A Dierentiable Distance Approximation for Fairer Image Classication Nicholas Rosa1 Tom Drummond12 and Mehrtash Harandi1

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A Diﬀerentiable Distance Approximation for

Fairer Image Classiﬁcation

Nicholas Rosa1, Tom Drummond1,2, and Mehrtash Harandi1

1Monash University, Australia

2The University of Melbourne, Australia

Abstract. Na¨ıvely trained AI models can be heavily biased. This can

be particularly problematic when the biases involve legally or morally

protected attributes such as ethnic background, age or gender. Existing

solutions to this problem come at the cost of extra computation, unstable

adversarial optimisation or have losses on the feature space structure that

are disconnected from fairness measures and only loosely generalise to

fairness. In this work we propose a diﬀerentiable approximation of the

variance of demographics, a metric that can be used to measure the

bias, or unfairness, in an AI model. Our approximation can be optimised

alongside the regular training objective which eliminates the need for

any extra models during training and directly improves the fairness of

the regularised models. We demonstrate that our approach improves the

fairness of AI models in varied task and dataset scenarios, whilst still

maintaining a high level of classiﬁcation accuracy. Code is available at

https://bitbucket.org/nelliottrosa/base_fairness.

1 Introduction

In recent times, the use of Artiﬁcial Intelligence (AI) has permeated many pro-

cesses that are used to make important decisions, such as ﬁltering applicants

for jobs, deciding if an applicant should receive credit and recognizing people

in images [27,15]. Given this, it is essential to ensure that AI-driven models are

not exhibiting behaviour which is morally or legally undesirable. In AI, data is

a collection of attributes, which can either be explicit (e.g. labels) or implicit

(e.g. information from an image). Some of these attributes are referred to as

protected attributes as they should not be used to discriminate (e.g. gender,

race or age). However, it has been shown numerous times that AI models which

are na¨ıvely trained are biased against one or more of these protected attributes,

as they exhibit lower accuracy for some demographics [4,11,19]. This behaviour

is discriminatory against these demographics and is morally or legally undesir-

able, or simply unfair. There are two common sources of unfair behaviour that

can present itself in AI systems. The ﬁrst source is biases that are present in

the data used for training AI models. Biases in the data with respect to pro-

tected attributes can cause an AI model trained upon that data to discriminate

against the protected attribute [2]. For example, if a dataset used to train a

facial recognition model for unlocking doors, only contains images of men (i.e.

arXiv:2210.04369v1 [cs.CV] 9 Oct 2022

2 N. Rosa et al.

bias with respect to gender) then the learned model will not accurately recognise

and admit women (i.e. unfair behaviour). The second source of bias is due to

some values or demographics of a protected attribute being inherently harder

for AI to recognize than others. For example, it has been shown that even when

training with a balanced dataset, faces with a darker skin tone are harder to

recognize for facial recognition algorithms [30].

Various solutions to the fairness problem have been proposed. We focus on

algorithmic in-processing methods for reducing the bias[9,36,6,31,8,10,5,14]. In-

processing aims to address the bias of a model by applying an extra objective

during training which makes the model bias-aware and consequentially learns a

fairer model. In-processing has proven to be quite eﬀective at reducing the un-

fair behaviour of AI. However, in-processing methods often include extra models

which can increase training cost and complexity [16]; use adversarial training

[9,36,8,6] which has proven to be notoriously unstable [26] or make assump-

tions about the representation space of the model which may not hold in all

cases[10,23,35]. Creating fair AI models is particularly diﬃcult in the computer

vision domain as any problems with extra computational cost and complexity

are exacerbated by the large models utilized. Additionally the high dimensional-

ity of images means they can contain many implicit attributes, which are often

highly correlated to each other and to protected attributes. Disentangling the

implicit factors is extra challenging in these cases.

In this paper, we introduce Bias Accuracy Standard deviation Estimation or

BASE, a novel fairness algorithm, which optimizes a diﬀerentiable approxima-

tion of the fairness metric standard deviation of accuracy across demographics

(σacc) to learn an AI model which is fair with respect to equalized odds (EO).

Models that exhibit a low standard deviation of accuracy across demographics

or variance of demographics have the property of equal performance on a target

task regardless of the demographic of the protected attribute. For example, a

facial recognition model which has low variance of demographics for ethnicity,

is equally likely to correctly recognize the identity of a person from an image

regardless of their ethnicity. Reducing the variance of demographics of a model

makes it fairer w.r.t. EO. However, for an AI model that is trained with gradient

based optimization the variance of demographics is diﬃcult to use. This is due to

the accuracy of a single sample - an integral part of the variance of demograph-

ics (Section 2.3) - having an undeﬁned gradient at 0 and being 0 everywhere

else, which leads to zero inﬂuence on the model parameters. BASE overcomes

this diﬃculty by instead using a sigmoid based approximation of accuracy which

we call soft-accuracy inside the variance of demographics metric. This approach

has multiple advantages. Firstly computational eﬃciency, for example, training

a classiﬁer on images with BASE incurs only the extra computation of calcu-

lating the variance of demographics. Compare this to training a classiﬁer with

knowledge distillation [16] or adversarial debiasing [36], where additional models

are used which incur extra memory usage for the model parameters and gradi-

ents, alongside with extra computation for the forward pass of the additional

model. Secondly, BASE makes no assumptions about the representation space.

A Diﬀerentiable Distance Approximation for Fairer Image Classiﬁcation 3

The model will automatically learn the representation space structure required

to reduce the variance of demographics. Furthermore, due to its simplicity BASE

can be combined with other solutions.

To summarize the main contributions of our work are:

–Provide a novel method for improving the fairness on AI models trained with

gradient based optimization, that increases algorithmic simplicity and does

not rely on training additional models (Section 3.1).

–Show that our method is competitive with and in some cases outperforms

current state-of-the-art fair image classiﬁers when using either a biased

dataset or an unbiased dataset (Section 4.4, Section 4.4).

–Show that our method increasingly outperforms the fairness of a naive clas-

siﬁer when exposed to increasingly biased training sets in which target and

protected attributes are strongly correlated. Our method also achieves higher

over-all accuracy on heavily biased datasets (Section 4.4).

2 Related Work and Preliminaries

Fair AI has received increasing attention in the past few years and a varied range

of solutions has been proposed. Algorithmic methods for reducing the bias can

be broken down into three main categories based upon when they apply their

fairness constraint. Pre-processing methods aim to change the distribution of

the data used for training such that a fairer model is produced. These methods

include re-sampling, which changes the sampling rate of data during training

to ensure each protected class is equally represented [1,25,28] and augmentation

methods which add synthetic data to the dataset [24,34,3,37] to balance the

protected classes. The second class of methods, post -processing methods, aim to

adjust the prediction after the fact to compensate for the bias [32]. Pre-processing

and post-processing have some major drawbacks. Pre-processing only addresses

the bias in the dataset and the inherent diﬃculties of some demographics can

still cause a biased model [31,30]. On the other hand post-processing methods

require that protected attribute labels to be known at inference time or assume

that the target and protected attribute are independent [32]. Our method is

related to the ﬁnal category of in-processing, which is discussed further below.

In-processing methods typically run under a constrained optimization scheme

where a loss penalty or a special construction of the AI model is used to reduce

the bias during optimization.

2.1 In-processing for Fair Classiﬁcation

Like many machine learning tasks, the fairness problem is diﬃcult to optimize

directly and adversarial training became a common method to create fair repre-

sentations and predictors [9,36,6,31,8]. These methods use an adversarial model,

or adversary, whose purpose is to learn the relationship between the predictor

and the protected attribute. The output of the adversary is then used to enforce a

4 N. Rosa et al.

fairness constraint upon the predictor. This is achieved either by gradient rever-

sal of the adversary or by maximising the entropy of the adversaries predictions.

If a strong adversary is unable to determine a relationship between the predictor

and the protected attribute then fairness of the predictor can be guaranteed [36]

Other constrained optimization methods have been proposed and their ap-

proaches vary greatly. Gong et al. [10] minimize the variance of sample density

across diﬀerent demographics within the representation space. Cho et al. [5]

use a kernel density estimate to approximate the conditional distributions used

for measuring fairness in a diﬀerentiable manner. Hwang et al. [14] reduce the

Wasserstein distance between protected groups within the representation space.

Finally, in a work most similar to our own Shen et al. [29] use cross-entropy loss

as a proxy for probability during training to optimise for fairness. Our method

diﬀers in two main aspects; our objective directly considers the two elements of

the models output vector responsible for determining accuracy and we evaluate

our work in the computer vision domain.

2.2 Problem deﬁnition

The ultimate goal of fair machine learning is to create predictors which con-

tain no bias. There is, however, many diﬀerent forms of bias that can present

themselves and as a consequence there are multiple diﬀerent deﬁnitions of fair-

ness. The three most common deﬁnitions are Demographic parity [36], Equalized

Odds [12] and Equalized Opportunity [12]. In the following section A,ˆ

Yand Y

are random variables which represent the protected attribute, the output of a

predictor and the true value of the target attribute respectively.

Demographic Parity Demographic parity is the simplest form of fairness since

it only considers the output of the predictor and the protected attribute. A pre-

dictor satisﬁes demographic parity when its output is independent of the pro-

tected attribute. That is ∀a∈ A; Pr( ˆ

Y= ˆy|A=a) = Pr( ˆ

Y= ˆy). However, this

deﬁnition does not always allow for perfect classiﬁcation [12]. If there is any cor-

relation between the protected attribute and the target task then maintaining

independence forces a reduction in performance. For example, if we learned a pre-

dictor for university admittance with age as a protected attribute, then achieving

demographic parity would require our predictor to admit young children with

the same probability as those who had just ﬁnished high school, regardless of

each individuals suitability.

Equalized Odds Equalized Odds is another deﬁnition of fairness that is more

commonly applied for computer vision tasks. A predictor satisﬁes equalized odds

when its output is conditionally independent of the protected attribute for all

classes of the target class. That is ∀y∈ Y,∀a, a0∈ A,Pr( ˆ

Y=y|A=a, Y =y) =

Pr( ˆ

Y=y|A=a0, Y =y). This deﬁnition allows us to maintain performance

as it is satisﬁed when a predictor achieves the same level of accuracy for each

demographic of the protected attribute.

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ADierentiableDistanceApproximationforFairerImageClassicationNicholasRosa1,TomDrummond1;2,andMehrtashHarandi11MonashUniversity,Australia2TheUniversityofMelbourne,AustraliaAbstract.NavelytrainedAImodelscanbeheavilybiased.Thiscanbeparticularlyproblematicwhenthebiasesinvolvelegallyormorallyprotected...

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A Dierentiable Distance Approximation for Fairer Image Classication Nicholas Rosa1 Tom Drummond12 and Mehrtash Harandi1

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