# Fair Visual Recognition via Intervention with Proxy Features

Yi Zhang,1 Jitao Sang,1 Junyang Wang1

###### Abstract

Deep learning models often learn to make predictions that rely on sensitive
social attributes like gender and race, which poses significant fairness
risks, especially in societal applications, e.g., hiring, banking, and
criminal justice. Existing work tackles this issue by minimizing information
about social attributes in models for debiasing. However, the high correlation
between target task and social attributes makes bias mitigation incompatible
with target task accuracy. Recalling that model bias arises because the
learning of features in regard to bias attributes (i.e., bias features) helps
target task optimization, we explore the following research question: _Can we
leverage proxy features to replace the role of bias feature in target task
optimization for debiasing?_ To this end, we propose _Proxy Debiasing_ , to
first transfer the target task’s learning of bias information from bias
features to artificial proxy features, and then employ causal intervention to
eliminate proxy features in inference. The key idea of _Proxy Debiasing_ is to
design controllable proxy features to on one hand replace bias features in
contributing to target task during the training stage, and on the other hand
easily to be removed by intervention during the inference stage. This
guarantees the elimination of bias features without affecting the target
information, thus addressing the fairness-accuracy paradox in previous
debiasing solutions. We apply _Proxy Debiasing_ to several benchmark datasets,
and achieve significant improvements over the state-of-the-art debiasing
methods in both of accuracy and fairness.

## Introduction

Figure 1: Illustration of the algorithmic bias problem, conventional debiasing
method (Adversarial Debiasing) and the proposed proxy debiasing. Adversarial
Debiasing method potentially removes partial target features in removing bias
features, while our method uses proxy features to replace bias feature in
learning of target task, which avoids unwittingly harming target features.

Machine learning algorithms have achieved notable progress nowadays, and are
increasingly being deployed in sensitive/high-stake environments to make
important and life-changing decision, such as hiring, criminal justice,
banking. Nevertheless, there is growing evidence (Buolamwini and Gebru 2018;
Wang et al. 2019a; Grother, Ngan, and Hanaoka 2019) that state-of-the-art
models can perform potential discrimination based on bias attributes like
gender and race, e.g., the popular COMPAS algorithm for recidivism prediction
was found biased against black inmates and prone to make unfair sentencing
decisions (Lagioia, Rovatti, and Sartor 2022). These ethical issues have
sparked a lot of research into fair machine learning.

Recent studies (Locatello et al. 2019; Creager et al. 2019) realized that
learning bias features (e.g., gender features) is one of the key factors
causing unfairness. As shown in the first row in Figure 1, models with
standard learning inherit biased patterns in training data, and the learned
decision rules thus depend on both target and bias features. This realization
spawned a lot of works to prevent models from learning bias features. Towards
this goal, the most direct method (d’Alessandro, O’Neil, and LaGatta 2017)
removes bias features from the training data (e.g., directly removing all
information about gender). However, this only works for structured data and
not for visual data, because the target features and bias features in the
sample are tightly entangled. In visual recognition, popular bias mitigation
methods (Raff and Sylvester 2018; Kim et al. 2019; Jung et al. 2021) employ
regularization terms to train models not to encode bias features of samples.
Typical approaches, such as Adversarial Debiasing, adversarially train models
to discriminate target attribute labels but fail to discriminate bias
attribute labels. These works remove bias features in data representation,
therefore enhancing output invariance to bias attribute. However, since target
features and bias features have strong correlations in biased training data,
these methods potentially remove partial target features and cause accuracy
degradation in debiasing (cf., Figure 1). Also due to this correlation,
solving the target task inevitably promotes the representation of bias
features, leading to limited debiasing effects. This zero-sum game between
target task learning and debiasing task leads to the fairness-accuracy
paradox.

In this paper, we aim to address the incompatibility between fairness and
accuracy in debiasing. To this end, we introduce _Proxy Debiasing_ that
eliminates model bias without destroying the information of the target task.
As illustrated in Figure 1, the key idea of _Proxy Debiasing_ is to use the
artificial proxy features to replace the model’s dependence on bias features
in target task learning. The basic premise that the proxy feature can act as a
proxy for the bias feature is that the proxy feature distribution should be
consistent with the bias feature. To the end, we attach corresponding proxy
features to samples with different bias attributes to satisfy distribution
consistency, e.g., _male_ sample and _female_ sample are respectively attached
with different proxy features in training, as shown in Figure 4. Then, to
eliminate the influence of proxy features on inference stage, we replace proxy
features with intervention features based on causal intervention. Note that we
do not need any prior information of sample, i.e., the intervention features
imposed on all samples are the same.

We also conducted proxy effect analysis and reached a concluding observation:
the model does not naturally learn bias information entirely from proxy
features, and still learns bias information from bias features, which results
in the inability to completely eliminate bias. To solve this issue, we propose
to maximize the contribution of proxy features to the target task to enhance
the proxy effect of proxy features on bias features in the training of target
task, which we call _Active Proxy Debiasing_. For the contribution of proxy
features, we borrow the idea of counterfactual explanations to measure.
Avoiding the zero-sum game between debiasing and target task learning in
previous methods, our proxy debiasing method improves over previous methods on
both fairness and accuracy.

We summarize our main contributions as follows:

  * •

We propose a novel debiasing method _Proxy Debiasing_ that employ proxy
features to replace bias features in the target task’s learning of bias
information, which avoids the competition between target task and debias task
in previous methods.

  * •

We introduce proxy effect enhancement that actively enhances the contribution
of proxy features to the target task to improve the proxy effect of proxy
features on bias features.

  * •

Extensive experiments demonstrate that our method significantly improves over
baselines on both accuracy and fairness. The effectiveness on debiasing
multiple bias attributes is also verified.

Figure 2: The causal graph of the proposed model. (a) The output $T$ of biased
model is directly affected by the target feature $X_{T}$ and bias feature
$X_{B}$ in input $X$. The training and inference stage of _Proxy Debiasing_
are illustrated in (b) and (c), respectively.

## Related Work

Bias mitigation. Existing bias mitigation methods can be roughly divided into
three families depending on the training pipelines they are applied to: pre-
processing methods (Louizos et al. 2015; Quadrianto, Sharmanska, and Thomas
2019) refine dataset to mitigate the source of unfairness before training; in-
processing methods (Elkan 2001; Jiang and Nachum 2020) introduce fairness
constraints into the training process; and post-processing methods (Kamiran,
Karim, and Zhang 2012; Pleiss et al. 2017) adjust the prediction of models
according to fairness criterion after training. Among them, in-processing
methods have been the most studied due to no data recollection burden and
significant accuracy drop.

Typical in-processing researches employ additional fairness constraint as
regularization term for mitigating bias. (Zhang, Lemoine, and Mitchell 2018;
Wang et al. 2019b) enforce the model to produce fair outputs with adversarial
training techniques by minimizing the ability of a discriminator to predict
the bias attribute. (Kim et al. 2019) further minimizes the mutual information
between representation and bias attributes to eliminate their correlations for
debiasing. (Tartaglione, Barbano, and Grangetto 2021) devises a regularization
term with a triplet loss formulation to minimize the entanglement of bias
features. (Jung et al. 2021) tries to distill fair knowledge by enforcing the
representation of student model to get close to that of the teacher model
averaged over the bias attributes. However, the high correlation between
target task and bias attributes that exist in the data itself leads to the
limited accuracy in debiasing. Meanwhile, some methods try to convert the
target task to not actively extract bias information. (Wang et al. 2020b)
trains different target models separately for each group in terms of bias
attributes so that the target task does not attempt to rely on bias features.
(Du et al. 2021) trains classification head with neutralized representations,
which discourages the classification head from capturing the undesirable
correlation between target and bias information. However, these methods still
suffer from fairness-accuracy paradox due to the bias in the data itself. In
this paper, our method leverages artifacts features to proxy the bias feature
in data itself for unraveling the fairness-accuracy paradox.

Proxy features. (Arpit et al. 2017) finds that models tend to learn features
of easy patterns to proxy features of complex patterns in the data.
Furthermore, the underlying mechanism of Shortcut (Geirhos et al. 2020) can be
seen as shortcut features proxying the intended features that humans want the
model to use. Inspired by this, we propose the concept of _proxy feature_ that
actively replaces essence-related features with essence-independent features
in model learning.

Figure 3: Framework of Proxy Debiasing. Active Proxy Debiasing contains
additional proxy effect enhancement module (highlighted with red dash line) to
Naive Proxy Debiasing.

Causal intervention. Causal intervention has been widely used across many
tasks to improve the robustness of deep learning models. Backdoor adjustment
(Pearl 2014) is one of the most widely used implementations of causal
intervention. (Yue et al. 2020; Zhang et al. 2020) leverage backdoor
adjustment for eliminating the confounding factor in few-shot classification
and weakly supervised segmentation. (Wang et al. 2020a) employs backdoor
adjustment to train feature extractors with commonsense knowledge. Unlike
existing work that applies causal intervention in the training phase, we apply
causal intervention in the inference phase to remove the influence of proxy
features.

## Methodology

Visual recognition models, which are expected to only rely on target feature
$X_{T}$ of the input $X$, are susceptible to making predictions based on the
bias features $X_{B}$ of the data $X$, as illustrated in Figure 2(a). We aim
to eliminate the model’s dependence on $X_{B}$, i.e., the model output $T$ is
independent of the bias features $X_{B}$, and prevent useful target features
$X_{T}$ from being unintentionally corrupted in debiasing.

Inspired by (Arpit et al. 2017), it is observed that among multiple features
containing the same information, the model may only learn partial features,
such as features with simple patterns. We propose a _Proxy Debiasing_ method
that performs debiasing in two stages: (1) Guide the model to preferentially
use proxy features $P$ with simple patterns to learn bias information in
target task training learning, so the model no longer needs to pay attention
to bias features$X_{B}$ (cf., Figure 2(b)); (2) Introduce causal intervention
mechanism in testing to eliminate the influence of proxy features on output
$T$ (cf., Figure 2(c)).

The direct way to realize _Proxy Debiasing_ is to attach pre-defined proxy
features with simple patterns to original features, and the model then learns
from this composite feature (see Figure 3). This leads to the basic version of
our solution, which we call _Naive Proxy Debiasing_ and will be introduced in
the next subsection. However, subsequent analysis shows that proxy features
with simple patterns do not naturally replace bias features. To ensure the
proxy effect of proxy features, we further propose to enhance the target
task’s attention to proxy features, which we call _Active Proxy Debiasing_ and
as a complete version of our solution.

Figure 4: Examples of Naive Proxy Debiasing for gender debiasing. In training,
images of different genders are assigned different proxy features, while all
images are assigned the same intervention feature in testing.

### Naive Proxy Debiasing

Training with proxy features. In fair visual recognition problem, input $x\in
X$ is given two types of labels: target task attribute $t\in T$ and bias
attribute $b\in B$.

The premise of realizing proxying to bias features $X_{B}$ is that the proxy
features $P$ should provide the same bias information as the bias features. To
this end, we construct proxy features that are consistent with the
distribution of bias features. As illustrated in Figure 4, due to the simple
pattern is easy to learn, we preset all zeros or all ones vector as proxy
features, and then utilize bias attribute label $b$ to select the
corresponding proxy feature $p_{b}\in P$ and append it to the feature
representation of the sample $x$.

Then, we train the target task in this composite data:

$\min L_{\text{target}}(\\{{x},p_{b}\\},t)$ (1)

Where $\\{{x},p_{b}\\}$ is the model input that composite image $x$ and proxy
feature $P_{b}$, $t$ is the target task label of $x$.

Inference with intervention feature. Then, the dependence of trained models on
bias information is based on proxy features $P$ rather than bias features
$X_{B}$. However, as shown in Figure 2, this introduces $P$ as a new source of
bias in model inference:

$Pr(T\mid X)=Pr(T\mid X_{T},P)$ (2)

And now, we need to remove the model bias brought about by proxy features $P$
in testing. Inspired by causal intervention use _Do_ operation to exclude the
influence of confounder, we employ _Do_ operation to eliminate the effect of
$P$ in the inference stage. Toward this, using the _do_ to prevent the
introduction of causal effects of $P$ to $T$, the causal effects of target
features $X_{T}$ to model output $T$ can be derived:

$Pr(T\mid do(X_{T}))=\sum_{b}Pr(T\mid X_{T},p_{b})Pr(p_{b})$ (3)

Where $p_{b}$ is proxy feature corresponding to bias labels $b$. The
underlying mechanism of _Do_ is to force $X_{T}$ to incorporate every $p_{b}$
fairly, subject to its prior $Pr(p_{b})$. For low computation cost in testing,
we replace $\sum_{b}Pr(Y\mid X_{T},P_{b})Pr(x_{b})$ with $Pr(Y\mid
X_{T},\mathbb{E}_{\bm{b}}\left[p_{b}\right])$ due to NWGM linear approximation
proved in (Xu et al. 2015):

$Pr(Y\mid do(X_{T}))=Pr(Y\mid X_{T},\mathbb{E}_{\bm{b}}\left[p_{b}\right]))$
(4)

Where $\mathbb{E}_{\bm{b}}\left[p_{b}\right]$ is mathematical expectation of
$p_{b}$ subject to $b$, i.e., the mean of $p_{\bm{male}}$, and is called
intervention feature.

Finally, we use intervention feature $\mathbb{E}_{\bm{b}}\left[p_{b}\right]$
to instead specific proxy features $p_{b}$ in inference. As shown in Figure 4,
We use a vector of all 0.5. Note that another benefit of using intervention
features is that we do not need to know the bias label of samples in
inference.

Task | Method | Acc.($\uparrow$) | Bias($\downarrow$) | Counter@P
---|---|---|---|---
Blonde | Vanilla | 78.76 | 40.82 | -
Naive PD |  91.53(+12.77) |  10.09(-30.73) | 0.26
Attractive | Vanilla | 76.71 | 26.09 | -
Naive PD |  77.25(+0.54) |  24.06(-2.03) | 0.01

Table 1: The accuracy(in $\%$), model bias (described in Sec.4) and
Counter@$P$ of Naive Proxy Debiasing (Naive PD).

### Analysis of the Proxy Features

Taking face attribute recognition in CelebA (Liu et al. 2015) as an example,
we examine the gender debiasing performance of Naive Proxy Debiasing on Blonde
and Attractive recognition tasks. As shown in Table 1, compared to vanilla, we
improve both fairness (lower model bias) and accuracy. However, neither model
bias nor accuracy changes significantly in attractive recognition.

Since we use the same configuration for both tasks, we conjecture that the
reason for the above inconsistency in the two tasks might lie in the
differences in the two tasks learning of proxy features. To test that, we look
into the effect of proxy features on model output using counterfactual
contrast, i.e., how the change of proxy features in test samples influences
the model’s decision-making:

$Counter_{p}=\mathbb{E}_{i}\left|P(Y\mid x_{i},p_{\bm{male}})-P(Y\mid
x_{i},p_{\bm{female}})\right|$ (5)

As reported in Table 1, we note that in Naive Proxy Debaisng, for poor
debiasing performance task (Attractive), the model has no significant
dependence on proxy features(lower $Counter_{p}$). However, high debiasing
performance task (Blonde) achieves significantly high $Counter_{p}$. This
depicts that models do not always learn the simple pattern proxy features
preferentially, even prioritizing learning of bias features, and therefore the
proxy features $P$ cannot replace the model’s reliance on bias features
$X_{B}$.

### Active Proxy Debiasing

The above observations suggest that simple proxy features may be trivial to
target task, we propose _Active Proxy Debiasing_ that adds additional Proxy
Effect Enhancement module (red dash line in Figure 3) to _Naive Proxy
Debiasing_.

To this end, we guide the model actively to learn bias information from proxy
features during target task training (Eq. 1) so that the target task does not
need to focus on bias features $X_{b}$.

Specifically, instead of using preset proxy features, we use trainable proxy
features to better satisfy the model’s reliance on bias information in proxy
features. Then, we borrow and revise the feature attribution strategy of
counterfactual analysis (Lang et al. 2021; Zhang, Wang, and Sang 2022) to
measure the importance of proxy features by counterfactually changing the
proxy features:

$\alpha^{c}=Y_{c}(x,p_{{b}})-Y_{c}(x,anchor)$ (6)

Where $\alpha^{c}$ indicates the importance of proxy features to target class
$c$ (e.g., attractive or non-attractive), $Y_{c}(\cdot)$ denotes the logit
output corresponding to class $c$, $p$ is the trainable proxy features
corresponding to bias label $b$ of $x$. The $anchor$ is the preset
counterfactual contrast point by randomly initializing, which is used as the
counterfactual feature of $p$.

To reinforce the importance of proxy features for the model, we update proxy
features $P$ and target task head $h$ to maximize the importance of proxy
features with softmax normalization:

$\mathop{max}\limits_{P,h}\frac{\exp\left(\alpha^{t}\right)}{\sum_{c=1}^{C}\exp\left(\alpha^{c}\right)}$
(7)

Where $t$ is the target label of input $x$. By iteratively optimizing Eq. 1
and Eq. 7, the trainable proxy features $P$ are guaranteed to continuously
hold the proxy effect to bias feature $X_{b}$.

Algorithm 1 Active Proxy Debiasing (Active PD)

Input: Training set $\mathcal{D}=\\{(x_{k},t_{k},b_{k})\\}_{k=1}^{D}$, the
dimension of proxy features $\mathcal{M}$, the number of bias classes
$\mathcal{N}$

Output: Fair model

1: Initialization: Model parameter $\theta$, $\mathcal{N}$
$\mathcal{M}$-dimensional trainable proxy features $P$, one
$\mathcal{M}$-dimensional counterfactual contrast point $anchor$

2: for epoch 1,…,K do

3: for minibatch $\\{(x_{k},t_{k},b_{k})\\}_{k=1}^{N}$ do

4: Step 1: Select $\\{(p_{b_{k}})\\}_{k=1}^{N}$ form $P$ according to
$\\{(b_{k})\\}_{k=1}^{N}$

5: Step 2: Update $\theta$ by minimizing target task loss (using Eq. 1)

6: Step 3: Get factual output $Y(x_{k},p_{k})$ of model

7: Step 3: Get counterfactual output $Y(x_{k},anchor)$ of model with replacing
${(p_{b_{k}})}_{k=1}^{N}$ with $anchor$

8: Step 4: update trainable proxy features $P$ and target task head
$h\in\theta$ to enhance proxy effect of proxy features for model (using Eq. 7)

9: end for

10: end for

11: Compute $\mathbb{E}_{\bm{b}}\left[p_{b}\right]$

12: Set the proxy feature of model to $\mathbb{E}_{\bm{b}}\left[p_{b}\right]$

13: return model $\theta$

Inference with intervention feature. Similar to Eq. 4 in _Naive Proxy
Debiasing_ , we also use intervention feature
$\mathbb{E}_{\bm{b}}\left[p_{b}\right]$ to replace proxy feature. The
difference is that proxy features $P$ here are trainable.

In summary, Algorithm 1 depicts the complete procedure of Active Proxy
Debiasing (Active PD).

## Experiments

### Experiment Setup

Fairness metrics. Many fairness criteria have been proposed including
Statistical parity (Feldman et al. 2015), Equal opportunity and Equalodds
(Hardt, Price, and Srebro 2016). Statistical parity requires that the
probability of positive output of different groups is exactly equal, ignoring
the label distribution of the test set itself. Equal opportunity measure bias
by comparing true positive rate between different groups. However, the
fairness of positive and negative outputs is equally important, such as
_blonde_ (Pos.) and _non-blonde_ (Neg.) in hair color recognition. Equalodds
comprehensively considers fairness on all target labels as follows:

$\frac{1}{|T|}\sum_{t}\left|\operatorname{Pr}_{b^{0}}(\tilde{T}=t\mid
T=t)-\operatorname{Pr}_{b^{1}}(\tilde{T}=t\mid T=t)\right|$ (8)

where $T$ denotes target labels such as _blonde_ , $\tilde{T}$ denotes target
outputs, and $b^{0}$ and $b^{1}$ represents different groups in terms of bias
attributes such as _male_ and _female_.

Method | T=a , B=m |  | T=bl , B=m |  | T=bn , B=m |  | T=a , B=y |  | T=bl , B=y |  | T=bn , B=y |  | Avg.
---|---|---|---|---|---|---|---|---|---|---|---|---|---
Acc. | Bias |  | Acc. | Bias |  | Acc. | Bias |  | Acc. | Bias |  | Acc. | Bias |  | Acc. | Bias |  | Acc. | Bias
Vanilla | 76.72 | 26.24 |  | 78.77 | 40.82 |  | 70.04 | 23.93 |  | 77.58 | 20.52 |  | 91.36 | 4.05 |  | 73.83 | 18.49 |  | 78.05 | 22.34
AdvDebias | 77.54 | 11.56 |  | 79.24 | 33.44 |  | 70.86 | 15.96 |  | 77.71 | 10.48 |  | 91.30 | 3.74 |  | 71.07 | 7.12 |  | 77.95 | 13.71
LNL | 76.91 | 26.43 |  | 79.55 | 33.17 |  | 69.87 | 28.07 |  | 76.79 | 19.19 |  | 90.96 | 5.14 |  | 73.86 | 16.54 |  | 77.99 | 21.42
EnD | 77.11 | 24.64 |  | 81.47 | 33.73 |  | 68.61 | 22.04 |  | 77.11 | 21.57 |  | 91.05 | 3.91 |  | 74.18 | 17.65 |  | 78.25 | 20.59
MFD | 77.22 | 20.17 |  | 79.85 | 38.84 |  | 71.07 | 28.86 |  | 77.31 | 22.00 |  | 90.92 | 5.16 |  | 75.39 | 16.12 |  | 78.62 | 21.85
DI | 77.53 | 23.01 |  | 91.44 | 7.76 |  | 73.03 | 15.89 |  | 77.69 | 17.17 |  | 91.05 | 4.66 |  | 73.98 | 10.64 |  | 80.78 | 13.18
RNF | 79.08 | 40.15 |  | 75.88 | 24.01 |  | 70.92 | 23.58 |  | 76.55 | 22.42 |  | 90.42 | 5.23 |  | 73.19 | 14.36 |  | 77.67 | 21.62
Active PD | 79.70 | 7.33 |  | 92.02 | 4.97 |  | 72.11 | 2.56 |  | 77.57 | 14.31 |  | 91.38 | 3.62 |  | 75.84 | 5.56 |  | 81.43 | 6.36

Table 2: The accuracy(in $\%$) and model bias(Equalodds) of models trained on
CelebA. Here T and B respectively represent target and bias attributes. Here
a, bl, bn, m, and y respectively denote attractive, blonde, bignose, male, and
young.

Datasets. We evaluate the debiasing performance of Proxy Debiasing on CelebA
(Liu et al. 2015) and UTKFace (Zhang, Song, and Qi 2017). CelebA consists of
more than 200,000 face images annotated with 40 binary attributes including
two social concepts: _Male_ and _Young_. We set Male(_m_) and Young(_y_) as
bias attributes, and select Attractive(_a_), Blonde(_bl_) and BigNose(_bn_) as
target attributes, due to vanilla trained models show unfairness in these
target attributes. For UTKFace, we set Male(_m_) and Ethnicity(_e_) as target
and bias attributes. For construct biased dataset, we truncate a portion of
data to force the correlation $Pr(T|B)$ between target(T) and bias(B)
attributes to be 0.9. For unbiased evaluation of the accuracy and fairness,
the test set was constructed to have same number of samples for each target
and each bias on both CelebA and UTKFace.

Baselines. We compare our Active Proxy DebiasingActive PD against baselines
such as: (1) Training DNN using cross-entropy loss without any debiasing
technique(referred as Vanilla), (2) Adding regularization term regarding
fairness constraints in the model optimization objective, including AdvDebias
(Wang et al. 2019b) LNL (Kim et al. 2019), End (Tartaglione, Barbano, and
Grangetto 2021), and MFD (Jung et al. 2021), and (3) Controlling the
contribution of bias features to target task toward fair generalization,
including DI (Wang et al. 2020b) and RNF (Du et al. 2021).

Implementation details. We use ResNet-18 (He et al. 2016) as the backbone
network, and we initialize ResNet-18 with pretrained parameters. The vector
dimension of proxy features is set to 100. For all baselines, we randomly
sample the data with batchsize=128 and use Adam optimizer with learning
rate=1e-3 and weight decay=1e-4.

Method | T=e , B=m |  | T=m , B=e |  | Avg.
---|---|---|---|---|---
Acc. | Bias |  | Acc. | Bias |  | Acc. | Bias
Vanilla | 84.98 | 24.14 |  | 88.53 | 15.70 |  | 86.74 | 18.42
AdvDebias | 69.89 | 36.35 |  | 74.15 | 27.94 |  | 71.50 | 32.14
LNL | 85.01 | 22.28 |  | 87.31 | 19.13 |  | 86.16 | 20.70
EnD | 84.96 | 20.94 |  | 88.95 | 14.29 |  | 86.95 | 17.61
MFD | 84.19 | 24.79 |  | 87.75 | 17.74 |  | 85.97 | 21.26
DI | 88.24 | 2.50 |  | 89.81 | 1.62 |  | 89.02 | 2.06
RNF | 84.88 | 20.79 |  | 88.99 | 13.75 |  | 86.93 | 17.27
Active PD | 90.34 | 0.99 |  | 91.10 | 0.96 |  | 90.72 | 0.97

Table 3: The accuracy(in $\%$) and model bias(Equalodds) of models trained on
UTKFace. Here e and m respectively denote ethnicity and male.

### Debiasing Performance Comparison

We compare our Active Proxy Debiasing to state-of-the-art methods on both
CelebA and UTKFace. Table 2 shows the accuracy and the model bias(EqualOdds)
of models on diverse combinations of target and bias attributes of CelebA.
Averaging over all combinations, _Vanilla_ records the most severe model bias
due to it is optimized to capture the statistical properties of training data
without hindrance. Notably, our Active Proxy Debiasing(Active PD for short)
outperforms the previous methods on model bias and accuracy with a large
margin. The fairness-accuracy compatibility validates our motivation that
utilizes proxy features to prevent the zero-sum game between target task
learning and debiasing, which results in a win-win for our method in terms of
accuracy and fairness. Furthermore, methods (AdvDebias, LNL, END and MFD)
based on removing bias features from representation demonstrate insignificant
debiasing performance. This suggests that the zero-sum game between target
task learning and debiasing limits not only the accuracy but also the
performance of debiasing. Other methods solve this issue by controlling the
contribution of bias attributes to indirect debiasing. Notably, the accuracy
and model bias of DI is second only to ours. We conjecture that this is
because DI is an implicit form of avoiding competition between target tasks
and debiasing, where separate target task classifiers are trained for each
bias group.

Method | Acc. | Acc.@2 | Biasm | Biasm@2 | Biasy | Biasy@2
---|---|---|---|---|---|---
Vanilla | 77.15 | 77.15 | 26.24 | 26.24 | 20.52 | 20.52
AdvDebias | 77.62 | 64.21 | 11.56 | 48.28 | 10.48 | 7.98
LNL | 76.85 | 76.85 | 26.43 | 28.83 | 19.19 | 23.91
EnD | 77.11 | 76.83 | 24.64 | 24.95 | 21.57 | 25.88
MFD | 77.26 | 77.20 | 20.17 | 26.23 | 22.00 | 21.42
DI | 77.61 | 77.41 | 23.01 | 24.48 | 17.17 | 17.59
Active PD | 78.63 | 77.84 | 7.33 | 3.73 | 14.31 | 14.57

Table 4: The results of multiple biases debiasing. Biasm and Biasy
respectively represent the _male_ bias and _young_ bias in mitigation of
corresponding single bias. Acc.$@$2, Bias${}_{m}@$2 and Bias${}_{y}@$2 denote
accuracy, _male_ bias and _young_ bias, when both biases are eliminated
simultaneously.

Table 3 summarizes the performance for different methods on UTKFace. The
consistent observations with the above CelebA debiasing evaluation include:
(1) Vanilla records the most severe model bias. (2) Our Active PD outperforms
the previous methods in both model bias and accuracy (3) DI performs second
best in both model bias and accuracy due to DI trains separate target task
classifiers for each group. New observations include: For the case where the
target attribute and the bias attribute are interchanged (T=e/B=g and
T=g/B=e), our method can significantly eliminate the model bias, which shows
that the debiasing ability of our method is independent of the setting of
target attribute and bias attribute.

### Mitigation of Multiple Biases

Previous debiasing researches focus only on the debiasing of single bias. To
verify the debiasing performance on multiple biases, we modify these methods
to debiasing for two biases. For Active Proxy Debiasing, we construct two
types of proxy features in each sample, representing male/female and
young/old, respectively. For AdvDebias, LNL and MFD, we incorporate fairness
constraint in two bias attributes to eliminate two biases. For DI, we train 4
classifiers in terms of the male and young. And RNF cannot be adapted to
multiple bias attributes debiasing by simple modification.

Taking _male_ and _young_ as two bias attributes, as shown in Table 4, we
report the debiasing performance in the attractive recognition task. The
results show that Active Proxy Debiasing outperforms other methods in both
accuracy and fairness, and the negligible model bias and accuracy gap between
Multiple biases and single bias demonstrate our method can be applied to real-
world multiple biases debiasing scenarios rather than only single bias
debiasing simulations in laboratory settings. Besides, other methods are not
suitable for the mitigation of multiple biases. Particularly, Mitigation of
Multiple biases by AdvDebias severely reduces accuracy compared to mitigation
of single bias (from 77.62$\%$ to 64.21$\%$). Degradation of accuracy in
AdvDebias suggests that the fairness constraints on multiple biases have
stronger competition with the learning of the target task, and result in the
further fairness-accuracy paradox of mixing two biases. In contrast, our
debiasing method avoids being an adversary for target task learning, thereby
having the ability to eliminate multiple biases.

Figure 5: Performance of Active Proxy Debiasing on UTKFace with varying ratio
of $Pr$(_male_ $|$_ethnicity_).

### Controlled Experiments in Various Data Bias

There are many cases of data imbalance in the real world. To simulate various
data imbalances, we construct different datasets with various data imbalance
ratio on UTKFace to evaluate the effectiveness and robustness of each method
in various imbalance ratios. For more details, we truncate a portion of data
to force the correlation $Pr(T|B)$ between target(male) and bias(ethnicity)
attributes to be a list from 0.3 to 0.9 to simulate varying bias levels.

In Figure 5, we show the accuracy and model bias of vanilla and our method in
various $Pr(T|B)$. It can be clearly noticed that both accuracy and fairness
of Active Proxy Debiasing are basically not changed by the improvement of data
bias $Pr(T|B)$, maintaining a greater advantage over Vanilla at all the
intensities. And as $Pr(T|B)$ increases, accuracy gap between ours and vanilla
becomes larger. This indicates that our method is robust to a variety of data
bias scenarios, and our method can bring more gains in scenarios with more
severe data bias.

### Qualitative Analysis with t-SNE Visualization

To qualitatively investigate how _Active Proxy Debiasing_ successfully reduces
the discrimination, we visualize t-SNE embeddings of models trained with
_Vanilla_ and _Active Proxy Debiasing_ in Figure 6(a) and (b). The points of
the figure are divided into two groups in terms of bias attribute (i.e.,
_male_ and _female_), which are visualized in different colors.

Figure 6: Qualitative comparison using t-SNE visualizations.

In _Vanilla_ , the representation has separability for two bias attributes,
especially in the oval region in Figure 6(a), suggesting that the models learn
bias features attribute in target task learning. In contrast, in _Active Proxy
Debiasing_ , the representation cannot be divided by bias attribute, that is,
our method does not learn biased features in data. This visualization shows
that our method mitigates the discrepancies between different groups.

### The Effectiveness of Proxy Effect Enhancement

We qualitatively validate the effectiveness of proxy effect enhancement
module, i.e., optimizing proxy features and models to actively make the target
task depend on proxy features so that the model can obtain sufficient bias
information only from the proxy features.

Figure 7: The effect of proxy effect enhancement on CelebA. It clearly shows
that as Counter$@P$ is improved by the proxy effect enhancement module in
Active Proxy Debiasing (left), the debiasing effect is further improved
(right).

To validate, we use Counter$@P$ described in Eq. 5 to measure how dependent
the model is on proxy features in the _Naive_ and _Active Proxy Debiasing_. In
Figure 7(a), we report the Counter$@P$ of two methods in six debiasing tasks
on CelebA. The plots demonstrate that _Active Proxy Debiasing_ significantly
improves the dependence of the target task on proxy features (i.e., higher
Counter$@P$ in all debiasing tasks). Also, we use model bias to measure how
dependent the model is on real bias features in two Proxy Debiasing methods as
shown in Figure 7(b). Combining the two plots, we can find that the stronger
the model’s dependence on proxy features, the more the model does not rely on
real bias features. This indicates that when our active proxy strategy makes
the target task already obtain enough bias information from the proxy
features, the model will no longer use the real bias features as a decision-
making basis.

### Proxy Feature Dimension Sensitivity

Figure 8: Parameter sensitivity of Active Proxy Debiasing on Proxy Feature
Dimension. The proxy effect of proxy features (a) and debiasing performance
(b) are basically unaffected by the choice of dimension.

We also conduct parameter sensitivity studies on proxy feature dimension on
UTKFace. We ran Active Proxy Debiasing at different proxy feature dimension
settings, and Figure 8 reports the Counter@$P$ (a) and debiasing performance
(b). It clearly shows that the choice of proxy feature dimension has no
significant effect on proxy effort (Counter@$P$) and debiasing. This result
shows that we can achieve debiasing using lower-dimensional proxy features,
which means that debiasing can be achieved with lower computational cost in
our method.

## Conclusion

In this paper, we propose to employ proxy features to replace the target
task’s dependence on bias features towards visual debiasing. The proposed
solution couples the operation of proxy effect enhancement and inference with
the intervention feature, avoiding the use of bias features in training and
proxy features in testing, respectively. The introduction of proxy features
breaks through the fairness-accuracy paradox in previous methods, and the
experimental results demonstrate its effectiveness in consistently improving
fairness and accuracy.

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