Jaehoon<EMAIL_ADDRESS>Minki<EMAIL_ADDRESS>Taekyung
<EMAIL_ADDRESS>Changick<EMAIL_ADDRESS>School of Electrical
Engineering
Korea Advanced Institute of Science
and Technology (KAIST)
Daejeon, Korea Pseudo-Labeling Curriculum

# Pseudo-Labeling Curriculum for Unsupervised Domain Adaptation

###### Abstract

To learn target discriminative representations, using pseudo-labels is a
simple yet effective approach for unsupervised domain adaptation. However, the
existence of false pseudo-labels, which may have a detrimental influence on
learning target representations, remains a major challenge. To overcome this
issue, we propose a pseudo-labeling curriculum based on a density-based
clustering algorithm. Since samples with high density values are more likely
to have correct pseudo-labels, we leverage these subsets to train our target
network at the early stage, and utilize data subsets with low density values
at the later stage. We can progressively improve the capability of our network
to generate pseudo-labels, and thus these target samples with pseudo-labels
are effective for training our model. Moreover, we present a clustering
constraint to enhance the discriminative power of the learned target features.
Our approach achieves state-of-the-art performance on three benchmarks:
Office-31, imageCLEF-DA, and Office-Home.

##  1 Introduction

In computer vision, large-scale datasets have played an essential role in the
success of deep neural networks. However, creating a large amount of labeled
data is expensive and time-consuming. To overcome this problem, unsupervised
domain adaptation approaches leverage the labeled data in a source domain to
train a high-performance model on unlabeled data in a target domain. Such
unsupervised domain adaptation methods suffer from the covariate shift between
source and target data distributions due to different characteristics of both
domains [Shimodaira(2000)]. To tackle the covariate shift problem, many domain
adaptation methods aim to jointly learn domain-invariant representations by
minimizing domain divergence [Ben-David et al.(2010)Ben-David, Blitzer,
Crammer, Kulesza, Pereira, and Vaughan].

Recently, adversarial domain adaptation methods [Ganin and Lempitsky(2015),
Tzeng et al.(2017)Tzeng, Hoffman, Saenko, and Darrell] have received lots of
attention. Similar to generative adversarial networks (GANs) [Goodfellow et
al.(2014)Goodfellow, Pouget-Abadie, Mirza, Xu, Warde-Farley, Ozair, Courville,
and Bengio], these methods employ two players, namely domain discriminator and
feature extractor, to align feature distributions across domains in an
adversarial manner. The core module for domain adaptation is domain
discriminator, which is trained to discriminate the domain labels of features
generated by the feature extractor. Conversely, the feature extractor is
trained to provide transferable features that fool the domain discriminator by
minimizing the divergence between features generated from the source and the
target domain. Although their general efficacy shows impressive results in
various tasks like segmentation [Hoffman et al.(2016)Hoffman, Wang, Yu, and
Darrell, Tsai et al.(2018)Tsai, Hung, Schulter, Sohn, Yang, and Chandraker],
detection [Chen et al.(2018)Chen, Li, Sakaridis, Dai, and Van Gool, Kim et
al.(2019)Kim, Jeong, Kim, Choi, and Kim], and depth estimation [Nath Kundu et
al.(2018)Nath Kundu, Krishna Uppala, Pahuja, and Venkatesh Babu], the
adversarial domain adaptation methods suffer from a major problem. Since the
domain discriminator only focuses on aligning global domain features, these
methods often fail to consider the category information of target samples.
Thus, category-level domain alignment enforced by adversarial domain
adaptation methods does not guarantee the good target performance due to the
lack of categorical target information [Saito et al.(2018)Saito, Watanabe,
Ushiku, and Harada]. To learn target categorical representation, recent
studies [Xie et al.(2018)Xie, Zheng, Chen, and Chen, Shu et al.(2018)Shu, Bui,
Narui, and Ermon, Zhang et al.(2018)Zhang, Ouyang, Li, and Xu] utilize pseudo-
labels for target samples, thus encouraging a low-density separation between
classes [Lee(2013)]. Although these methods rely on the assumption that the
source-trained classifier assigns pseudo-labels to target samples with high
confidence, it is difficult to satisfy this assumption especially when domain
discrepancy is large. Training the network with false pseudo-labels may
degrade the capability of distinguishing discriminant target samples by
accumulating classification errors.

Figure 1: Learning process of the proposed method. $D_{\mathcal{S}}$ is a set
of all source samples, and $D_{\mathcal{T}}$ is a set of all target samples.
$D_{1}$, $D_{2}$, $\dotsb$, and $D_{P}$ are data subsets obtained from
$D_{\mathcal{T}}$. $C$ is the number of classes. By using a density-based
clustering algorithm, we split our target dataset into a number of data
subsets for each category and give these subsets following training process.

To alleviate this issue, we introduce a curriculum learning strategy for
unsupervised domain adaptation. The curriculum learning [Bengio et
al.(2009)Bengio, Louradour, Collobert, and Weston] is motivated by the
cognitive process of humans that gradually learn from easy to complex samples.
Inspired by this concept, we propose a novel algorithm called pseudo-labeling
curriculum for unsupervised domain adaptation (PCDA). For designing this
pseudo-labelling curriculum, we apply a density-based clustering algorithm in
[Guo et al.(2018)Guo, Huang, Zhang, Zhuang, Dong, Scott, and Huang] to divide
target dataset into a number of data subsets relying on both pseudo-labels and
features generated by our network. Then, we sequentially train target specific
network from target samples whose pseudo-labels have a high chance of being
correct to those which are highly likely to be misclassified. Our learning
process is demonstrated in Fig. 1. In this process, we only use some target
data subsets with correct pseudo-labels at the early training stage. As the
training proceeds, our classifier can generate progressively reliable pseudo-
labels for other target data subsets which are utilized at the later stage.
Training with the pseudo-labeling curriculum boosts the robustness of the
training target specific network with pseudo-labels by sequentially providing
target data subsets. PCDA is effective to suppress the negative influence of
false pseudo-labeled target samples. Furthermore, we suggest the constraints
for clustering on the target data to reduce the intra-class variance of target
representations and to enlarge the inter-class variance of target
representations. This constraint reinforces the assumption of the density-
based clustering that target samples with a high density value are more likely
to have correct pseudo-labels. Our experimental results suggest that PCDA
achieves comparable or even better results compared with the state-of-the-art
domain adaptation methods.

##  2 Related Works

Several types of adversarial learning methods for unsupervised domain
adaptation have been shown to match distributions of the features generated
from source and target examples ([Ganin and Lempitsky(2015)], [Long et
al.(2015)Long, Cao, Wang, and Jordan], [Bousmalis et al.(2016)Bousmalis,
Trigeorgis, Silberman, Krishnan, and Erhan], [Long et al.(2017)Long, Zhu,
Wang, and Jordan], [Tzeng et al.(2017)Tzeng, Hoffman, Saenko, and Darrell],
[Saito et al.(2018)Saito, Watanabe, Ushiku, and Harada]). However, they mainly
focus on aligning domain-level feature distributions without considering
category-level alignment. Xie _et al_[Xie et al.(2018)Xie, Zheng, Chen, and
Chen] match the labeled source centroid and the pseudo-labeled target centroid
to learn semantic representations for target samples. This moving average
centroid alignment guides the feature extractor to consider category-level
information for target samples. Pei _et al_[Pei et al.(2018)Pei, Cao, Long,
and Wang] exploit multiple domain discriminators to enable fine-grained
distribution alignment.

Some studies [Sener et al.(2016)Sener, Song, Saxena, and Savarese, Saito et
al.(2017)Saito, Ushiku, and Harada, Shu et al.(2018)Shu, Bui, Narui, and
Ermon, French et al.(2018)French, Mackiewicz, and Fisher, Zhang et
al.(2018)Zhang, Ouyang, Li, and Xu] use pseudo-labeled target samples to learn
target discriminative representations. Sener _et al_[Sener et al.(2016)Sener,
Song, Saxena, and Savarese] adopt clustering techniques and pseudo-labels to
learn discriminative features. In [Shu et al.(2018)Shu, Bui, Narui, and Ermon]
and [French et al.(2018)French, Mackiewicz, and Fisher], they apply a Mean
Teacher framework [Tarvainen and Valpola(2017)] to domain adaptation with the
consistency regularization. Saito _et al_[Saito et al.(2017)Saito, Ushiku, and
Harada] employ the asymmetric tri-training (ATT), which leverages target
samples labeled by the source-trained classifier to learn target
discriminative features. Zhang _et al_[Zhang et al.(2018)Zhang, Ouyang, Li,
and Xu] iteratively select pseudo-labeled target samples based on their
proposed criterion and retrain the model with a training set including pseudo-
labeled samples. However, these methods based on pseudo-labeled target samples
have a critical bottleneck that false pseudo-labels can impede learning target
discriminative features and further their categorical error is easily
accumulated, which hurt the performance.

Curriculum learning proposed by [Bengio et al.(2009)Bengio, Louradour,
Collobert, and Weston] is a learning paradigm based on ranking the training
samples from easiest to the most difficult to classify. The curriculum based
on ranking is used to guide the order of training procedure. Previous studies
([Kumar et al.(2010)Kumar, Packer, and Koller, Lin et al.(2018)Lin, Wang,
Meng, Zuo, and Zhang, Jiang et al.(2018)Jiang, Zhou, Leung, Li, and Fei-Fei,
Guo et al.(2018)Guo, Huang, Zhang, Zhuang, Dong, Scott, and Huang]) have
demonstrated that curriculum learning is useful in handling problems with
noisy labels. Guo _et al_[Guo et al.(2018)Guo, Huang, Zhang, Zhuang, Dong,
Scott, and Huang] propose a learning curriculum to handle massive, noisy sets
of labels. They measure data complexity using cluster density and split all
training samples into a number of subsets ordered by data complexity. By
utilizing these subsets, they design a curriculum to train the network. We
recast their strategy to design curriculum into our training algorithm.

##  3 Method

In this section, we explain details of the proposed algorithm. Our proposed
network structure is demonstrated in Fig. 2. We let $G_{f}$ denote the shared
feature extractor for source and target data. $C_{s}$ and $C_{t}$ are
classifiers which distinguish features generated from $G_{f}$. Here,
$\theta_{f}$, $\theta_{s}$, and $\theta_{t}$ denote the model parameters of
the respective $G_{f}$, $C_{s}$, and $C_{t}$. $C_{s}$ learns from the source
samples and $C_{t}$ learns from pseudo-labeled target samples. $G_{d}$ is the
domain discriminator which aims to label all source samples as 1 and all
target samples as 0. GRL stands for Gradient Reversal Layer, which inversely
back-propagate gradients by changing the sign of the gradient [Ganin and
Lempitsky(2015)]. The shared feature extractor $G_{f}$ is trained from all
gradients back-propagated by $C_{s}$, $C_{t}$, and $G_{d}$. Our goal is
training $C_{t}$ to be able to learn discriminative representations for the
target domain. We have access to $N_{s}$ labeled image samples from the source
domain $D_{\mathcal{S}}=\\{(x_{i}^{s},y_{i}^{s})\\}_{i=1}^{N_{s}}$ and $N_{t}$
unlabeled image samples from the target domain
$D_{\mathcal{T}}=\\{x_{i}^{t}\\}_{i=1}^{N_{t}}$. $\hat{y_{i}}^{t}$ denotes a
pseudo-label for the target sample. We assume that $D_{\mathcal{S}}$ and
$D_{\mathcal{T}}$ completely share the C classes.

Figure 2: Pipeline of the proposed method: (a) The curriculum design from
density-based clustering, (b) The structure of training our model. In (a), we
use all target samples and pseudo-labels from $C_{s}$ or $C_{t}$ to generate
data subsets, which form our curriculum for training our model. In (b), we
train $G_{f}$, $C_{s}$, $C_{t}$ and $G_{d}$ with all source samples and
selected data subsets of target samples following curriculum.

###  3.1 Domain Adversarial Learning Scheme

Before obtaining pseudo-labeled target samples, we do not train the target
specific classifier $C_{t}$. We only train $G_{f}$, $C_{s}$, and $G_{d}$ by
using supervised classification loss and domain adversarial loss following the
idea of domain adversarial neural networks (DANN) [Ganin and Lempitsky(2015)].
The overall loss function in this stage is the following:

$\begin{split}J_{1}(\theta_{f},\theta_{d},\theta_{s})&=\frac{1}{N_{s}}\sum_{i=1}^{N_{s}}L_{y}(C_{s}(f_{i}^{s}),y_{i}^{s})-\frac{\lambda}{N_{s}}\sum_{i=1}^{N_{s}}L_{d}(G_{d}(f_{i}^{s}),d_{i})-\frac{\lambda}{N_{t}}\sum_{i=1}^{N_{t}}L_{d}(G_{d}(f_{i}^{t}),d_{i})\>,\end{split}$
(1)

where $L_{y}$ is the cross-entropy loss and $L_{d}$ is the binary cross-
entropy loss. $f_{i}^{s}$ and $f_{i}^{t}$ generated by $G_{f}$ are the feature
representations of source and target samples, i.e.,
$f_{i}^{s}=G_{f}(x_{i}^{s})$ and $f_{i}^{t}=G_{f}(x_{i}^{t})$.
$d_{i}\in\\{0,1\\}$ is the domain label and $\lambda$ is a trade-off
parameter. The overall objective is written as follows

$\min_{\theta_{f},\,\theta_{s}}\max_{\theta_{d}}\>J_{1}(\theta_{f},\theta_{d},\theta_{s}).$
(2)

In the early stage of training, since $C_{s}$ is highly likely to generate
false pseudo-labeled target examples, we do not train $C_{t}$ at all. After a
few epochs, we start to train $C_{t}$ with pseudo-labeled target examples.

###  3.2 Density-Based Clustering for Pseudo-Labeling Curriculum

We modify the curriculum learning method from [Guo et al.(2018)Guo, Huang,
Zhang, Zhuang, Dong, Scott, and Huang] to enable domain adaptation. To design
the curriculum, we should address two questions: how to rank the training
samples, and how to construct the training schedule. We adopt the ranking
method using their clustering density in order to split the target samples.
$C_{s}$ generates pseudo-labels $\hat{y_{i}}^{t}$ for target samples and then
it separates all features $f_{i}^{t}$ into each category. Then, we conduct the
following process for each category. We first determine a matrix
$\mathbf{E}\in\rm I\\!R^{n\times n}$, where $n$ is the number of target
samples in a certain category. The matrix $\mathbf{E}$ is composed of elements
$\mathbf{E}_{ij}=\|f_{i}^{t}-f_{j}^{t}\|^{2}$ indicating the Euclidean
distance between $f_{i}^{t}$ and $f_{j}^{t}$. A local density of each sample
in a current category is defined as

$\rho_{i}=\sum_{j}I(\mathbf{E}_{ij}-e_{c})\>,\enskip\>I(x)=\begin{cases}1\quad
x<0\\\ 0\quad\textrm{otherwise}\end{cases}.$ (3)

We determine $e_{c}$ by sorting all $\mathbf{E}_{ij}$ elements in ascending
order and select a number ranked at $k$% from the smallest value. We
empirically set $k=40$ in all experiments because the result of clustering is
consistent when the value of $k$ is between 40 and 70. The implication of
$\rho_{i}$ is the number of target samples whose distances are smaller than
$e_{c}$.

Target samples with correct pseudo-labels often share similar visual
characteristics, and thus features generated from these samples tend to form a
cluster for each category. By contrast, target samples with a high chance of
being false pseudo-labels often have a visual difference, leading to a sparse
distribution which results in a small value of local density. Therefore, we
select a sample with the highest local density value as a cluster center for
each category. Since target samples close to the cluster center are more
likely to have a correct pseudo-label, we divide target samples into a number
of clusters according to their corresponding distances from the cluster
center. For each category, we respectively apply the k-means algorithm to the
set of distances between the target sample and cluster center for generating
$P$ clusters. Now, we acquire $P$ clusters in each category, and each cluster
can be thought of as a data subset, see Fig. 1. In all our experiments, we
empirically set the number of clusters ($P$), i.e., $P$ to 3. Hence, each
category contains three subsets, and we combine the overall categories. We can
obtain three data subsets $D_{e}$, $D_{m}$, and $D_{h}$, which involve easy,
moderate, and hard samples, respectively. The easy samples consist of target
samples with a high density value, while the hard samples comprise target
samples with a low density value.

In other words, it is challenging for the classifier $C_{s}$ learned from the
source samples to assign correct pseudo-labels for target samples due to the
domain gap. In particular, the target samples far from corresponding cluster
centers, or distributed near the boundary of the clusters are more likely to
have false pseudo-labels. To minimize such an adverse effect, we firstly opt
to use the data subset with low intra-class variance and high inter-class
variance, such as the easy samples, at the early stage of training. By
employing a subset with a high density value, the classifier $C_{t}$ can learn
target discriminative representations from correct pseudo-labeled target
samples.

###  3.3 Training with Pseudo-Labeling Curriculum

Our training procedure is proceeded with four stages in conjunction with the
ordered sequence of training subsets from easy to hard samples. At the first
stage, we train $G_{f}$, $C_{s}$, and $G_{d}$ with $D_{\mathcal{S}}$ and
$D_{\mathcal{T}}$, while $C_{t}$ is not trained at all. It is described
specifically in Section 3.1. Here $G_{f}$, $C_{s}$ and $G_{d}$ are optimized
by Eq. (2). At the second stage, pseudo-labels for the easy samples
$D_{e}=\\{(x_{i}^{t},\hat{y_{i}}^{t})\\}_{i=1}^{N_{e}}$ generated by $C_{s}$
are highly reliable for training target classifier $C_{t}$. According to the
terminology in Section 3.1, the loss function of the second stage can be
written as follows,

$\begin{split}J_{2}(\theta_{f},\theta_{d},\theta_{s},\theta_{t})&=\frac{1}{N_{s}}\sum_{i=1}^{N_{s}}L_{y}(C_{s}(f_{i}^{s}),y_{i}^{s})+\frac{1}{N_{e}}\sum_{i=1}^{N_{e}}L_{y}(C_{t}(f_{i}^{t}),\hat{y_{i}}^{t})\\\
&-\frac{\lambda}{N_{s}}\sum_{i=1}^{N_{s}}L_{d}(G_{d}(f_{i}),d_{i})-\frac{\lambda}{N_{e}}\sum_{i=1}^{N_{e}}\beta
L_{d}(G_{d}(f_{i}),d_{i})\>,\end{split}$ (4)

where $\beta$ is a hyperparameter that re-weights the contributions of the
data subset which is newly added to the training process at the current stage.
Compared to the early training samples which are already aligned between the
source and target domains, the source and target features generated from newly
added samples are poorly aligned. Then, the newly added samples may impede
fine-tuning the feature extractor and learning the target classifier. A higher
$\beta$ value encourages the $G_{f}$ to learn domain invariant features for
the newly added samples. Thus, we enable effective domain adaptation based on
the curriculum learning by focusing on the contribution of newly added
samples. Third, we generate pseudo-labels for the easy samples $D_{e}$ and the
moderate samples $D_{m}$ by using $C_{t}$ and also train $C_{t}$ with $D_{e}$
and $D_{m}$. We use the same form of loss function in Eq. (4) with adding
$D_{m}$. Lastly, the model is further trained by adding the hard samples
$D_{h}$ according to the learning strategy of the previous stage. Details are
included in the supplementary material. We optimize the following minimax
objective:

$\min_{\theta_{f},\,\theta_{s},\,\theta_{t}}\max_{\theta_{d}}\>J_{2}(\theta_{f},\theta_{d},\theta_{s},\theta_{t})\>.$
(5)

###  3.4 Clustering Constraint

A clustering constraint is motivated by the need to boost the effectiveness of
the density-based clustering algorithm in order to reduce the number of false
pseudo-labeled target samples. For this purpose, the features from target
samples with the same category should be as close as possible, while the
features from target samples with different categories should be far from each
other. We apply the concept of contrastive loss [Chopra et al.(2005)Chopra,
Hadsell, and LeCun], which takes pairs of examples as input and trains a model
to predict whether pairs of inputs are from the same category or not. Unlike
[Chopra et al.(2005)Chopra, Hadsell, and LeCun, Schroff et al.(2015)Schroff,
Kalenichenko, and Philbin] which utilize all pairs of images as ground-truth
labels, our method is based on the pseudo-labels in order to create pairs of
inputs. We propose to formulate the Euclidean-based clustering loss (ECL) as
follows,

$J_{ECL}(C_{t})=\sum_{\forall{(i,j)}\in\mathcal{T}}L_{ECL}(h_{i},h_{j}),\>\>L_{ECL}(h_{i},h_{j})=\begin{cases}\|h_{i}^{t}-h_{j}^{t}\|^{2}&I_{ij}=1\\\
max(0,\>m-\|h_{i}^{t}-h_{j}^{t}\|)^{2}&I_{ij}=0\end{cases}\>,\\\ $ (6)

where $h_{i}^{t}$ denotes the output of the target classifier $C_{t}$ before
the softmax layer with respect to the $i$-th training sample in the mini-
batch. $\|\cdot\|^{2}$ is the squared Euclidean distance and $m>0$ is a
margin. $I_{ij}=1$ means that $h_{i}$ and $h_{j}$ belong to the same category,
while $I_{ij}=0$ indicates that $h_{i}$ and $h_{j}$ are from the different
categories. $i$ and $j$ denote the indices of target samples inside the mini-
batch. The ECL loss encourages target features from the same category to be
closer and enforce the distance between those from the different categories no
more than $m$. This loss can be combined with $J_{2}$ in Eq. (4) to optimize
$G_{f}$ and $C_{t}$.

##  4 Experiments

###  4.1 Setups

Office-31 [Saenko et al.(2010)Saenko, Kulis, Fritz, and Darrell], the most
popular benchmark dataset for visual domain adaptation, contains 4652 images
and 31 categories from three distinct domains: Amazon (A), Webcam (W), and
DSLR (D). We comprise all domain combinations and build 6 transfer tasks:
A$\rightarrow$W, D$\rightarrow$W, W$\rightarrow$D, A$\rightarrow$D,
D$\rightarrow$A, and W$\rightarrow$A.

ImageCLEF-DA111https://www.imageclef.org/2014/adaptation, a benchmark dataset
for Image-CLEF 2014 domain adaptation challenge, consists of three domains
including Caltech-256 (C), ImageNet ILSVRC 2012 (I) and Pascal VOC 2012 (P).
Each domain contains 600 images and 50 images for each category. We evaluate
our method on all possible domain adaptation tasks: I$\rightarrow$P,
P$\rightarrow$I, I$\rightarrow$C, C$\rightarrow$I, C$\rightarrow$P, and
P$\rightarrow$C. Different from Office-31, all images have equal size and the
number of images in each category is well-balanced.

Office-Home [Venkateswara et al.(2017)Venkateswara, Eusebio, Chakraborty, and
Panchanathan], a more challenging dataset for domain adaptation evaluation,
contains around 15,500 images with 65 categories consisting of four
significantly different domains: Artistic images (Ar), Clipart images (Cl),
Product images (Pr) and Real-World images (Rw). We can build possible twelve
transfer tasks and evaluate our method on all possible tasks.

Implementation Details. The base network for both the baseline and our method
is the ResNet-50 [He et al.(2016)He, Zhang, Ren, and Sun]. For domain
discriminator, we chose to use the architecture consisting of three fully
connected layers with dropout [Srivastava et al.(2014)Srivastava, Hinton,
Krizhevsky, Sutskever, and Salakhutdinov] and sigmoid layers. We fine-tuned
all feature layers $G_{f}$ pre-trained on the ImageNet dataset [Russakovsky et
al.(2015)Russakovsky, Deng, Su, Krause, Satheesh, Ma, Huang, Karpathy, Khosla,
Bernstein, et al.], following the standard settings for unsupervised domain
adaptation [Ganin and Lempitsky(2015), Long et al.(2017)Long, Zhu, Wang, and
Jordan, Long et al.(2018)Long, CAO, Wang, and Jordan]. The classifier layers
$C_{s}$, $C_{t}$ and the domain discriminator layers $G_{d}$ are trained from
the scratch via back-propagation. We set the learning rate of the feature
extractor ten times smaller than other layers. According to the learning rate
strategy employed in DANN [Ganin and Lempitsky(2015)], we utilized mini-batch
stochastic gradient descent (SGD) with momentum of 0.9 and the learning rate
adjusted by $\eta=\frac{\eta_{0}}{(1+\alpha p)^{\gamma}}$, where p is linearly
increasing from 0 to 1, $\alpha=10$, and $\gamma=0.75$. The total batch size
was set to 64, and we selected training samples for each stage in the mini-
batch ($D_{e},\>D_{m},\>D_{h}$) as follows: (64, 0, 0), (32, 32, 0), and (32,
16, 16) for the stage 1 to 3 in all our experiments. Additionally, we set
$\beta$ to $2$ or $3$ in Eq. (4) and margin $m$ to $2$ in Eq. (6).

###  4.2 Evaluation Results

We complied with standard evaluation protocols for unsupervised domain
adaptation [Ganin and Lempitsky(2015)] and used all source samples with labels
and all target samples without labels. For all tasks, we performed three
experiments and report the averaged results. We compare our methods with the
basic ResNet50 [He et al.(2016)He, Zhang, Ren, and Sun], DAN [Long et
al.(2015)Long, Cao, Wang, and Jordan], RTN [Long et al.(2016)Long, Zhu, Wang,
and Jordan], DANN [Ganin and Lempitsky(2015)], ADDA [Tzeng et al.(2017)Tzeng,
Hoffman, Saenko, and Darrell], JAN [Long et al.(2017)Long, Zhu, Wang, and
Jordan], GTA [Sankaranarayanan et al.(2018)Sankaranarayanan, Balaji, Castillo,
and Chellappa], CAN [Zhang et al.(2018)Zhang, Ouyang, Li, and Xu], and CDAN
[Long et al.(2018)Long, CAO, Wang, and Jordan]. All these methods are based on
ResNet50, and results of baselines are directly reported from original papers.

We report the classification accuracies of the networks in Table 2, Table 2,
and Table 3. Our proposed PCDA is comparable with the state-of-the-art methods
in that it achieves the best average accuracy on the three unsupervised domain
adaptation benchmarks.

Method | A$\rightarrow$W | D$\rightarrow$W | W$\rightarrow$D | A$\rightarrow$D | D$\rightarrow$A | W$\rightarrow$A | Avg
---|---|---|---|---|---|---|---
ResNet-50 [He et al.(2016)He, Zhang, Ren, and Sun] | 68.4$\pm$ 0.2 | 96.7$\pm$ 0.1 | 99.3$\pm$ 0.1 | 68.9$\pm$ 0.2 | 62.5$\pm$ 0.3 | 60.7$\pm$ 0.3 | 76.1
DAN [Long et al.(2015)Long, Cao, Wang, and Jordan] | 80.5$\pm$ 0.4 | 97.1$\pm$ 0.2 | 99.6$\pm$ 0.1 | 78.6$\pm$ 0.2 | 63.6$\pm$ 0.3 | 62.8$\pm$ 0.2 | 80.4
RTN [Long et al.(2016)Long, Zhu, Wang, and Jordan] | 84.5$\pm$ 0.2 | 96.8$\pm$ 0.1 | 99.4$\pm$ 0.1 | 77.5$\pm$ 0.3 | 66.2$\pm$ 0.2 | 64.8$\pm$ 0.3 | 81.6
DANN [Ganin and Lempitsky(2015)] | 82.0$\pm$ 0.4 | 96.9$\pm$ 0.2 | 99.1$\pm$ 0.1 | 79.7$\pm$ 0.4 | 68.2$\pm$ 0.4 | 67.4$\pm$ 0.5 | 82.2
ADDA [Tzeng et al.(2017)Tzeng, Hoffman, Saenko, and Darrell] | 86.2$\pm$ 0.5 | 96.2$\pm$ 0.3 | 98.4$\pm$ 0.3 | 77.8$\pm$ 0.3 | 69.5$\pm$ 0.4 | 68.9$\pm$ 0.5 | 82.9
JAN [Long et al.(2017)Long, Zhu, Wang, and Jordan] | 85.4$\pm$ 0.3 | 97.4$\pm$ 0.2 | 99.8$\pm$ 0.2 | 84.7$\pm$ 0.3 | 68.6$\pm$ 0.3 | 70.0$\pm$ 0.4 | 84.3
GTA [Sankaranarayanan et al.(2018)Sankaranarayanan, Balaji, Castillo, and Chellappa] | 89.5$\pm$ 0.5 | 97.9$\pm$ 0.3 | 99.8$\pm$ 0.4 | 87.7$\pm$ 0.5 | 72.8$\pm$ 0.3 | 71.4$\pm$ 0.4 | 86.5
CAN [Zhang et al.(2018)Zhang, Ouyang, Li, and Xu] | 92.5 | 98.8 | 100.0 | 90.1 | 72.1 | 69.9 | 87.2
CDAN [Long et al.(2018)Long, CAO, Wang, and Jordan] |  93.1$\pm$ 0.1 | 98.6$\pm$ 0.1 | 100.0$\pm$ 0.0 | 92.9$\pm$ 0.2 | 71.0$\pm$ 0.3 | 69.3$\pm$ 0.3 | 87.5
PCDA (ours, wo ECL) | 90.9$\pm$ 0.4 | 98.1$\pm$ 0.1 | 100.0$\pm$ 0 | 91.0$\pm$ 0.2 | 73.3$\pm$ 0.2 | 71.5$\pm$ 0.3 | 87.5
PCDA (ours) | 92.5$\pm$ 0.3 |  98.7$\pm$ 0.2 |  100.0$\pm$ 0 |  93.0$\pm$ 0.2 |  73.5$\pm$ 0.3 |  72.5$\pm$ 0.3 | 88.3

Table 1: Accuracy(%) on Office-31.

Method | I$\rightarrow$P | P$\rightarrow$I | I$\rightarrow$C | C$\rightarrow$I | C$\rightarrow$P | P$\rightarrow$C | Avg
---|---|---|---|---|---|---|---
ResNet-50 [He et al.(2016)He, Zhang, Ren, and Sun] | 74.8$\pm$0.3 | 83.9$\pm$0.1 | 91.5$\pm$0.3 | 78.0$\pm$0.2 | 65.5$\pm$0.3 | 91.2$\pm$0.3 | 80.7
DAN [Long et al.(2015)Long, Cao, Wang, and Jordan] | 74.5$\pm$0.4 | 82.2$\pm$0.2 | 92.8$\pm$0.2 | 86.3$\pm$0.4 | 69.2$\pm$0.4 | 89.8$\pm$0.4 | 82.5
DANN [Ganin and Lempitsky(2015)] | 75.0$\pm$0.6 | 86.0$\pm$0.3 | 96.2$\pm$0.4 | 87.0$\pm$0.5 | 74.3$\pm$0.5 | 91.5$\pm$0.6 | 85.0
JAN [Long et al.(2017)Long, Zhu, Wang, and Jordan] | 76.8$\pm$0.4 | 88.0$\pm$0.2 | 94.7$\pm$0.2 | 89.5$\pm$0.3 | 74.2$\pm$0.3 | 91.7$\pm$0.3 | 85.8
CAN [Zhang et al.(2018)Zhang, Ouyang, Li, and Xu] | 79.5 | 89.7 | 94.7 | 89.9 | 78.5 | 92.0 | 87.4
CDAN [Long et al.(2018)Long, CAO, Wang, and Jordan] | 78.3$\pm$0.3 | 91.2$\pm$0.2 | 96.7$\pm$0.3 |  91.2$\pm$0.3 | 77.2$\pm$0.2 | 93.7$\pm$0.3 | 88.1
PCDA (ours, wo ECL) | 78.2$\pm$0.2 | 91.0$\pm$0.3 | 96.5$\pm$0.5 | 90.0$\pm$0.3 | 70.8$\pm$0.3 | 96.0$\pm$0.3 | 87.1
PCDA (ours) |  80.2$\pm$0.2 |  92.5$\pm$0.3 |  96.7$\pm$0.3 | 90.3$\pm$0.1 | 75.2$\pm$0.3 |  97.0$\pm$0.1 | 88.7

Table 2: Accuracy(%) on imageCLEF-DA.

Method | Ar$\rightarrow$Cl | Ar$\rightarrow$Pr | Ar$\rightarrow$Rw | Cl$\rightarrow$Ar | Cl$\rightarrow$Pr | Cl$\rightarrow$Rw | Pr$\rightarrow$Ar | Pr$\rightarrow$Cl | Pr$\rightarrow$Rw | Rw$\rightarrow$Ar | Rw$\rightarrow$Cl | Rw$\rightarrow$Pr | Avg
---|---|---|---|---|---|---|---|---|---|---|---|---|---
ResNet-50 [He et al.(2016)He, Zhang, Ren, and Sun] | 34.9 | 50.0 | 58.0 | 37.4 | 41.9 | 46.2 | 38.5 | 31.2 | 60.4 | 53.9 | 41.2 | 59.9 | 46.1
DAN [Long et al.(2015)Long, Cao, Wang, and Jordan] | 43.6 | 57.0 | 67.9 | 45.8 | 56.5 | 60.4 | 44.0 | 43.6 | 67.7 | 63.1 | 51.5 | 74.3 | 56.3
DANN [Ganin and Lempitsky(2015)] | 45.6 | 59.3 | 70.1 | 47.0 | 58.5 | 60.9 | 46.1 | 43.7 | 68.5 | 63.2 | 51.8 | 76.8 | 57.6
JAN [Long et al.(2017)Long, Zhu, Wang, and Jordan] | 45.9 | 61.2 | 68.9 | 50.4 | 59.7 | 61.0 | 45.8 | 43.4 | 70.3 | 63.9 | 52.4 | 76.8 | 58.3
CDAN [Long et al.(2018)Long, CAO, Wang, and Jordan] | 50.6 | 65.9 | 73.4 | 55.7 | 62.7 | 64.2 | 51.8 | 49.1 | 74.5 | 68.2 | 56.9 | 80.7 | 62.8
PCDA (ours, wo ECL) | 50.7 | 72.2 | 78.3 | 57.2 | 68.0 | 71.0 | 54.6 | 52.4 | 78.3 | 67.2 | 54.0 | 80.8 | 65.4
PCDA (ours) | 50.8 | 73.7 | 78.5 | 58.6 | 70.4 | 71.2 | 53.9 | 53.5 | 79.0 | 65.6 | 53.6 | 80.2 | 65.8

Table 3: Accuracy(%) on Office-Home.

| A$\rightarrow$W | A$\rightarrow$D | D$\rightarrow$A | W$\rightarrow$A
---|---|---|---|---
$\beta$=1 | 87.8 | 89.4 | 70.8 | 71.0
$\beta$=2 | 90.3 | 89.0 | 73.3 | 71.5
$\beta$=3 | 90.9 | 91.0 | 70.9 | 71.1

Table 4: The effectiveness of $\beta$.

| D$\rightarrow$A | Ar$\rightarrow$Pr
---|---|---
$P$=2 | 70.5 | 47.6
$P$=3 | 73.5 | 50.8
$P$=4 | 72.8 | 51.3

Table 5: The effectiveness of $P$.

| D$\rightarrow$A | W$\rightarrow$A | I$\rightarrow$P | Cl$\rightarrow$Rw
---|---|---|---|---
Model-1 | 70.4 | 70.3 | 76.2 | 70.6
Model-2 | 71.8 | 71.4 | 77.3 | 71.0
Model-3 | 73.3 | 72.5 | 80.2 | 71.2

Table 6: Test accuracy of three different models.

###  4.3 Analysis

Ablation Study. We perform an ablation study to check the efficacy of each
component in our work. First of all, the above Tables 2, 2, and 3 show the
results of PCDA (wo ECL) and PCDA. PCDA (wo ECL) denotes our training method
without clustering constraint. The performance gap between PCDA and PCDA (wo
ECL) in Office31 and imageCLEF-DA demonstrate the effectiveness of the
clustering constraint. However, regarding Office-Home experiment, PCDA with
clustering constraint fails to enhance the classification performance in some
tasks such as Rw$\rightarrow$Cl and Rw$\rightarrow$Ar. This is presumably
because the training method does not have sufficient mini-batch size to
guarantee that similar pairs are somewhat sampled.

Hyperparameter Study. Our approach sets the hyperparameter $\beta$ to learn
domain-invariant features from newly added target samples. If $\beta$ is one,
our loss function for adversarial adaptation learning becomes equivalent to
DANN’s loss function in Eq. (1). We used the Office-31 dataset to validate the
effectiveness of $\beta$ in Table 6. When $\beta$ is one, the performance of
our training process degrades. In contrast, when we set $\beta$ between 2 or
3, our method achieves better performance. This results prove our assumption
that the weight $\beta$ helps the network to extract domain invariant features
for the newly added target samples.

The number of clusters $P$ is important hyperparameter for our pseudo-labeling
curriculum. When $P$ is set to 4, We observe that most tasks in Office-Home
shows performance improvement, while some tasks in Office-31 present the
performance degradation shown in Table 6. This is because large $P$ is
effective to improve models that tend to generate relatively many incorrect
pseudo-labels for target samples. On the contrary, large $P$ may not be
helpful to enhance the capability of models which already show good
performance on target data. We set $P$ to 3 because the pseudo-labeling
curriculum becomes simple to implement and achieves the best performance on
all benchmarks.

(a) Easy samples $D_{e}$

(b) Moderate samples $D_{m}$

(c) Hard samples $D_{h}$

(d) All target samples $D_{\mathcal{T}}$

Figure 3: T-SNE visualization of features from easy, moderate, and hard
samples by using our PCDA method on the D$\rightarrow$A task.

(a) DANN (D$\rightarrow$A)

(b) PCDA (D$\rightarrow$A)

(c) Test accuracy ($W\rightarrow A$)

(d) Test accuracy ($D\rightarrow A$)

Figure 4: On $D\rightarrow A$ task, (a) and (b) are T-SNE visualization of
features. Red points are source samples and blue are target samples. (c) and
(d) shows the comparison of test accuracy and pseudo-labeling accuracy. Red
line, blue and green are the pseudo-labeling accuracy of easy, moderate and
hard target samples at every epoch. Black line is test accuracy of PCDA over
the training epochs. The red vertical dotted line indicates the training epoch
when the target data subset $D_{e}$ is added for training our model. The green
and blue vertical dotted lines are training epochs for adding $D_{m}$ and
$D_{h}$.

Feature Visualization. To have an intuitive understanding of PCDA for domain
adaptation, we visualize the target representations of the easy, moderate, and
hard samples from the feature extractor $G_{f}$ using t-SNE embedding [Maaten
and Hinton(2008)] on the difficult D$\rightarrow$A task. In Fig. 3(a), we can
observe that the features of the easy samples in each category are tightly
clustered and distinguishable from samples in the different categories. In
contrast, those of the hard samples in each category are dispersed in Fig.
3(c). Since PCDA is developed from DANN, it is necessary to confirm whether
the proposed model generates target discriminative features compared to DANN.
We visualize the both source and target features of DANN and PCDA in Fig. 4(a)
and Fig. 4(b). Compared with the features obtained by DANN (Fig. 4(a)), Fig.
4(b) indicates that PCDA learns more category-level discriminative features.
The result corroborates the efficacy of our approach.

Effectiveness of Curriculum. To verify the effectiveness of pseudo-labeling
curriculum, we evaluate three models for the comparison. We further
investigated Model-1 trained by only using the easy data subset $D_{e}$,
Model-2 trained by using $D_{e}$ and the moderate data subset $D_{m}$ with a
2-subset curriculum, and Model-3 trained by using $D_{e}$, $D_{m}$, and
$D_{h}$ with a 3-subset curriculum. Model-3 is equivalent to our proposed
PCDA. In Table 6, Model-3 outperforms other methods through most tasks.
Although $D_{h}$ is more likely to have false pseudo-labels, utilizing $D_{h}$
is helpful for improving the test accuracies in most cases. It implies that
the pseudo-labeling curriculum suppresses the adverse effects of the target
samples with false pseudo-labels in most tasks. This table proves that our
proposed method benefits the performance. However, regarding some challenging
tasks in the Office-Home dataset such as $Rw\rightarrow Cl$ or $Pr\rightarrow
Ar$, the usage of $D_{h}$ slightly degrades the performance due to the
excessive number of false-labeled target samples. Thus, if the target specific
network $C_{t}$ still provides too many false pseudo-labels for $D_{h}$, the
effect of the pseudo-labeling curriculum degrades.

We report the test accuracy and pseudo-labeling accuracy in Fig. 4(c) and Fig.
4(d). The pseudo-labeling accuracy indicates whether pseudo-labels are
assigned correctly. The test accuracy of our method is increasing when we give
new additional target samples with pseudo-labels such as $D_{m}$ or $D_{h}$.
These accord with our previous results in Table 6 in that supplementing target
samples with generated pseudo-labels is effectual to boost the performance. We
observe that the reliability of the generated pseudo-labels is improved
iteratively as training proceeds. This proves that our training scheme with
pseudo-labeling curriculum progressively improves the capability of our
network to generate pseudo-labels and leads to better predictions. Moreover,
the pseudo-labeling accuracies of easy samples are higher than those of both
the moderate and hard samples in Fig. 4(c) and Fig. 4(d). Also, the pseudo-
labeling accuracies of the moderate samples are higher than those of hard
samples. These experimental results provide support for our main assumption
that target samples with high density values are highly likely to have correct
pseudo-labels. We confirm that this assumption is valid for all our
experiments including Fig. 4(c) and Fig. 4(d).

##  5 Conclusion

We have proposed a novel learning scheme for unsupervised domain adaptation
with the pseudo-labeling curriculum. Different from the existing works that
exploit pseudo-labeled target samples, our method is robust to the adverse
effect of false pseudo-labeled target samples due to the pseudo-labeling
curriculum. The proposed method enables our model to generate reliable pseudo-
labels progressively, and then the target specific network is able to learn
target discriminative features. Furthermore, we introduce the clustering
constraint on creating target features to improve the performance. Our
approach surpasses the state-of-the-art classification results on three
benchmarks. We also provide extensive analysis to validate the effectiveness
of our method by utilizing visualization results and various ablation studies.

## References

  * [Ben-David et al.(2010)Ben-David, Blitzer, Crammer, Kulesza, Pereira, and Vaughan] Shai Ben-David, John Blitzer, Koby Crammer, Alex Kulesza, Fernando Pereira, and Jennifer Wortman Vaughan.  A theory of learning from different domains.  _Machine learning_ , 79(1-2):151–175, 2010.
  * [Bengio et al.(2009)Bengio, Louradour, Collobert, and Weston] Yoshua Bengio, Jérôme Louradour, Ronan Collobert, and Jason Weston.  Curriculum learning.  In _Proceedings of the 26th annual international conference on machine learning_ , pages 41–48. ACM, 2009.
  * [Bousmalis et al.(2016)Bousmalis, Trigeorgis, Silberman, Krishnan, and Erhan] Konstantinos Bousmalis, George Trigeorgis, Nathan Silberman, Dilip Krishnan, and Dumitru Erhan.  Domain separation networks.  In _Advances in Neural Information Processing Systems_ , pages 343–351, 2016.
  * [Chen et al.(2018)Chen, Li, Sakaridis, Dai, and Van Gool] Yuhua Chen, Wen Li, Christos Sakaridis, Dengxin Dai, and Luc Van Gool.  Domain adaptive faster r-cnn for object detection in the wild.  In _Proceedings of the IEEE conference on computer vision and pattern recognition_ , pages 3339–3348, 2018.
  * [Chopra et al.(2005)Chopra, Hadsell, and LeCun] Sumit Chopra, Raia Hadsell, and Yann LeCun.  Learning a similarity metric discriminatively, with application to face verification.  In _Computer Vision and Pattern Recognition, 2005. CVPR 2005. IEEE Computer Society Conference on_ , volume 1, pages 539–546. IEEE, 2005.
  * [French et al.(2018)French, Mackiewicz, and Fisher] Geoff French, Michal Mackiewicz, and Mark Fisher.  Self-ensembling for visual domain adaptation.  In _International Conference on Learning Representations_ , 2018.  URL https://openreview.net/forum?id=rkpoTaxA-.
  * [Ganin and Lempitsky(2015)] Yaroslav Ganin and Victor Lempitsky.  Unsupervised domain adaptation by backpropagation.  In _International Conference on Machine Learning_ , pages 1180–1189, 2015.
  * [Goodfellow et al.(2014)Goodfellow, Pouget-Abadie, Mirza, Xu, Warde-Farley, Ozair, Courville, and Bengio] Ian Goodfellow, Jean Pouget-Abadie, Mehdi Mirza, Bing Xu, David Warde-Farley, Sherjil Ozair, Aaron Courville, and Yoshua Bengio.  Generative adversarial nets.  In _Advances in neural information processing systems_ , pages 2672–2680, 2014.
  * [Guo et al.(2018)Guo, Huang, Zhang, Zhuang, Dong, Scott, and Huang] Sheng Guo, Weilin Huang, Haozhi Zhang, Chenfan Zhuang, Dengke Dong, Matthew R. Scott, and Dinglong Huang.  Curriculumnet: Weakly supervised learning from large-scale web images.  In _The European Conference on Computer Vision (ECCV)_ , September 2018.
  * [He et al.(2016)He, Zhang, Ren, and Sun] Kaiming He, Xiangyu Zhang, Shaoqing Ren, and Jian Sun.  Deep residual learning for image recognition.  In _Proceedings of the IEEE conference on computer vision and pattern recognition_ , pages 770–778, 2016.
  * [Hoffman et al.(2016)Hoffman, Wang, Yu, and Darrell] Judy Hoffman, Dequan Wang, Fisher Yu, and Trevor Darrell.  Fcns in the wild: Pixel-level adversarial and constraint-based adaptation.  _arXiv preprint arXiv:1612.02649_ , 2016.
  * [Jiang et al.(2018)Jiang, Zhou, Leung, Li, and Fei-Fei] Lu Jiang, Zhengyuan Zhou, Thomas Leung, Li-Jia Li, and Li Fei-Fei.  Mentornet: Learning data-driven curriculum for very deep neural networks on corrupted labels.  In _International Conference on Machine Learning_ , pages 2309–2318, 2018.
  * [Kim et al.(2019)Kim, Jeong, Kim, Choi, and Kim] Taekyung Kim, Minki Jeong, Seunghyeon Kim, Seokeon Choi, and Changick Kim.  Diversify and match: A domain adaptive representation learning paradigm for object detection.  In _The IEEE Conference on Computer Vision and Pattern Recognition (CVPR)_ , June 2019.
  * [Kumar et al.(2010)Kumar, Packer, and Koller] M Pawan Kumar, Benjamin Packer, and Daphne Koller.  Self-paced learning for latent variable models.  In _Advances in Neural Information Processing Systems_ , pages 1189–1197, 2010.
  * [Lee(2013)] Dong-Hyun Lee.  Pseudo-label: The simple and efficient semi-supervised learning method for deep neural networks.  In _Workshop on Challenges in Representation Learning, ICML_ , volume 3, page 2, 2013.
  * [Lin et al.(2018)Lin, Wang, Meng, Zuo, and Zhang] Liang Lin, Keze Wang, Deyu Meng, Wangmeng Zuo, and Lei Zhang.  Active self-paced learning for cost-effective and progressive face identification.  _IEEE transactions on pattern analysis and machine intelligence_ , 40(1):7–19, 2018.
  * [Long et al.(2015)Long, Cao, Wang, and Jordan] Mingsheng Long, Yue Cao, Jianmin Wang, and Michael Jordan.  Learning transferable features with deep adaptation networks.  In _Proceedings of the 32nd International Conference on Machine Learning_ , pages 97–105, 2015.
  * [Long et al.(2016)Long, Zhu, Wang, and Jordan] Mingsheng Long, Han Zhu, Jianmin Wang, and Michael I Jordan.  Unsupervised domain adaptation with residual transfer networks.  In _Advances in Neural Information Processing Systems_ , pages 136–144, 2016.
  * [Long et al.(2017)Long, Zhu, Wang, and Jordan] Mingsheng Long, Han Zhu, Jianmin Wang, and Michael I. Jordan.  Deep transfer learning with joint adaptation networks.  In _Proceedings of the 34th International Conference on Machine Learning_ , pages 2208–2217, 2017.
  * [Long et al.(2018)Long, CAO, Wang, and Jordan] Mingsheng Long, ZHANGJIE CAO, Jianmin Wang, and Michael I Jordan.  Conditional adversarial domain adaptation.  In S. Bengio, H. Wallach, H. Larochelle, K. Grauman, N. Cesa-Bianchi, and R. Garnett, editors, _Advances in Neural Information Processing Systems 31_ , pages 1647–1657. Curran Associates, Inc., 2018.
  * [Maaten and Hinton(2008)] Laurens van der Maaten and Geoffrey Hinton.  Visualizing data using t-sne.  _Journal of machine learning research_ , 9(Nov):2579–2605, 2008.
  * [Nath Kundu et al.(2018)Nath Kundu, Krishna Uppala, Pahuja, and Venkatesh Babu] Jogendra Nath Kundu, Phani Krishna Uppala, Anuj Pahuja, and R Venkatesh Babu.  Adadepth: Unsupervised content congruent adaptation for depth estimation.  In _Proceedings of the IEEE Conference on Computer Vision and Pattern Recognition_ , pages 2656–2665, 2018.
  * [Pei et al.(2018)Pei, Cao, Long, and Wang] Zhongyi Pei, Zhangjie Cao, Mingsheng Long, and Jianmin Wang.  Multi-adversarial domain adaptation.  In _AAAI Conference on Artificial Intelligence_ , 2018.
  * [Russakovsky et al.(2015)Russakovsky, Deng, Su, Krause, Satheesh, Ma, Huang, Karpathy, Khosla, Bernstein, et al.] Olga Russakovsky, Jia Deng, Hao Su, Jonathan Krause, Sanjeev Satheesh, Sean Ma, Zhiheng Huang, Andrej Karpathy, Aditya Khosla, Michael Bernstein, et al.  Imagenet large scale visual recognition challenge.  _International journal of computer vision_ , 115(3):211–252, 2015.
  * [Saenko et al.(2010)Saenko, Kulis, Fritz, and Darrell] Kate Saenko, Brian Kulis, Mario Fritz, and Trevor Darrell.  Adapting visual category models to new domains.  In _European conference on computer vision_ , pages 213–226. Springer, 2010.
  * [Saito et al.(2017)Saito, Ushiku, and Harada] Kuniaki Saito, Yoshitaka Ushiku, and Tatsuya Harada.  Asymmetric tri-training for unsupervised domain adaptation.  In _International Conference on Machine Learning_ , pages 2988–2997, 2017.
  * [Saito et al.(2018)Saito, Watanabe, Ushiku, and Harada] Kuniaki Saito, Kohei Watanabe, Yoshitaka Ushiku, and Tatsuya Harada.  Maximum classifier discrepancy for unsupervised domain adaptation.  In _The IEEE Conference on Computer Vision and Pattern Recognition (CVPR)_ , June 2018.
  * [Sankaranarayanan et al.(2018)Sankaranarayanan, Balaji, Castillo, and Chellappa] Swami Sankaranarayanan, Yogesh Balaji, Carlos D. Castillo, and Rama Chellappa.  Generate to adapt: Aligning domains using generative adversarial networks.  In _The IEEE Conference on Computer Vision and Pattern Recognition (CVPR)_ , June 2018.
  * [Schroff et al.(2015)Schroff, Kalenichenko, and Philbin] Florian Schroff, Dmitry Kalenichenko, and James Philbin.  Facenet: A unified embedding for face recognition and clustering.  In _Proceedings of the IEEE conference on computer vision and pattern recognition_ , pages 815–823, 2015.
  * [Sener et al.(2016)Sener, Song, Saxena, and Savarese] Ozan Sener, Hyun Oh Song, Ashutosh Saxena, and Silvio Savarese.  Learning transferrable representations for unsupervised domain adaptation.  In _Advances in Neural Information Processing Systems_ , pages 2110–2118, 2016.
  * [Shimodaira(2000)] Hidetoshi Shimodaira.  Improving predictive inference under covariate shift by weighting the log-likelihood function.  _Journal of statistical planning and inference_ , 90(2):227–244, 2000.
  * [Shu et al.(2018)Shu, Bui, Narui, and Ermon] Rui Shu, Hung Bui, Hirokazu Narui, and Stefano Ermon.  A DIRT-t approach to unsupervised domain adaptation.  In _International Conference on Learning Representations_ , 2018.
  * [Srivastava et al.(2014)Srivastava, Hinton, Krizhevsky, Sutskever, and Salakhutdinov] Nitish Srivastava, Geoffrey Hinton, Alex Krizhevsky, Ilya Sutskever, and Ruslan Salakhutdinov.  Dropout: a simple way to prevent neural networks from overfitting.  _The Journal of Machine Learning Research_ , 15(1):1929–1958, 2014.
  * [Tarvainen and Valpola(2017)] Antti Tarvainen and Harri Valpola.  Mean teachers are better role models: Weight-averaged consistency targets improve semi-supervised deep learning results.  In _Advances in neural information processing systems_ , pages 1195–1204, 2017.
  * [Tsai et al.(2018)Tsai, Hung, Schulter, Sohn, Yang, and Chandraker] Yi-Hsuan Tsai, Wei-Chih Hung, Samuel Schulter, Kihyuk Sohn, Ming-Hsuan Yang, and Manmohan Chandraker.  Learning to adapt structured output space for semantic segmentation.  In _Proceedings of the IEEE Conference on Computer Vision and Pattern Recognition_ , pages 7472–7481, 2018.
  * [Tzeng et al.(2017)Tzeng, Hoffman, Saenko, and Darrell] Eric Tzeng, Judy Hoffman, Kate Saenko, and Trevor Darrell.  Adversarial discriminative domain adaptation.  In _Computer Vision and Pattern Recognition (CVPR)_ , volume 1, page 4, 2017.
  * [Venkateswara et al.(2017)Venkateswara, Eusebio, Chakraborty, and Panchanathan] Hemanth Venkateswara, Jose Eusebio, Shayok Chakraborty, and Sethuraman Panchanathan.  Deep hashing network for unsupervised domain adaptation.  In _Computer Vision and Pattern Recognition (CVPR), 2017 IEEE Conference on_ , pages 5385–5394. IEEE, 2017.
  * [Xie et al.(2018)Xie, Zheng, Chen, and Chen] Shaoan Xie, Zibin Zheng, Liang Chen, and Chuan Chen.  Learning semantic representations for unsupervised domain adaptation.  In _International Conference on Machine Learning_ , pages 5419–5428, 2018.
  * [Zhang et al.(2018)Zhang, Ouyang, Li, and Xu] Weichen Zhang, Wanli Ouyang, Wen Li, and Dong Xu.  Collaborative and adversarial network for unsupervised domain adaptation.  In _Proceedings of the IEEE Conference on Computer Vision and Pattern Recognition_ , pages 3801–3809, 2018.