ | $0.612(\pm 0.026)$ | $0.617(\pm 0.118)$ | $0.617(\pm 0.118)$ | ${\bf 0.721(\pm 0.014)}$ | $0.742(\pm 0.031)$
7 $\rightarrow$ 18 | $0.684(\pm 0.048)$ | $0.734(\pm 0.029)$ | $0.734(\pm 0.029)$ | ${\it 0.741(\pm 0.011)}$ | $0.71(\pm 0.067)$ | $0.749(\pm 0.02)$ | $0.745(\pm 0.025)$ | ${\bf 0.764(\pm 0.002)}$ | $0.768(\pm 0.059)$
9 $\rightarrow$ 14 | $0.62(\pm 0.04)$ | ${\it 0.832(\pm 0.024)}$ | $0.832(\pm 0.024)$ | $0.827(\pm 0.018)$ | $0.815(\pm 0.018)$ | $0.784(\pm 0.046)$ | $0.576(\pm 0.154)$ | ${\bf 0.828(\pm 0.021)}$ | $0.823(\pm 0.024)$
Avg. | $0.653(\pm 0.049)$ | ${\it 0.74(\pm 0.028)}$ | $0.74(\pm 0.028)$ | $0.732(\pm 0.027)$ | $0.728(\pm 0.032)$ | $0.712(\pm 0.053)$ | $0.589(\pm 0.077)$ | ${\bf 0.757(\pm 0.021)}$ | $0.758(\pm 0.029)$

Table 23: Mean and standard deviation (after $\pm$) of target classification
accuracy on UCI-HAR (Part 1) over $3$ repetitions with different random
initialization of model weights.

| HoMM
---|---
|  | Heuristic | Theoretical error guarantees |
Task | SO | TMV | TMR | TCR | SOR | IWV | DEV | IWA (ours) | TB
12 $\rightarrow$ 16 | $0.674(\pm 0.012)$ | $0.667(\pm 0.036)$ | $0.667(\pm 0.036)$ | $0.667(\pm 0.036)$ | ${\it 0.688(\pm 0.0)}$ | $0.674(\pm 0.012)$ | $0.674(\pm 0.012)$ | ${\bf 0.688(\pm 0.0)}$ | $0.715(\pm 0.012)$
2 $\rightarrow$ 11 | $1.0(\pm 0.0)$ | ${\it 1.0(\pm 0.0)}$ | $1.0(\pm 0.0)$ | $1.0(\pm 0.0)$ | $0.938(\pm 0.031)$ | $0.99(\pm 0.018)$ | $1.0(\pm 0.0)$ | ${\bf 1.0(\pm 0.0)}$ | $1.0(\pm 0.0)$
6 $\rightarrow$ 23 | $0.854(\pm 0.036)$ | ${\it 0.896(\pm 0.0)}$ | $0.896(\pm 0.0)$ | $0.896(\pm 0.0)$ | $0.889(\pm 0.012)$ | $0.854(\pm 0.036)$ | $0.854(\pm 0.036)$ | ${\bf 0.903(\pm 0.012)}$ | $0.938(\pm 0.0)$
7 $\rightarrow$ 13 | $0.889(\pm 0.052)$ | ${\it 0.91(\pm 0.024)}$ | $0.91(\pm 0.024)$ | $0.91(\pm 0.024)$ | $0.889(\pm 0.052)$ | $0.889(\pm 0.052)$ | $0.889(\pm 0.052)$ | ${\bf 0.91(\pm 0.024)}$ | $0.944(\pm 0.024)$
9 $\rightarrow$ 18 | $0.493(\pm 0.032)$ | ${\it 0.618(\pm 0.105)}$ | $0.618(\pm 0.105)$ | $0.618(\pm 0.105)$ | $0.514(\pm 0.188)$ | ${\bf 0.639(\pm 0.043)}$ | $0.583(\pm 0.116)$ | $0.632(\pm 0.079)$ | $0.715(\pm 0.024)$
Avg. | $0.782(\pm 0.026)$ | ${\it 0.818(\pm 0.033)}$ | $0.818(\pm 0.033)$ | $0.818(\pm 0.033)$ | $0.783(\pm 0.057)$ | $0.809(\pm 0.032)$ | $0.8(\pm 0.043)$ | ${\bf 0.826(\pm 0.023)}$ | $0.862(\pm 0.012)$

| AdvSKM
---|---
|  | Heuristic | Theoretical error guarantees |
Task | SO | TMV | TMR | TCR | SOR | IWV | DEV | IWA (ours) | TB
12 $\rightarrow$ 16 | $0.59(\pm 0.103)$ | $0.681(\pm 0.012)$ | $0.681(\pm 0.012)$ | $0.681(\pm 0.012)$ | ${\it 0.708(\pm 0.021)}$ | $0.59(\pm 0.103)$ | $0.59(\pm 0.103)$ | ${\bf 0.688(\pm 0.0)}$ | $0.722(\pm 0.012)$
2 $\rightarrow$ 11 | $0.979(\pm 0.018)$ | ${\it 1.0(\pm 0.0)}$ | $1.0(\pm 0.0)$ | $1.0(\pm 0.0)$ | $0.854(\pm 0.065)$ | $0.896(\pm 0.1)$ | $0.917(\pm 0.118)$ | ${\bf 1.0(\pm 0.0)}$ | $1.0(\pm 0.0)$
6 $\rightarrow$ 23 | $0.826(\pm 0.084)$ | ${\it 0.896(\pm 0.0)}$ | $0.896(\pm 0.0)$ | $0.896(\pm 0.0)$ | $0.889(\pm 0.012)$ | $0.826(\pm 0.084)$ | $0.826(\pm 0.084)$ | ${\bf 0.896(\pm 0.0)}$ | $0.896(\pm 0.0)$
7 $\rightarrow$ 13 | $0.833(\pm 0.036)$ | $0.91(\pm 0.024)$ | $0.91(\pm 0.024)$ | ${\it 0.917(\pm 0.036)}$ | $0.896(\pm 0.036)$ | $0.833(\pm 0.036)$ | $0.833(\pm 0.036)$ | ${\bf 0.903(\pm 0.024)}$ | $0.924(\pm 0.012)$
9 $\rightarrow$ 18 | $0.389(\pm 0.151)$ | $0.514(\pm 0.079)$ | $0.514(\pm 0.079)$ | ${\it 0.556(\pm 0.064)}$ | $0.493(\pm 0.064)$ | $0.389(\pm 0.151)$ | $0.389(\pm 0.151)$ | ${\bf 0.514(\pm 0.024)}$ | $0.597(\pm 0.052)$
Avg. | $0.724(\pm 0.078)$ | $0.8(\pm 0.023)$ | $0.8(\pm 0.023)$ | ${\it 0.81(\pm 0.022)}$ | $0.768(\pm 0.04)$ | $0.707(\pm 0.095)$ | $0.711(\pm 0.098)$ | ${\bf 0.8(\pm 0.01)}$ | $0.828(\pm 0.015)$

| DIRT
---|---
|  | Heuristic | Theoretical error guarantees |
Task | SO | TMV | TMR | TCR | SOR | IWV | DEV | IWA (ours) | TB
12 $\rightarrow$ 16 | $0.667(\pm 0.075)$ | ${\it 0.778(\pm 0.012)}$ | $0.778(\pm 0.012)$ | $0.75(\pm 0.0)$ | $0.736(\pm 0.012)$ | $0.667(\pm 0.075)$ | $0.667(\pm 0.075)$ | ${\bf 0.764(\pm 0.032)}$ | $0.819(\pm 0.064)$
2 $\rightarrow$ 11 | $1.0(\pm 0.0)$ | ${\it 1.0(\pm 0.0)}$ | $1.0(\pm 0.0)$ | $1.0(\pm 0.0)$ | $0.854(\pm 0.079)$ | $1.0(\pm 0.0)$ | $1.0(\pm 0.0)$ | ${\bf 1.0(\pm 0.0)}$ | $1.0(\pm 0.0)$
6 $\rightarrow$ 23 | $0.903(\pm 0.084)$ | ${\it 0.938(\pm 0.0)}$ | $0.938(\pm 0.0)$ | $0.938(\pm 0.0)$ | $0.847(\pm 0.06)$ | $0.847(\pm 0.06)$ | $0.847(\pm 0.06)$ | ${\bf 0.938(\pm 0.0)}$ | $0.938(\pm 0.0)$
7 $\rightarrow$ 13 | $0.833(\pm 0.0)$ | ${\it 0.958(\pm 0.0)}$ | $0.958(\pm 0.0)$ | $0.958(\pm 0.0)$ | $0.924(\pm 0.06)$ | $0.854(\pm 0.036)$ | $0.861(\pm 0.032)$ | ${\bf 0.958(\pm 0.0)}$ | $0.958(\pm 0.0)$
9 $\rightarrow$ 18 | $0.514(\pm 0.024)$ | ${\it 0.861(\pm 0.122)}$ | $0.861(\pm 0.122)$ | $0.806(\pm 0.032)$ | $0.417(\pm 0.075)$ | $0.667(\pm 0.225)$ | $0.667(\pm 0.225)$ | ${\bf 0.84(\pm 0.048)}$ | $0.986(\pm 0.012)$
Avg. | $0.783(\pm 0.037)$ | ${\it 0.907(\pm 0.027)}$ | $0.907(\pm 0.027)$ | $0.89(\pm 0.006)$ | $0.756(\pm 0.057)$ | $0.807(\pm 0.079)$ | $0.808(\pm 0.078)$ | ${\bf 0.9(\pm 0.016)}$ | $0.94(\pm 0.015)$

| DDC
---|---
|  | Heuristic | Theoretical error guarantees |
Task | SO | TMV | TMR | TCR | SOR | IWV | DEV | IWA (ours) | TB
12 $\rightarrow$ 16 | $0.681(\pm 0.024)$ | ${\it 0.681(\pm 0.012)}$ | $0.681(\pm 0.012)$ | $0.674(\pm 0.012)$ | $0.674(\pm 0.012)$ | $0.681(\pm 0.024)$ | $0.604(\pm 0.108)$ | ${\bf 0.681(\pm 0.012)}$ | $0.715(\pm 0.073)$
2 $\rightarrow$ 11 | $1.0(\pm 0.0)$ | ${\it 1.0(\pm 0.0)}$ | $1.0(\pm 0.0)$ | $1.0(\pm 0.0)$ | $0.74(\pm 0.213)$ | $0.74(\pm 0.213)$ | $0.802(\pm 0.266)$ | ${\bf 1.0(\pm 0.0)}$ | $1.0(\pm 0.0)$
6 $\rightarrow$ 23 | $0.889(\pm 0.012)$ | ${\it 0.896(\pm 0.0)}$ | $0.896(\pm 0.0)$ | $0.896(\pm 0.0)$ | $0.882(\pm 0.012)$ | $0.889(\pm 0.012)$ | $0.896(\pm 0.021)$ | ${\bf 0.896(\pm 0.0)}$ | $0.889(\pm 0.0)$
7 $\rightarrow$ 13 | $0.868(\pm 0.012)$ | $0.896(\pm 0.036)$ | $0.896(\pm 0.036)$ | ${\it 0.91(\pm 0.032)}$ | $0.903(\pm 0.024)$ | $0.868(\pm 0.012)$ | $0.868(\pm 0.012)$ | ${\bf 0.903(\pm 0.024)}$ | $0.917(\pm 0.021)$
9 $\rightarrow$ 18 | $0.514(\pm 0.043)$ | $0.562(\pm 0.091)$ | $0.562(\pm 0.091)$ | $0.569(\pm 0.115)$ | ${\it 0.583(\pm 0.165)}$ | $0.444(\pm 0.103)$ | $0.5(\pm 0.127)$ | ${\bf 0.542(\pm 0.091)}$ | $0.59(\pm 0.189)$
Avg. | $0.79(\pm 0.018)$ | $0.807(\pm 0.028)$ | $0.807(\pm 0.028)$ | ${\it 0.81(\pm 0.032)}$ | $0.756(\pm 0.085)$ | $0.724(\pm 0.073)$ | $0.734(\pm 0.107)$ | ${\bf 0.804(\pm 0.025)}$ | $0.822(\pm 0.057)$

| CMD
---|---
|  | Heuristic | Theoretical error guarantees |
Task | SO | TMV | TMR | TCR | SOR | IWV | DEV | IWA (ours) | TB
12 $\rightarrow$ 16 | $0.694(\pm 0.012)$ | ${\it 0.729(\pm 0.0)}$ | $0.729(\pm 0.0)$ | $0.722(\pm 0.012)$ | $0.688(\pm 0.0)$ | $0.694(\pm 0.012)$ | $0.694(\pm 0.012)$ | ${\bf 0.729(\pm 0.0)}$ | $0.75(\pm 0.036)$
2 $\rightarrow$ 11 | $1.0(\pm 0.0)$ | ${\it 1.0(\pm 0.0)}$ | $1.0(\pm 0.0)$ | $1.0(\pm 0.0)$ | $0.771(\pm 0.036)$ | $0.812(\pm 0.272)$ | $0.812(\pm 0.272)$ | ${\bf 1.0(\pm 0.0)}$ | $1.0(\pm 0.0)$
6 $\rightarrow$ 23 | $0.896(\pm 0.042)$ | ${\it 0.938(\pm 0.0)}$ | $0.938(\pm 0.0)$ | $0.931(\pm 0.012)$ | $0.889(\pm 0.012)$ | $0.903(\pm 0.032)$ | $0.896(\pm 0.042)$ | ${\bf 0.938(\pm 0.0)}$ | $0.938(\pm 0.0)$
7 $\rightarrow$ 13 | $0.826(\pm 0.073)$ | ${\it 0.938(\pm 0.0)}$ | $0.938(\pm 0.0)$ | $0.938(\pm 0.0)$ | $0.91(\pm 0.024)$ | $0.826(\pm 0.073)$ | $0.826(\pm 0.073)$ | ${\bf 0.938(\pm 0.0)}$ | $0.944(\pm 0.012)$
9 $\rightarrow$ 18 | $0.521(\pm 0.095)$ | ${\it 0.639(\pm 0.043)}$ | $0.639(\pm 0.043)$ | $0.604(\pm 0.055)$ | $0.396(\pm 0.11)$ | $0.785(\pm 0.146)$ | ${\bf 0.833(\pm 0.163)}$ | $0.604(\pm 0.075)$ | $0.882(\pm 0.079)$
Avg. | $0.788(\pm 0.044)$ | ${\it 0.849(\pm 0.009)}$ | $0.849(\pm 0.009)$ | $0.839(\pm 0.016)$ | $0.731(\pm 0.036)$ | $0.804(\pm 0.107)$ | $0.812(\pm 0.112)$ | ${\bf 0.842(\pm 0.015)}$ | $0.903(\pm 0.025)$

| MMDA
---|---
|  | Heuristic | Theoretical error guarantees |
Task | SO | TMV | TMR | TCR | SOR | IWV | DEV | IWA (ours) | TB
12 $\rightarrow$ 16 | $0.674(\pm 0.012)$ | ${\it 0.694(\pm 0.012)}$ | $0.694(\pm 0.012)$ | $0.688(\pm 0.0)$ | $0.681(\pm 0.012)$ | $0.674(\pm 0.012)$ | $0.674(\pm 0.012)$ | ${\bf 0.688(\pm 0.0)}$ | $0.757(\pm 0.043)$
2 $\rightarrow$ 11 | $1.0(\pm 0.0)$ | ${\it 1.0(\pm 0.0)}$ | $1.0(\pm 0.0)$ | $1.0(\pm 0.0)$ | $0.844(\pm 0.125)$ | $0.927(\pm 0.065)$ | $0.927(\pm 0.065)$ | ${\bf 1.0(\pm 0.0)}$ | $1.0(\pm 0.0)$
6 $\rightarrow$ 23 | $0.847(\pm 0.032)$ | ${\it 0.896(\pm 0.0)}$ | $0.896(\pm 0.0)$ | $0.896(\pm 0.0)$ | $0.847(\pm 0.067)$ | $0.847(\pm 0.032)$ | $0.847(\pm 0.032)$ | ${\bf 0.896(\pm 0.0)}$ | $0.91(\pm 0.024)$
7 $\rightarrow$ 13 | $0.882(\pm 0.043)$ | $0.903(\pm 0.012)$ | $0.903(\pm 0.012)$ | $0.917(\pm 0.021)$ | ${\it 0.924(\pm 0.024)}$ | $0.882(\pm 0.043)$ | $0.882(\pm 0.043)$ | ${\bf 0.931(\pm 0.024)}$ | $0.944(\pm 0.012)$
9 $\rightarrow$ 18 | $0.521(\pm 0.072)$ | ${\it 0.569(\pm 0.139)}$ | $0.569(\pm 0.139)$ | $0.5(\pm 0.104)$ | $0.5(\pm 0.095)$ | ${\bf 0.535(\pm 0.064)}$ | $0.507(\pm 0.024)$ | $0.521(\pm 0.091)$ | $0.688(\pm 0.075)$
Avg. | $0.785(\pm 0.032)$ | ${\it 0.812(\pm 0.033)}$ | $0.812(\pm 0.033)$ | $0.8(\pm 0.025)$ | $0.759(\pm 0.065)$ | $0.773(\pm 0.043)$ | $0.767(\pm 0.035)$ | ${\bf 0.807(\pm 0.023)}$ | $0.86(\pm 0.031)$

Table 24: Mean and standard deviation (after $\pm$) of target classification
accuracy on UCI-HAR (Part 2) over $3$ repetitions with different random
initialization of model weights.

| CoDATS
---|---
|  | Heuristic | Theoretical error guarantees |
Task | SO | TMV | TMR | TCR | SOR | IWV | DEV | IWA (ours) | TB
12 $\rightarrow$ 16 | $0.681(\pm 0.024)$ | ${\it 0.701(\pm 0.024)}$ | $0.701(\pm 0.024)$ | $0.688(\pm 0.0)$ | $0.694(\pm 0.024)$ | $0.681(\pm 0.024)$ | $0.694(\pm 0.024)$ | ${\bf 0.694(\pm 0.012)}$ | $0.708(\pm 0.021)$
2 $\rightarrow$ 11 | $1.0(\pm 0.0)$ | ${\it 1.0(\pm 0.0)}$ | $1.0(\pm 0.0)$ | $1.0(\pm 0.0)$ | $0.865(\pm 0.11)$ | $0.865(\pm 0.1)$ | $0.865(\pm 0.1)$ | ${\bf 1.0(\pm 0.0)}$ | $1.0(\pm 0.0)$
6 $\rightarrow$ 23 | $0.84(\pm 0.032)$ | ${\it 0.889(\pm 0.032)}$ | $0.889(\pm 0.032)$ | $0.889(\pm 0.032)$ | $0.882(\pm 0.064)$ | $0.84(\pm 0.048)$ | $0.896(\pm 0.083)$ | ${\bf 0.924(\pm 0.012)}$ | $0.951(\pm 0.043)$
7 $\rightarrow$ 13 | $0.75(\pm 0.217)$ | ${\it 0.944(\pm 0.012)}$ | $0.944(\pm 0.012)$ | $0.944(\pm 0.012)$ | $0.917(\pm 0.036)$ | $0.854(\pm 0.036)$ | $0.75(\pm 0.217)$ | ${\bf 0.938(\pm 0.0)}$ | $0.951(\pm 0.012)$
9 $\rightarrow$ 18 | $0.528(\pm 0.032)$ | $0.625(\pm 0.062)$ | $0.625(\pm 0.062)$ | ${\it 0.639(\pm 0.043)}$ | $0.569(\pm 0.305)$ | $0.764(\pm 0.12)$ | ${\bf 0.764(\pm 0.12)}$ | $0.674(\pm 0.115)$ | $0.826(\pm 0.012)$
Avg. | $0.76(\pm 0.061)$ | ${\it 0.832(\pm 0.026)}$ | $0.832(\pm 0.026)$ | $0.832(\pm 0.017)$ | $0.785(\pm 0.108)$ | $0.801(\pm 0.066)$ | $0.794(\pm 0.109)$ | ${\bf 0.846(\pm 0.028)}$ | $0.888(\pm 0.018)$

| Deep-Coral
---|---
|  | Heuristic | Theoretical error guarantees |
Task | SO | TMV | TMR | TCR | SOR | IWV | DEV | IWA (ours) | TB
12 $\rightarrow$ 16 | $0.681(\pm 0.012)$ | ${\it 0.681(\pm 0.012)}$ | $0.681(\pm 0.012)$ | $0.674(\pm 0.012)$ | $0.681(\pm 0.012)$ | $0.681(\pm 0.012)$ | $0.639(\pm 0.084)$ | ${\bf 0.688(\pm 0.0)}$ | $0.688(\pm 0.0)$
2 $\rightarrow$ 11 | $0.969(\pm 0.054)$ | ${\it 1.0(\pm 0.0)}$ | $1.0(\pm 0.0)$ | $1.0(\pm 0.0)$ | $0.875(\pm 0.094)$ | $0.875(\pm 0.083)$ | $0.885(\pm 0.095)$ | ${\bf 1.0(\pm 0.0)}$ | $1.0(\pm 0.0)$
6 $\rightarrow$ 23 | $0.826(\pm 0.084)$ | $0.882(\pm 0.012)$ | $0.882(\pm 0.012)$ | $0.889(\pm 0.012)$ | ${\it 0.896(\pm 0.0)}$ | $0.826(\pm 0.084)$ | $0.833(\pm 0.091)$ | ${\bf 0.896(\pm 0.0)}$ | $0.903(\pm 0.043)$
7 $\rightarrow$ 13 | $0.917(\pm 0.036)$ | ${\it 0.91(\pm 0.032)}$ | $0.91(\pm 0.032)$ | $0.91(\pm 0.032)$ | $0.896(\pm 0.021)$ | $0.917(\pm 0.036)$ | ${\bf 0.917(\pm 0.036)}$ | $0.903(\pm 0.024)$ | $0.931(\pm 0.012)$
9 $\rightarrow$ 18 | $0.556(\pm 0.087)$ | $0.528(\pm 0.043)$ | $0.528(\pm 0.043)$ | ${\it 0.569(\pm 0.115)}$ | $0.507(\pm 0.272)$ | $0.542(\pm 0.144)$ | ${\bf 0.59(\pm 0.032)}$ | $0.556(\pm 0.064)$ | $0.59(\pm 0.221)$
Avg. | $0.79(\pm 0.055)$ | $0.8(\pm 0.02)$ | $0.8(\pm 0.02)$ | ${\it 0.808(\pm 0.034)}$ | $0.771(\pm 0.08)$ | $0.768(\pm 0.072)$ | $0.773(\pm 0.068)$ | ${\bf 0.808(\pm 0.018)}$ | $0.822(\pm 0.055)$

| CDAN
---|---
|  | Heuristic | Theoretical error guarantees |
Task | SO | TMV | TMR | TCR | SOR | IWV | DEV | IWA (ours) | TB
12 $\rightarrow$ 16 | $0.674(\pm 0.043)$ | ${\it 0.722(\pm 0.012)}$ | $0.722(\pm 0.012)$ | $0.722(\pm 0.012)$ | $0.694(\pm 0.012)$ | $0.674(\pm 0.043)$ | $0.646(\pm 0.055)$ | ${\bf 0.715(\pm 0.024)}$ | $0.729(\pm 0.036)$
2 $\rightarrow$ 11 | $0.99(\pm 0.018)$ | ${\it 1.0(\pm 0.0)}$ | $1.0(\pm 0.0)$ | $1.0(\pm 0.0)$ | $0.865(\pm 0.065)$ | $0.792(\pm 0.28)$ | $0.802(\pm 0.29)$ | ${\bf 1.0(\pm 0.0)}$ | $1.0(\pm 0.0)$
6 $\rightarrow$ 23 | $0.854(\pm 0.042)$ | ${\it 0.924(\pm 0.024)}$ | $0.924(\pm 0.024)$ | $0.91(\pm 0.024)$ | $0.91(\pm 0.024)$ | $0.847(\pm 0.032)$ | $0.708(\pm 0.295)$ | ${\bf 0.924(\pm 0.024)}$ | $0.924(\pm 0.024)$
7 $\rightarrow$ 13 | $0.826(\pm 0.139)$ | ${\it 0.951(\pm 0.012)}$ | $0.951(\pm 0.012)$ | $0.951(\pm 0.012)$ | $0.944(\pm 0.012)$ | $0.896(\pm 0.021)$ | $0.812(\pm 0.108)$ | ${\bf 0.951(\pm 0.012)}$ | $0.958(\pm 0.0)$
9 $\rightarrow$ 18 | $0.438(\pm 0.055)$ | ${\it 0.618(\pm 0.064)}$ | $0.618(\pm 0.064)$ | $0.618(\pm 0.064)$ | $0.597(\pm 0.098)$ | ${\bf 0.694(\pm 0.126)}$ | $0.465(\pm 0.087)$ | $0.639(\pm 0.048)$ | $0.729(\pm 0.083)$
Avg. | $0.756(\pm 0.059)$ | ${\it 0.843(\pm 0.022)}$ | $0.843(\pm 0.022)$ | $0.84(\pm 0.022)$ | $0.802(\pm 0.042)$ | $0.781(\pm 0.1)$ | $0.687(\pm 0.167)$ | ${\bf 0.846(\pm 0.022)}$ | $0.868(\pm 0.029)$

| DANN
---|---
|  | Heuristic | Theoretical error guarantees |
Task | SO | TMV | TMR | TCR | SOR | IWV | DEV | IWA (ours) | TB
12 $\rightarrow$ 16 | $0.688(\pm 0.021)$ | $0.701(\pm 0.024)$ | $0.701(\pm 0.024)$ | $0.701(\pm 0.024)$ | ${\it 0.715(\pm 0.012)}$ | $0.701(\pm 0.012)$ | $0.701(\pm 0.012)$ | ${\bf 0.729(\pm 0.0)}$ | $0.722(\pm 0.0)$
2 $\rightarrow$ 11 | $1.0(\pm 0.0)$ | ${\it 1.0(\pm 0.0)}$ | $1.0(\pm 0.0)$ | $1.0(\pm 0.0)$ | $0.729(\pm 0.141)$ | $0.76(\pm 0.148)$ | $0.802(\pm 0.203)$ | ${\bf 1.0(\pm 0.0)}$ | $1.0(\pm 0.0)$
6 $\rightarrow$ 23 | $0.882(\pm 0.024)$ | $0.917(\pm 0.021)$ | $0.917(\pm 0.021)$ | ${\it 0.931(\pm 0.012)}$ | $0.889(\pm 0.032)$ | $0.868(\pm 0.024)$ | $0.868(\pm 0.024)$ | ${\bf 0.931(\pm 0.012)}$ | $0.958(\pm 0.036)$
7 $\rightarrow$ 13 | $0.806(\pm 0.127)$ | ${\it 0.944(\pm 0.012)}$ | $0.944(\pm 0.012)$ | $0.944(\pm 0.012)$ | $0.938(\pm 0.021)$ | $0.903(\pm 0.024)$ | $0.944(\pm 0.048)$ | ${\bf 0.944(\pm 0.012)}$ | $0.965(\pm 0.012)$
9 $\rightarrow$ 18 | $0.403(\pm 0.12)$ | $0.715(\pm 0.012)$ | $0.715(\pm 0.012)$ | $0.701(\pm 0.067)$ | ${\it 0.729(\pm 0.127)}$ | $0.583(\pm 0.11)$ | $0.583(\pm 0.11)$ | ${\bf 0.639(\pm 0.103)}$ | $0.674(\pm 0.127)$
Avg. | $0.756(\pm 0.058)$ | ${\it 0.856(\pm 0.014)}$ | $0.856(\pm 0.014)$ | $0.856(\pm 0.023)$ | $0.8(\pm 0.066)$ | $0.763(\pm 0.064)$ | $0.78(\pm 0.08)$ | ${\bf 0.849(\pm 0.025)}$ | $0.864(\pm 0.035)$

| DSAN
---|---
|  | Heuristic | Theoretical error guarantees |
Task | SO | TMV | TMR | TCR | SOR | IWV | DEV | IWA (ours) | TB
12 $\rightarrow$ 16 | $0.681(\pm 0.012)$ | $0.688(\pm 0.021)$ | $0.688(\pm 0.021)$ | ${\it 0.715(\pm 0.024)}$ | $0.694(\pm 0.012)$ | $0.681(\pm 0.012)$ | $0.556(\pm 0.229)$ | ${\bf 0.715(\pm 0.024)}$ | $0.736(\pm 0.012)$
2 $\rightarrow$ 11 | $1.0(\pm 0.0)$ | ${\it 1.0(\pm 0.0)}$ | $1.0(\pm 0.0)$ | $1.0(\pm 0.0)$ | $0.969(\pm 0.0)$ | $1.0(\pm 0.0)$ | $1.0(\pm 0.0)$ | ${\bf 1.0(\pm 0.0)}$ | $1.0(\pm 0.0)$
6 $\rightarrow$ 23 | $0.764(\pm 0.094)$ | ${\it 0.938(\pm 0.0)}$ | $0.938(\pm 0.0)$ | $0.917(\pm 0.021)$ | $0.847(\pm 0.052)$ | $0.785(\pm 0.103)$ | $0.785(\pm 0.103)$ | ${\bf 0.931(\pm 0.012)}$ | $0.938(\pm 0.0)$
7 $\rightarrow$ 13 | $0.854(\pm 0.036)$ | ${\it 0.951(\pm 0.012)}$ | $0.951(\pm 0.012)$ | $0.951(\pm 0.012)$ | $0.854(\pm 0.036)$ | $0.854(\pm 0.036)$ | $0.854(\pm 0.036)$ | ${\bf 0.951(\pm 0.012)}$ | $0.958(\pm 0.0)$
9 $\rightarrow$ 18 | $0.514(\pm 0.032)$ | $0.639(\pm 0.079)$ | $0.639(\pm 0.079)$ | ${\it 0.688(\pm 0.091)}$ | $0.382(\pm 0.012)$ | $0.556(\pm 0.067)$ | $0.528(\pm 0.067)$ | ${\bf 0.694(\pm 0.032)}$ | $0.743(\pm 0.087)$
Avg. | $0.762(\pm 0.035)$ | $0.843(\pm 0.022)$ | $0.843(\pm 0.022)$ | ${\it 0.854(\pm 0.03)}$ | $0.749(\pm 0.023)$ | $0.775(\pm 0.044)$ | $0.744(\pm 0.087)$ | ${\bf 0.858(\pm 0.016)}$ | $0.875(\pm 0.02)$

Table 25: Mean and standard deviation (after $\pm$) of target classification
accuracy on HHAR (Part 1) over $3$ repetitions with different random
initialization of model weights.

| HoMM
---|---
|  | Heuristic | Theoretical error guarantees |
Task | SO | TMV | TMR | TCR | SOR | IWV | DEV | IWA (ours) | TB
0 $\rightarrow$ 6 | $0.719(\pm 0.041)$ | ${\it 0.737(\pm 0.019)}$ | $0.737(\pm 0.019)$ | $0.735(\pm 0.024)$ | $0.635(\pm 0.122)$ | $0.704(\pm 0.011)$ | $0.703(\pm 0.013)$ | ${\bf 0.732(\pm 0.01)}$ | $0.733(\pm 0.019)$
1 $\rightarrow$ 6 | $0.788(\pm 0.11)$ | ${\it 0.871(\pm 0.011)}$ | $0.871(\pm 0.011)$ | $0.869(\pm 0.013)$ | $0.788(\pm 0.163)$ | $0.749(\pm 0.06)$ | $0.785(\pm 0.106)$ | ${\bf 0.879(\pm 0.011)}$ | $0.914(\pm 0.01)$
2 $\rightarrow$ 7 | $0.528(\pm 0.103)$ | $0.457(\pm 0.007)$ | $0.457(\pm 0.007)$ | $0.461(\pm 0.007)$ | ${\it 0.469(\pm 0.051)}$ | $0.497(\pm 0.105)$ | ${\bf 0.516(\pm 0.087)}$ | $0.455(\pm 0.015)$ | $0.546(\pm 0.071)$
3 $\rightarrow$ 8 | $0.797(\pm 0.007)$ | ${\it 0.818(\pm 0.002)}$ | $0.818(\pm 0.002)$ | $0.816(\pm 0.007)$ | $0.812(\pm 0.014)$ | $0.805(\pm 0.01)$ | $0.805(\pm 0.01)$ | ${\bf 0.818(\pm 0.005)}$ | $0.831(\pm 0.022)$
4 $\rightarrow$ 5 | $0.861(\pm 0.022)$ | ${\it 0.914(\pm 0.007)}$ | $0.914(\pm 0.007)$ | $0.911(\pm 0.005)$ | $0.798(\pm 0.164)$ | $0.844(\pm 0.016)$ | $0.855(\pm 0.01)$ | ${\bf 0.911(\pm 0.005)}$ | $0.94(\pm 0.04)$
Avg. | $0.739(\pm 0.057)$ | ${\it 0.759(\pm 0.009)}$ | $0.759(\pm 0.009)$ | $0.759(\pm 0.011)$ | $0.7(\pm 0.103)$ | $0.72(\pm 0.041)$ | $0.733(\pm 0.045)$ | ${\bf 0.759(\pm 0.009)}$ | $0.793(\pm 0.032)$

| AdvSKM
---|---
|  | Heuristic | Theoretical error guarantees |
Task | SO | TMV | TMR | TCR | SOR | IWV | DEV | IWA (ours) | TB
0 $\rightarrow$ 6 | $0.661(\pm 0.035)$ | $0.722(\pm 0.009)$ | $0.722(\pm 0.009)$ | ${\it 0.725(\pm 0.007)}$ | $0.629(\pm 0.076)$ | $0.699(\pm 0.013)$ | $0.699(\pm 0.013)$ | ${\bf 0.718(\pm 0.009)}$ | $0.731(\pm 0.013)$
1 $\rightarrow$ 6 | $0.821(\pm 0.046)$ | $0.849(\pm 0.002)$ | $0.849(\pm 0.002)$ | ${\it 0.851(\pm 0.006)}$ | $0.604(\pm 0.045)$ | $0.806(\pm 0.026)$ | $0.806(\pm 0.026)$ | ${\bf 0.857(\pm 0.006)}$ | $0.838(\pm 0.018)$
2 $\rightarrow$ 7 | $0.455(\pm 0.07)$ | $0.473(\pm 0.031)$ | $0.473(\pm 0.031)$ | $0.484(\pm 0.03)$ | ${\it 0.531(\pm 0.062)}$ | $0.497(\pm 0.067)$ | ${\bf 0.497(\pm 0.067)}$ | $0.49(\pm 0.014)$ | $0.574(\pm 0.112)$
3 $\rightarrow$ 8 | $0.79(\pm 0.011)$ | $0.799(\pm 0.008)$ | $0.799(\pm 0.008)$ | $0.803(\pm 0.005)$ | ${\it 0.805(\pm 0.01)}$ | $0.799(\pm 0.005)$ | $0.788(\pm 0.023)$ | ${\bf 0.81(\pm 0.002)}$ | $0.818(\pm 0.012)$
4 $\rightarrow$ 5 | $0.862(\pm 0.055)$ | $0.866(\pm 0.013)$ | $0.866(\pm 0.013)$ | ${\it 0.875(\pm 0.008)}$ | $0.809(\pm 0.094)$ | $0.85(\pm 0.025)$ | $0.85(\pm 0.025)$ | ${\bf 0.884(\pm 0.005)}$ | $0.895(\pm 0.014)$
Avg. | $0.718(\pm 0.044)$ | $0.742(\pm 0.013)$ | $0.742(\pm 0.013)$ | ${\it 0.748(\pm 0.011)}$ | $0.676(\pm 0.058)$ | $0.73(\pm 0.027)$ | $0.728(\pm 0.031)$ | ${\bf 0.752(\pm 0.007)}$ | $0.771(\pm 0.034)$

| DIRT
---|---
|  | Heuristic | Theoretical error guarantees |
Task | SO | TMV | TMR | TCR | SOR | IWV | DEV | IWA (ours) | TB
0 $\rightarrow$ 6 | $0.708(\pm 0.011)$ | $0.571(\pm 0.079)$ | $0.571(\pm 0.079)$ | ${\it 0.633(\pm 0.137)}$ | $0.629(\pm 0.085)$ | $0.708(\pm 0.011)$ | $0.708(\pm 0.011)$ | ${\bf 0.779(\pm 0.011)}$ | $0.739(\pm 0.011)$
1 $\rightarrow$ 6 | $0.756(\pm 0.058)$ | ${\it 0.938(\pm 0.004)}$ | $0.938(\pm 0.004)$ | $0.938(\pm 0.004)$ | $0.904(\pm 0.058)$ | $0.814(\pm 0.056)$ | $0.756(\pm 0.058)$ | ${\bf 0.938(\pm 0.0)}$ | $0.942(\pm 0.004)$
2 $\rightarrow$ 7 | $0.531(\pm 0.057)$ | $0.622(\pm 0.091)$ | $0.622(\pm 0.091)$ | $0.621(\pm 0.09)$ | ${\it 0.658(\pm 0.03)}$ | $0.548(\pm 0.049)$ | ${\bf 0.548(\pm 0.049)}$ | $0.53(\pm 0.025)$ | $0.688(\pm 0.004)$
3 $\rightarrow$ 8 | $0.807(\pm 0.008)$ | $0.846(\pm 0.022)$ | $0.846(\pm 0.022)$ | $0.837(\pm 0.015)$ | ${\it 0.857(\pm 0.087)}$ | $0.807(\pm 0.008)$ | $0.807(\pm 0.008)$ | ${\bf 0.848(\pm 0.007)}$ | $0.911(\pm 0.07)$
4 $\rightarrow$ 5 | $0.839(\pm 0.016)$ | ${\it 0.984(\pm 0.004)}$ | $0.984(\pm 0.004)$ | $0.984(\pm 0.004)$ | $0.93(\pm 0.061)$ | $0.839(\pm 0.016)$ | $0.878(\pm 0.074)$ | ${\bf 0.984(\pm 0.004)}$ | $0.984(\pm 0.002)$
Avg. | $0.728(\pm 0.03)$ | $0.792(\pm 0.04)$ | $0.792(\pm 0.04)$ | ${\it 0.803(\pm 0.05)}$ | $0.796(\pm 0.064)$ | $0.743(\pm 0.028)$ | $0.739(\pm 0.04)$ | ${\bf 0.816(\pm 0.009)}$ | $0.853(\pm 0.018)$

| DDC
---|---
|  | Heuristic | Theoretical error guarantees |
Task | SO | TMV | TMR | TCR | SOR | IWV | DEV | IWA (ours) | TB
0 $\rightarrow$ 6 | $0.575(\pm 0.083)$ | ${\it 0.693(\pm 0.017)}$ | $0.693(\pm 0.017)$ | $0.672(\pm 0.009)$ | $0.632(\pm 0.038)$ | $0.646(\pm 0.015)$ | $0.6(\pm 0.084)$ | ${\bf 0.697(\pm 0.013)}$ | $0.651(\pm 0.013)$
1 $\rightarrow$ 6 | $0.875(\pm 0.014)$ | $0.888(\pm 0.007)$ | $0.888(\pm 0.007)$ | ${\it 0.894(\pm 0.013)}$ | $0.886(\pm 0.019)$ | $0.856(\pm 0.067)$ | $0.856(\pm 0.067)$ | ${\bf 0.882(\pm 0.017)}$ | $0.899(\pm 0.016)$
2 $\rightarrow$ 7 | $0.487(\pm 0.016)$ | $0.457(\pm 0.03)$ | $0.457(\pm 0.03)$ | $0.455(\pm 0.029)$ | ${\it 0.497(\pm 0.028)}$ | $0.438(\pm 0.054)$ | $0.438(\pm 0.054)$ | ${\bf 0.439(\pm 0.041)}$ | $0.533(\pm 0.107)$
3 $\rightarrow$ 8 | $0.815(\pm 0.019)$ | $0.805(\pm 0.014)$ | $0.805(\pm 0.014)$ | ${\it 0.807(\pm 0.016)}$ | $0.797(\pm 0.022)$ | $0.827(\pm 0.025)$ | ${\bf 0.831(\pm 0.02)}$ | $0.818(\pm 0.008)$ | $0.822(\pm 0.02)$
4 $\rightarrow$ 5 | $0.831(\pm 0.048)$ | $0.908(\pm 0.011)$ | $0.908(\pm 0.011)$ | ${\it 0.911(\pm 0.01)}$ | $0.772(\pm 0.085)$ | $0.792(\pm 0.02)$ | $0.801(\pm 0.012)$ | ${\bf 0.905(\pm 0.008)}$ | $0.888(\pm 0.01)$
Avg. | $0.716(\pm 0.036)$ | ${\it 0.75(\pm 0.016)}$ | $0.75(\pm 0.016)$ | $0.748(\pm 0.015)$ | $0.717(\pm 0.038)$ | $0.711(\pm 0.036)$ | $0.705(\pm 0.047)$ | ${\bf 0.748(\pm 0.017)}$ | $0.758(\pm 0.033)$

| CMD
---|---
|  | Heuristic | Theoretical error guarantees |
Task | SO | TMV | TMR | TCR | SOR | IWV | DEV | IWA (ours) | TB
0 $\rightarrow$ 6 | $0.703(\pm 0.04)$ | $0.643(\pm 0.046)$ | $0.643(\pm 0.046)$ | ${\it 0.679(\pm 0.054)}$ | $0.672(\pm 0.103)$ | $0.743(\pm 0.021)$ | ${\bf 0.743(\pm 0.021)}$ | $0.693(\pm 0.012)$ | $0.724(\pm 0.021)$
1 $\rightarrow$ 6 | $0.861(\pm 0.035)$ | ${\it 0.915(\pm 0.009)}$ | $0.915(\pm 0.009)$ | $0.912(\pm 0.0)$ | $0.826(\pm 0.103)$ | $0.899(\pm 0.03)$ | $0.843(\pm 0.156)$ | ${\bf 0.907(\pm 0.006)}$ | $0.925(\pm 0.004)$
2 $\rightarrow$ 7 | $0.573(\pm 0.018)$ | $0.494(\pm 0.011)$ | $0.494(\pm 0.011)$ | $0.499(\pm 0.023)$ | ${\it 0.51(\pm 0.066)}$ | ${\bf 0.577(\pm 0.011)}$ | $0.557(\pm 0.039)$ | $0.482(\pm 0.008)$ | $0.603(\pm 0.016)$
3 $\rightarrow$ 8 | $0.799(\pm 0.016)$ | ${\it 0.816(\pm 0.0)}$ | $0.816(\pm 0.0)$ | $0.816(\pm 0.0)$ | $0.797(\pm 0.004)$ | $0.799(\pm 0.016)$ | $0.738(\pm 0.109)$ | ${\bf 0.811(\pm 0.011)}$ | $0.822(\pm 0.01)$
4 $\rightarrow$ 5 | $0.806(\pm 0.024)$ | ${\it 0.952(\pm 0.016)}$ | $0.952(\pm 0.016)$ | $0.93(\pm 0.007)$ | $0.879(\pm 0.054)$ | $0.854(\pm 0.063)$ | $0.332(\pm 0.051)$ | ${\bf 0.939(\pm 0.002)}$ | $0.961(\pm 0.024)$
Avg. | $0.748(\pm 0.026)$ | $0.764(\pm 0.016)$ | $0.764(\pm 0.016)$ | ${\it 0.767(\pm 0.017)}$ | $0.737(\pm 0.066)$ | ${\bf 0.775(\pm 0.028)}$ | $0.643(\pm 0.075)$ | $0.766(\pm 0.008)$ | $0.807(\pm 0.015)$

| MMDA
---|---
|  | Heuristic | Theoretical error guarantees |
Task | SO | TMV | TMR | TCR | SOR | IWV | DEV | IWA (ours) | TB
0 $\rightarrow$ 6 | $0.706(\pm 0.042)$ | ${\it 0.737(\pm 0.021)}$ | $0.737(\pm 0.021)$ | $0.737(\pm 0.018)$ | $0.704(\pm 0.037)$ | $0.699(\pm 0.055)$ | $0.725(\pm 0.018)$ | ${\bf 0.746(\pm 0.008)}$ | $0.732(\pm 0.008)$
1 $\rightarrow$ 6 | $0.792(\pm 0.098)$ | ${\it 0.91(\pm 0.002)}$ | $0.91(\pm 0.002)$ | $0.91(\pm 0.002)$ | $0.742(\pm 0.147)$ | $0.732(\pm 0.009)$ | $0.722(\pm 0.009)$ | ${\bf 0.897(\pm 0.002)}$ | $0.914(\pm 0.028)$
2 $\rightarrow$ 7 | $0.552(\pm 0.073)$ | $0.481(\pm 0.003)$ | $0.481(\pm 0.003)$ | $0.482(\pm 0.004)$ | ${\it 0.515(\pm 0.058)}$ | $0.496(\pm 0.027)$ | ${\bf 0.543(\pm 0.055)}$ | $0.488(\pm 0.01)$ | $0.552(\pm 0.073)$
3 $\rightarrow$ 8 | $0.79(\pm 0.016)$ | ${\it 0.862(\pm 0.026)}$ | $0.862(\pm 0.026)$ | $0.841(\pm 0.01)$ | $0.794(\pm 0.022)$ | $0.802(\pm 0.018)$ | $0.802(\pm 0.018)$ | ${\bf 0.839(\pm 0.012)}$ | $0.932(\pm 0.005)$
4 $\rightarrow$ 5 | $0.852(\pm 0.036)$ | $0.917(\pm 0.016)$ | $0.917(\pm 0.016)$ | ${\it 0.931(\pm 0.002)}$ | $0.733(\pm 0.061)$ | $0.865(\pm 0.055)$ | $0.865(\pm 0.055)$ | ${\bf 0.928(\pm 0.006)}$ | $0.947(\pm 0.022)$
Avg. | $0.738(\pm 0.053)$ | ${\it 0.781(\pm 0.014)}$ | $0.781(\pm 0.014)$ | $0.78(\pm 0.007)$ | $0.698(\pm 0.065)$ | $0.719(\pm 0.033)$ | $0.731(\pm 0.031)$ | ${\bf 0.78(\pm 0.008)}$ | $0.815(\pm 0.027)$

Table 26: Mean and standard deviation (after $\pm$) of target classification
accuracy on HHAR (Part 2) over $3$ repetitions with different random
initialization of model weights.

| CoDATS
---|---
|  | Heuristic | Theoretical error guarantees |
Task | SO | TMV | TMR | TCR | SOR | IWV | DEV | IWA (ours) | TB
0 $\rightarrow$ 6 | $0.64(\pm 0.096)$ | $0.497(\pm 0.005)$ | $0.497(\pm 0.005)$ | $0.499(\pm 0.006)$ | ${\it 0.582(\pm 0.122)}$ | $0.689(\pm 0.069)$ | $0.606(\pm 0.106)$ | ${\bf 0.718(\pm 0.017)}$ | $0.735(\pm 0.01)$
1 $\rightarrow$ 6 | $0.775(\pm 0.091)$ | ${\it 0.946(\pm 0.0)}$ | $0.946(\pm 0.0)$ | $0.946(\pm 0.0)$ | $0.683(\pm 0.076)$ | $0.896(\pm 0.069)$ | $0.896(\pm 0.069)$ | ${\bf 0.939(\pm 0.006)}$ | $0.947(\pm 0.009)$
2 $\rightarrow$ 7 | $0.527(\pm 0.076)$ | $0.473(\pm 0.012)$ | $0.473(\pm 0.012)$ | $0.475(\pm 0.01)$ | ${\it 0.534(\pm 0.052)}$ | $0.472(\pm 0.019)$ | ${\bf 0.555(\pm 0.069)}$ | $0.472(\pm 0.005)$ | $0.558(\pm 0.041)$
3 $\rightarrow$ 8 | $0.783(\pm 0.015)$ | ${\it 0.971(\pm 0.018)}$ | $0.971(\pm 0.018)$ | $0.969(\pm 0.018)$ | $0.97(\pm 0.025)$ | $0.789(\pm 0.01)$ | $0.789(\pm 0.01)$ | ${\bf 0.96(\pm 0.03)}$ | $0.987(\pm 0.002)$
4 $\rightarrow$ 5 | $0.827(\pm 0.039)$ | $0.971(\pm 0.013)$ | $0.971(\pm 0.013)$ | ${\it 0.978(\pm 0.002)}$ | $0.841(\pm 0.1)$ | $0.849(\pm 0.074)$ | $0.849(\pm 0.074)$ | ${\bf 0.973(\pm 0.004)}$ | $0.979(\pm 0.006)$