Learning an Ethical Module for Bias Mitigation of pre-trained Models
Authors: Jean-Rémy Conti
Nathan Noiry
Stephan CLEMENCON
Vincent Despiegel
Stéphane Gentric
Venue: ICLR 2022 Submitted (2022)
Keywords: Deep Learning
Bias
Fairness
Facial Recognition.

Abstract: In spite of the high performance and reliability of deep learning algorithms in broad range everyday applications, many investigations tend to show that a lot of models exhibit biases, discriminating against some subgroups of the population. This urges the practitioner to develop fair systems whose performances are uniform among individuals. In this work, we propose a post-processing method designed to mitigate bias of state-of-the-art models. It consists in learning a shallow neural network, called the Ethical Module, which transforms the deep embeddings of a pre-trained model in order to give more representation power to the disadvantaged subgroups. Its training is supervised by the von Mises-Fisher loss, whose hyperparameters allow to control the space allocated to each subgroup in the latent space. Besides being very simple, the resulting methodology is more stable and faster than most current bias mitigation methods. In order to illustrate our idea in a concrete use case, we focus here on gender bias in facial recognition and conduct extensive numerical experiments on standard datasets.

Under review as a conference paper at ICLR 2022
AN ETHICAL MODULE FOR BIAS MITIGATION OF TRAINED FACE RECOGNITION MODELS
Anonymous authors Paper under double-blind review
ABSTRACT
In spite of the high performance and reliability of deep learning algorithms in broad range everyday applications, many investigations tend show that lot of models exhibit biases, discriminating some subgroups of the population. This urges the practitioner to develop fair systems whose performances are uniform among individuals. In this work, we introduce post-processing method designed to mitigate bias of ofate-of-the-art models. consists in learning shallow neu- ral network, called the Ethical Module, which transforms the deep embeddings of a pre-trained model to give more representation power to the discriminated sub- groups. Its training is supervised by the von Mises-Fisher loss, whose hyperpa- rameters allow to control the space allocated to each subgroup in the latent space. Besides being very simple, the resulting methodology more stable and faster than most current methods of bias mitigation. In order to illustrate our idea in a concrete use case, we focus here on gender bias in facial recognition and conduct extensive numerical experiments on standard datasets.
INTRODUCTION
In the past few years, Face Recognition (FR) systems have reached extremely high levels of perfor- mance, paving the way to a broader range of applications, where the reliability levels were previously prohibitive to consider automation. This is mainly due to the adoption of deep learning techniques in computer vision since the famous breakthrough of Krizhevsky et al. (2012). The increasing use of deep FR systems has however raised concerns as any technological flaw could have strong soci- etal impact. Besides recent punctual events' that received significant media coverage, the academic community has studied bias of FR systems since many years (dating back at least to Phillips et al. (2003) who investigated racial bias of non-deep FR algorithms). Abdurrahim et al. (2018) identify three sources of biases: race (understood as biological attributes such as skin color), age Srinivas al. (2019) and gender Albiero al. (2020). The National Institute of Standards and Technology Grother et al. (2019) conducted a thorough analysis of the performances of several FR algorithms in function of these attributes and revealed high disparities. For instance, some of the top state- of-the-ar art algorithms in absolute performances have more than seven times false acceptances for females than for males. this paper, we introduce a methodology to mitigate gender bias for FR. Though focusing on single source of bias has obvious limitations regarding intersectional effects Buolamwini & Gebru (2018), it is a first step to gain insights into the mechanisms at work, before turning to more complex situations. Actually, the method promoted in this paper, much more gen- cral than the application considered here, could possibly alleviate many other types of bias. This will be the subject of a future work.
The topic corresponding to the study of different types of bias and to the elaboration of methods to alleviate them is referred to as fairness in machine learning, which has received increasing attention in recent years Mehrabi et al. (2019), Caton & Haas (2020), Du et al. (2020). Roughly speaking, achieving fairness means learning an algorithm that does not mistreat some predefined subgroups, while still exhibiting a good predictive performance on the overall population: in general, a trade-off has to be found between fair treatment and pure accuracy². In this regard, one needs carefully
See for instance the study conducted by the American Civil Liberties Union
"this dichotomy somewhat simplifies the problem since increase in accuracy could also lead to better treatment of each subgroup of the population.

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define what will be the relevant faireess metric. From theoretical viewpoint, several ones have been introduced Castelnovo et al. (2021), Garg et al. (2020) depending on how the concept of equity is understood. In practice, these very refined notions can be inadequate, they ignore specific use case issues, and one thus needs to adapt them carefully. This is particularly the case in FR, where high security standards cannot be negotiated. One of the contributions of our work is to introduce two new metrics that incorporate the needs for both security and fairness (see section 2.2). Once the metric has been chosen, different strategies can be considered alleviate bias of algorithms which can be roughly grouped in three categories: pre-, in- and post- proseercesssiing methods Caton & Haas (2020), depending on whether the practitioner "fairness" intervention occurs before, during or after the training phase.
In this work, we introduce a novel post-processing method allowing to correct gender bias of FR pre-trained models. It is based on the idea that state-of-the-art models Wang et al. (2018), Deng al. (2019a), Huang et al. (2020) offer already very good deep embeddings of face images, as witnessed by their high performances (2018)), although they could induce various bias. This indicates that the deep face embeddings obtained by these models quite relevant and be considered as initialization points to be en- hanced. As a result, our methodology consists in learning a shallow Multi- Laytes Perceptron (MLP) in order to transform the deep embeddings of the pre-trained model and balance the representation space used by the discriminated groups. The training of this shallow network is supervised by the von Fisser loss which is particularly well-suited for our purpose. Indeed, it incorporates an hyperparameter for females (resp. males), whose variation is directly linked with the area they cover in the latent space. To emphasize on both the post-processing aspect and the sought fairness, we call our methodology the Ethical Module.
large scaled evaluation datasets (e.g. IJB-C Maze et al.
Ethical
Misos Fisber
(312 3121
WOSEUVE
Figure Illustration of the Ethical Module methodology. In gray: our experiment choices.
The Ethical Module enjoys several benefits we would like to highlight.
Simplicity and interpretability. Though it of great simplicity, the method exhibits good performance. In addition, the von Mises-Fisher loss has a nice parametric interpretation which eases the understanding of the debiasing mechanisms at work.
Computational complexity and stability. The training of the shallow MLP is fast (few hours) and avoids the re-training of a full large-scale model, which can be costly and time- consuming. Moreover, the training process stable and supports the reliability of the method. This is in contrast with adversarial methods whose training losses tend to oscillate. Finally, our method is flexible and we conjecture could use small database to already debias representation since the shallow MLP has only few parameters.
Taking advantage of foundation models. In the recent survey Bommasani et al. (2021), the authors judiciously point out change of paradigm in deep learning: very efficient pre-trained models with billions of parameters they call foundation models are at our dis- posal such as BERT Devlin et al. (2018) in NLP or ArcFace Deng al. (2019a) in FR. Many works rely on these powerful models and fine tune them, inheriting from both their strengths and weaknesses such as their biases. Hence the need to focus on methods to investigate the fairness of foundation models: our method is in line with this approach.
Compliance with the fairness through unawareness principle. If the Ethical Module requires access to the sensitive label during its training phase, the latter only appears in the von Mises-Fisher Loss. As a result, face images are the only argument of the learned embedding function.
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Organization of the paper. Section 2.1 presents the widely spread usage of FR and its main chal- lenges. It is followed by section 2.2 where we discuss different fairness metrics that arise in FR and introduce two new ones think are more relevant with regards to operational use cases. In section 3, we present the von Mises-Fisher loss that is used for the training of the Ethical Module and discuss its benefits. Finally, in section 4, we present at length our numerical experiments, which consist in learning an Ethical Module on the ArcFace model, pre-trained on the MS dataset (Deng al. (2019b)). Our results show that, remarkably, some specific choices of hyperparameters provide high performance and low faimess metrics both at the same time.
Related works. The correction of bias in FR has been the subject of several recent papers. Liu et al. (2019) and Wang & Deng (2020) use reinforcement learning to learn fair decision rules but despite their mathematical relevance, such methods are computationally prohibitive. Another line of research followed by Yin et al. (2019), Wang et al. (2019a) and Huang et al. (2019) assume that bias come from the unbalanced nature of FR datasets and builds on imbalanced and transfer learning methods. Unfortunately, these methods do dot completely remove bias and it has been recently pointed out that balanced dataset are actually not enough to mitigate bias Wang et al. (2019b), Gong et al. (2019), Alasadi et al. (2019) and Dhar et al. (2020; 2021) rely adversarial methods that can reduce bias but are also known to be unstable and computationally expensive. All of the previously mentioned methods try to learn fair representations. In contrasts, some other works do not affect the latent space but modify the decision rule instead: Terhörst et al. (2020) act on the score function whereas Salvador et al. (2021) rely on calibration methods. Despite encouraging results, these approaches do not solve the source of the problem which is the bias incurred by the embeddings used.
ON FAIRNESS IN THE CONTEXT OF DEEP FACE RECOGNITION
In this section, we first briefly recall the main principles of deep face recognition and introduce some notations. The interested reader may consult Masi et al. (2018) or Wang & Deng (2018) for a detailed exposition. Then, we present the fairness metrics we adopt and argue of their relevance in our framework.
2.1 A QUICK OVERVIEW OF FACE RECOGNITION
typical FR dataset consists of N images (x::) ( of faces that have been pre- rre-processed and are all of size (h, c). It is assumed that there are K identities among the images and we denote by y: E {I,... K} the identity of æ; for = =, 1, ...: N. The goal a FR algorithm to learn proper d-dimensional representation of the face images, by means of function S Rhxwxe - Rd in order to minimize the intra-identity distances and maximize the inter-identity distances. We denote by 2, fxx) the face embedding æ,, Since the advent of deep learning, the function f is usually a deep Convolutional Neural Network (CNN) whose parameters are learned on a large FR dataset.
Test phase. There are generally two FR use cases: identification, which consists in finding the specific identity of a probe face among several previously enrolled identities, and verification (which focus throughout this article), which aims at deciding whether two face images correspond to the same identity or not. To do so, the closeness between two embeddings is usually quantified with the cosine similarity measure s(2,, 2,) == z 2/2,// ([] | |=,l)). where || stands for the usual Euclidean norm (the Euclidean metric ||z æ/|| is also used in some early works e.g. Schroff et al. (2015)). Therefore, an operating point & E [-1, 1] has to be chosen to classify a pair (z), 2z) as genuine (same identity) if s 2 t and impostor (distinct identities) otherwise.
Training. For the training phase only, a fully-connected layer is added on top of the deep embed- dings so that the output is K K--dimnnsiona vector, predicting the identity of each image within the training set. The full model (CNN + culle-coneetted layer) is trained as an identity classification task. Until 2018, most of the popular FR loss functions were of the form:
1 n
L L=
log
EK
where the fy's 's are the fully fully-connected layer's parameters, K > 0 the inverse temperature of the softmax function used in brackets and is the batch size. Early works (Taigman et al. (201 4); Sun
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et al. (2014)) took k and used bias term in the fully-connected layer but Wang et al. (2017) showed that the bias term degrades the performance of the model. It was thus quickly discarded in later work. Since the canonical similarity measure at the test stage is the cosine similarity, the decision rule only depends on the angle between two embeddings, whereas it could depend on the norms of [4 and 2; during training. This has led Wang et al. (2017) and Hasnat et al. (2017) to add a normalization step during training and take pk, 2; E -g-1 == {z E ET ||=|| = 1} as well as introducing the re-scaling parameter K in Eq. 1: these ideas significantly improved upon former models and are now widely adopted. Denoting by 8; the angle between My. and 2;, the major advance over the loss of Eq. (with normalization of 2,) in recent years was to consider large- margin losses which replace 1. 2; cos(O:) by function that reduces intra-class angle variation, such as the ( of Liu et al. (2017) or the cos (0:) of Wang et al. (2018). The most efficient choice is cos(0; + m) and due to Deng et al. (2019a) who called their model AreFace, on which we build methodology.
22)
A fine training should result in the alignment of each embedding z; with the vector py, The aim is to bring together embeddings with the same identity. Indeed, during the test phase, the learned algorithm will have to decide whether two face images are related to the same, potentially unseen, individual (one refers to open set framework).
Evaluation metrics. Denoting by 9 the set of genuine pairs and by I the set of impostor pairs in a given test set, we introduce the False Acceptance and False Rejection Rates, defined as follows:
FAR(t)= # #(2,,,2 2,) E I ::::s(z,. s(2,, 2 t} FRR(() = # #[ 23) G s(z,, 22) < <t
#1 (1),, Z
# #1 2,) E G]
These quantities are crucial to evaluate given algorithm in our context: face recognition is intrin- sically linked to biometric applications, where the usual accuracy evaluation metric is not sufficient to assess the quality of a learned decision rule. For instance, security automation in airport quires a very low FAR while keeping a reasonable FRR to ensure a pleasant user experience. As a result, the most widely used metric consists in first fixing threshold so that the FAR is equal to pre-defined value a E [0, 1J, and then computing the FRR at this threshold. We use the canonical FR notation to denote the resulting quantity:
FRR a) FRR(() with such that FAR(!) a.
(2)
The FAR level determines the operational point of the FR system and corresponds to the security risk one is ready to take. According to the use case, is typically set to 10-² with i E f1,....,6) 6).
2.2 FAIRNESS METRICS
While the FRR@FAR metric is the standard choice for measuring the performance of a FR algo- rithm, it does not take into account its variability among different subgroups of the population. In order to assess and correct for potential discriminatory biases, the practitioner must rely on suitable faireess metries. The first step is to define finite set A of sensitive attributes against which wish to assess fairness. Since we focus here on gender bias, we take A= {0, where 0 stands for "male" and for "female". We extend the notions of FAR R and FRR within the male (resp. female) subgroups, considering same-gender pairs only, and denote by FARg, FAR, and FRR, FRR, the resulting quantities.
Before specifying our choice for the fairness metric used here, let us review some existing ones Cavazos al. (2020) that derive from faimess in the context of binary classification (here, one classifies pairs in two groups: genuines or impostors). The Demographic Parity criterion requires the prediction to be independent of the sensitive attribute, which amounts to equalizing the likelihood of being genuine conditional to = 0 and a = 1. Besides heavily depending on the number and quality of impostors and genuines pairs among subgroups, this criterion does not take into account the FARs and FRRs, which are instrumental in FR as previously mentioned. An attempt to incorporate those criteria could be to compare the intra-group performances: FRR, @(FAR, = a) v.s. FRR, (FAR, = ax. However, the operational points i and é satisfying (AR)(to)) = and FAR, (tz) = a generically differ as pointed out by Krishnapriya et al. (2020). To fairly asses the equity of an algorithm, one needs compare intra- intra- groups FARs and FRRs at same threshold. Two such criteria exist in the fairness literature: the Equal Opportunity fairness criterion which requires FRR,(()= = FRR, (4) and the Equalized Odds criterion which additionally requires FA (t))
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FAR1(t), Nevertheless, working at an arbitrary threshold does not really make sense since, as previously mentioned, FR systems typically choose an operational point achieving a predefined FAR level so to limit security breaches. This is why most current papers consider a fixed operational point such that the population False Acceptance Rate equals a fixed value a. For instance, Dhar al. (2020) computes
(3) However, think the choice of threshold achieving global FAR is not entirely relevant for it depends on the relative proportions of females and males of the considered dataset together with the relative proportion of antra-groups impostors and genuines. For instance, at fixed images quality, if females represent a small proportion of the dataset, the threshold of Eq. is close to the male threshold tg satisfying FAR a and away from the female threshold i satisfying F a. Such variability among datasets could lead to incorrect conclusions.
(R) - FR)((t)) with FAR(() = =.
In this paper, we go one step further and work at threshold achieving max, FAR,, a instead of FAR a. This alleviates the previously proportions dependence. Besides, this allows to monitor the risk one is willing to take among each subgroup: for pre-definite rate a deemed acceptable, one typically would like to compare the performance among subgroups for a threshold where each subgroup satisfies FAR.- I a. Our two resulting metrics are thus:
BFRR(a) (0.1) (t)
with t such that max FAR aE(0,1)
(4)
(0.1 (t)
and
BFAR(a)) = (0.1) (t)
(0,1 (t) with such that max FAR,( = a. aE
(5)
One can read the above acronyms "Bias FRR/FAR". In addition to being more security demand- ing than previous metrics, BFRR and BFAR more amenable to interpretation: the ratios of FRRs or FARs corresponds to the number of times the algorithm makes more mistakes on the dis- criminated subgroup. Those metrics generalizes well for more than 2 distinct values of the sensitive attribute.
3 THE VON MISES-FISHER LOSS FOR BIAS MITIGATION
We now turn to detailed description of the von Mises- (vMF in abbreviated form) loss which supervises the training of our Ethical Module's s MLP. It stems from the vMF probability measure on the hypersphere and was first introduced in Hasnat et al. (2017) as a new powerful way to discrimi- nate different identities, before the advent of large-margin losses.
The von Mises-Fisher distribution. The vMF distribution in dimension d with mean direction a E Sd-1 and concentration parameter 0 is probability measure defined on the hypersphere gd-1 by the following density:
Va(x; pI == Ca( with Ca(R) (2x) 2 (1))
where I, stands for the modified Bessel function of the first kind order v, whose logarithm can be computed with high precision (Kim (2021)). Figure 2 illustrates the influence of the concentration parameter x on the vMF distribution.
The vMF distribution corresponds to a Gaussian distribution in dimension d with mean and variance-covarraacce matrix (I/x) conditioned to live on the hypersphere. makes it very natural directional law: for instance, it has maximal entropy among all probability measures on the hypersphere with fixed variance.
A Fair von Mises-Fisher loss. The general form of the vMF Loss on the face embeddings is
1 Σ log
(e
LYMF
EK Ca(Ka)e
where a scalar Kę is affected to each identity E {I...., K}. Notice that there are two ways of minimizing LyME: either by aligning ground-truth bly with associated normalized face embeddings
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K
K = 10
K = 20
== 100
1
1
1
1
Figure 2: 500 samples from the vMF in dimension with parameters μ =0.5, 0, v0.75) and K.
2; or by pushing back wrong (with k * yi) from H, The vMF Loss was first introduced in the context of FR by Hasnat et (2017), who took unique value k. In that case, the vMF loss reduces to the classical loss L of Eq. 1 (when and μı; are normalized). This makes LoME a natural losses which are at the basis of refined state-of-the-ar
generalization of cosine similarity- models that also incorporate margins.
Building on LyME. we consider gender- based hyperparameters. If ag E {0. 1) denotes the gender of identity & E (1...., K). the fair version of the vMF-loss we consider to train the Ethical Module is:
CalMiay (elMaa,Definn Je Mi 4b,
1 n1
CNMME =
log
ER=1 Ca(Eaa)ee )e
depends on two hyper-parameter Ko, A2 > O, respectively corresponding to the concentration parameters of male and female. By tuning Ko and K1, one modify the surfaces covered by the male/ / female and therefore plays on their representative powers.
maximum likelihood interpretation of the von Mises-Fisher loss. It is common knowledge that, besides its high performances in many contexts, the Cross-Entropp (CE) loss is also attractive because of its interpretation in terms of maximum likelihood estimation. Indeed, minimizing the CE amounts maximizing the likelihood with respects to the network parameters.
Interestingly, the vMF loss also enjoys this property if one places a proper model on the face embeddings. Let us describe this model, which is a mixture of vMF distributions. Recall that K 2 1 is the number of identities in the dataset. The model consists in assuming that the dataset consists of i.i.d. realizations of a probability law with density:
ga xx; ((TK, ua, kx) mk)ssk
Σ Te Valæ; p4, KN).
110
06
-1
Let us discuss its parameters O == {(Ti, M4, Re,, Bi)gs.... Each identity & E (1...., K} is represented by a vMF distribution with mean f4 and concentration Ka. In this vision, the mean a4 an abstraction of the identity and Kg takes into account its variability (caused by lightening conditions, aging..... We also denote by Ti the proportion of identity k in the overall population. Figure 3 il- lustrates this vMF mixture in the case K 4 (the detail of the parameters is given in the supplementary material). Under the vMF mixture model assumption, the probability Pay that face embedding z; belongs to identity is given by
Figure 3: Illustration of vMF mixture model.
Pij Va(2o1145:83
n. CTCKk)))))))))))))))))))( e MT=
D Va(zi (An KK)
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Therefore, the negative log- liglliielhoodd of the model is given by
N
Ty. Ca(Ke))) ) &o p 2;
1 N
NLI OME) ==
log
Lk=1 E T& m&Ca(()))))))))))))))))))))))( e 14) x:
At least at heuristical level, both playing on the parameters T&S and K&S affects the surfaces covered by the different classes. It thus natural to restrict the scope the case where the T&S are all equal and only adjust the concentration parameters. In that case, the above NLL is in fact the vMF Loss LEMP F previously introduced.
4 NUMERICAL EXPERIMENTS
Pre-trained model. We use the trained model ArcFace' whose CNN architecture is ResNet100 (Han et al. (2017)). As emphasized before, it achieves statc-of-the-art performances in FR. It has been trained on the R-etinaai dataset (also called MS1MV3), introduced by Deng et al. (2019b) in the ICCV 2019 Lightweight Face Recognition Challenge. MSIMV3 is a cleaned ver- sion of the MS-CelebIM dataset (Guo et al. (2016)); all its face images have been pre-processed by the Retina-Face detector of Deng et al. (2019c) and are of size 112 x 112 pixels. It contains 5.1M images of 93k identities. We also consider other pre-trained models (AdaCos Zhang et al. (2019), CosFace Wang et al. (2018), CurricularFace Huang et al. (2020)) whose backbone is Mo- bileFaceNet Chen et al. (2018) and trained on the MS-Celeb- IM-vIc-r dataset'. This dataset is another cleaned version of the MS-Celebl M dataset and it contains 3. 3.28M images of 73k identities. The images are also pre-processed by the Retina-Face detector and are of size 112 x 112 pixels.
Gender labels. For fair comparison, we train our Ethical Module on the training set used train the pre-trained models (MSIMV3 for ArcFace, MS-Celeb-IM-vIE for the models with Mobile- FaceNet backbone). However, ground-truth gender labels for not available. As the training of our Ethical Module needs the gender label of each face image within the training set, we use a private gender classifier to get those gender labels. Current gender classifiers achieve around 95% prediction accuracy on standard evaluation datasets and are widely used in FR to get gender annotations (Acien et al. (2018); Gong et al. (2020)). Since some images from the same identity might be assigned different gender predictions, it is common practice to use a majority vote to decide the correct gender for each identity. We follow Albiero et al. (2020) and only keep in our training sets the identities for which at least 75% of the same-identity face images are assigned the same gender. Doing so, we discard 25k images and 835 identities for MSIMV3, 10k images and 500 identities for MS-Celeb-IMN IM-vlc-r.
Ceeleb-MM-llee are
Ethical Module. The face embeddings output by the pre-trained models are of dimension 512. Thus, the MLP within our Ethical Module has an input layer of 512 units. To emphasize the fact that our gender bias mitigation solution is much less costly than current solutions such as Wang & Deng (2020) and Dhar et al. (2020) in terms of both training time and computation power (see supplementary material A. 1), we choose a shallow MLP of size (512, 1024, 512), the output dimension being the same than for Arcface. This MLP is trained with the fair version LFMM of the vMF loss introduced in Eq. 7. For each experiment, we train the Ethical Module during 50 epoch with the Adam optimizer (Kingma& & Ba (2014)). The batch size is set to 1024 and the learning rate to 0.01. The training is efficient as we first compute the face embeddings of the pre-trained models (on MS MV3 for AreFace on MS-Celeb- -B--Ceee--IM-vc-- for the models with MobileFaceNet backbone), store them, and then train shallow MIP on those embeddings. Using one single GPU (NVIDIA RTX 3090), the computation of the embeddings takes 4 hours and each training takes & hours.
Reproducibility. We plan to release the code used to conduct our experiments.
4.1 GRIID-SEARH ON IJBCC AND FAIRNESS EVALUATION
In order to select relevant pairs of gender-hyper hyperparameters (Ko, k1), we perform a grid-search and keep track of the canonical performance metric FRR& = 10-3) together with our two fairness
thub. com areface torch. 'https:/ / http://wwww.aacccc////////////aa
md.
"See footmote 4.
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metrics BFRR(10 and BFAR(10-3) introduced in Eq. 4 and 5. To obtain reliable results, need to compute the latter metrics on a sufficiently large dataset containing gender labels. We choose UJBC (Maze et al. (2018)), which contains about 3,5k identities for a total number of about 31k images and 117k unconstrained video frames. The 1:1 verification protocol is performed on 19k genuine pairs and 15M impostor pairs.
6-122
25
20
25
15
25
24
BPAR Far Fond
and vary
2758 forfees B1C VRISAIS
FRA for feed varylng
24-
22-
3.02
3328
Figure 4: Ablation study of the considered metrics when one of the two hyperparameters is fixed. The FAR level defining the threshold t is set to 10-3; the pre-trained model ArcFace with ResNet100 backbone.
heatmap representation of the grid-search is provided in the supplementary material A.2. Several interesting trends emerge from the ablation study of Figure 4, suggesting underlying regularity of the model with respect to the hyperparameters space. More precisely:
when Kig is fixed and K1 increases, BFAR tends to decrease, BFRR first increases and then decreases and FRR@FAR tends to increase,
when 11 is fixed and Ko increases, BFAR first increases and then decreases, BFRR tends decrease and and FRR&FAR increases.
strength of our approach is that lends itself well geometric interpretation. The latter al- lows to derive two heuristic views on the problem, whose details are provided in the supplementary material A.3. a nutshell, we are able (i) identify a pair of hyperparameters with a priori good fairness properties, without relying on grid-search study, and (ii) provide explanations for the trends of Figure strategy for finding the best hyperparameters by selecting an initial point (No. x1) with (i) and then navigating the hyperparameter space with (ii).
very promising route for future work would be to investigate two-step
Many (No, R1) pairs could be considered as relevant and instead of defining objective criterion, select three them in order to illustrate the trade-off one needs to make between fairness metrics and pure performance. The point (No 25, K1 20) is quite relevant regarding BFRR and performance (F FFRR FRR&FAR) R). but is not adapted for BFAR. On the other hand, the point (15, 20) good when it comes BFAR and performance. Finally, the point (45,30) is interesting when considering BFRR and BFAR. In Table 1, we summarize the different metrics evaluated for these three points on the LFW dataset (Huang et al. (2008), see A.4) and compare them with the ArcFace pre-trained baseline, at two FAR levels. We also conduct these experiments on different pre-trained models with MobileFaceNet backbone. Additional results (using the IJB BB-C dataset for evaluation, considering several types of ResNet backbones for ArcFace) can be found in the supplementary material A.5.
Senerr/rriiillmmmommmmmmmmmmmeee evaluation /ijb.
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FAR level:
10-4
10-3
model
FRR (%)
BFRR
BFAR
FRR@FAR (%)
BFRR
BFAR
original
0.063
10.76
3.98
0.052
2.23
1.81
(15,20)
0.119
12.73
1.72
0.067
8.43
1.04
ArcFace
(25,20)
0.076
5.35
29.33
0.052
1.94
3.96
(45,30)
0.129
13.47
2.99
0.067
6.02
1.24
original
2.97
3.64
3.84
0.98
5.29
2.23
(15,20)
4.56
4.42
1.41
1.33
6.34
1.01
AdaCos
(25,20)
3.12
2.71
8.37
0.91
4.23
3.71
(45,30)
4.05
4.51
1.57
1.26
7.28
1.08
original
1.73
5.89
2.51
0.58
8.18
1.74
(15,20)
3.69
5.76
1.13
1.05
8.41
1.02
CosFace
(25,20)
2.41
3.03
9.66
0.67
5.09
4.75
(45,30)
2.60
4.30
3.69
0.82
6.81
1.87
original
2.52
3.67
2.92
0.81
4.88
1.91
(15,20)
3.86
5.26
1.16
1.17
6.35
1.10
Curricular
(25,20)
2.82
2.58
9.10
0.82
3.89
4.28
(45,30)
3.61
3.40
2.30
1.02
5.63
1.27
Table Evaluation on LFW for ArcFace with ResNer100 backbone and different pre-trained models (AdaCos, CosFace, CurricularFace) with MobileFaceNet backbone. By "original" we mean no Ethical Module added to the pre-trained model. The tuples correspond to the choices of no (first argument) and (second argument). FRR@FA expressed percentage (%).
4.2 VERIFICATION EVALUATION ON IJB-B
We finally investigate the
FRR@FAR metric (Table 2)
Methods (%)
10-4
10
of the three selected points (Kg, K1) on UB-B (Whitelam et al. (2017)). In the verification setting, this dataset contains 10k genuine pairs and SM impostor pairs. Notice that we do not lose too much in performance with respect to the original model.
original
5.38
3.78
(15, 20)
6.79
4.11
(25, 20)
6.00
3.84
(45, 30)
7.03
4.81
Table 2: FRR = a) on IJB-B for ArcFace with ResNet100 backbone, for a 10-1,
5 CONCLUSION
In this paper, we introduce novel method, the Ethical Module, mitigate gender bias of Face Recognition state-of-the-arr models. It consists in learning a shallow MI.P on top of frozen pre- trained model, so fairness, we rely on a fair version of the von Mises-Fisher loss that incorporates an hyperparameter per gender, the variation of which allowing to monitor the space covered by males and females in the latent space. Measuring the fairness of Face Recognition systems is a very challenging task and we introduce two new metrics that both respond the need for security and equity.
correct the biases that could exist in the embedding space. To achieve
Besides being very simple, the resulting methodology is more stable and faster than most current methods of bias mitigation. both leverages the strong accuracy of pre-trained models while cor- recting their bias. We illustrate the soundness of our methodology and strongly believe could also be used to alleviate other types bias. Our work opens several lines of research: for instance, it would be interesting to extend our ideas to the context of mul- ticlass sensitive attributes and of continuous sensitive attributes such as age. Another idea would be to somehow incorporate our faimess criteria during the training of the Ethical Module. Finally, we think that incorporating large-margin constraints into the loss used to train the Ethical Module would be promising attempt to go beyond the trade-off between faimess and performance.
several pre-trained models,

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Under review as a conference paper at ICLR 2022
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13


Reviews:
[{"review_id": "WdLGG0mJrzw", "reviewer": "Reviewer_k7gc", "summary": "", "questions": "", "limitations": "", "rating": 5, "confidence": 4, "soundness": null, "presentation": null, "contribution": null, "strengths": "", "weaknesses": "", "quality": null, "clarity": null, "significance": null, "originality": null, "strengths_and_weaknesses": "", "was_revised": false, "final_justification": "", "rebuttal": "", "claims_and_evidence": "", "methods_and_evaluation_criteria": "", "theoretical_claims": "", "experimental_designs_or_analyses": "", "relation_to_broader_scientific_literature": "", "essential_references_not_discussed": "", "other_strengths_and_weaknesses": "", "other_comments_or_suggestions": "", "questions_for_authors": "", "summary_of_paper": "", "summary_of_recommendation": "", "technical_quality": "", "clarity_of_presentation": "", "potential_impact": "", "robotics_focus": "", "quality_of_limitations": "", "questions_for_rebuttal": "", "reasons_to_accept": "", "reasons_to_reject": "", "questions_to_authors": "", "main_review": "\nStrengths:\n\n- The paper proposes an effective post-processing ethical module, which helps to improve the fairness of the pre-trained face recognition models. \n- The paper discusses how to measure fairness in the image verification tasks and suggests ratio-based metrics with an additional constraint. The fairness metrics seem to be inspired by Equalized Odds, which is one of the promising group fairness definitions. \n \nWeaknesses:\n\n<Algorithm>\n\n   - Several design choices are unclear. For example, is the von Mises-Fisher loss (vMF loss) used because it has suitable characteristics for combining fairness features into the face recognition framework? Or, was it chosen because vMF is recently-used in the face recognition field? Such details should be added.\n   - Also, it is unclear how the final vML loss and the fairness metrics (BFRR, BFAR) are linked. It seems that the current algorithm just adjusts the influence of each group in the loss function through a grid search on hyperparameters. This approach seems a bit naive. Moreover, the effects of the hyperparameters $\\kappa_0$ and $\\kappa_1$ are not clear. Thus, it would be better to explain why this algorithm is suitable for achieving the fairness metrics.\n\n<Experiments>\n\n- The comparison with existing fairness algorithms is missing. Although the paper mentions several previous algorithms (Wang & Deng, 2020, Dhar et al., 2020), the experiments compared neither fairness nor training efficiency. Also, the paper claims that the proposed algorithm is faster and stable than the previous approaches, but these arguments lack justification.\n- It is less convincing that the proposed algorithm would work well in other scenarios. The current experiments only use one pre-trained model (ArcFace), and the fairness performances (i.e., BFAR and BFRR) are mainly tested on the IJB-C dataset. Thus, it would be better if the proposed algorithm is tested on other scenarios as well.\n- The fairness results in Section 4.1 are hard to understand. For example, in Figure 4(b), is not the fairness value (FAR1/FAR0) decreased when $\\kappa_1$ increased (i.e., opposite from the page 8 explanation)? Also, all the contents in Figure 4 are too small to recognize easily, and the point (20, 26) seems not to appear in Figure 4. The interval of the ticks is five, then where does the number 26 come from? Moreover, it is hard to compare the fairness performances in Figures 4(a), 4(b), and 4(c), as all color bars' scales are different. It would be much better to clarify the descriptions.\n\n-------------------------------------------\nAfter reading the authors' response: \n\nThanks for your answers and more works on the experiments. I have raised my score to 5 since the experimental results became more convincing and clear. However, I still have some concerns about Sections 3 & 4. I understood that the vMF loss is an appropriate loss function for face recognition, and there is some link between the groups in the data and the vMF loss. However, the fairness metrics that the paper suggested are only empirically connected to the loss design. Thus, the paper needs a more precise explanation of why the simple modification of the vMF loss is enough to improve the target fairness (or types of bias). There may be other choices like adding unfairness penalty terms that can directly minimize fairness loss (which might be related to the brief discussion in the Conclusion section). I am not yet convinced why the current loss design is the most suitable way to improve fairness in face recognition. Based on the above reasons, I decided to raise my score to 5.", "summary_of_the_paper": "This paper proposes a post-processing approach for fair face recognition, especially the verification tasks (i.e., predicting whether two images correspond to the same group or not). The key idea is to add a shallow MLP on the pre-trained embedding models such as ArcFace, and this new MLP is trained using von Mises-Fisher loss. The paper discusses that fairness in face recognition techniques should be evaluated by comparing two groups’ false rates while preserving a security constraint. The algorithm tries to find good hyperparameters (i.e., the concentration parameters in the loss) for high fairness by grid search.", "summary_of_the_review": "Although the motivation and the target problem are promising, this paper has a large room for improvement (as explained in the main review). Thus, I believe that this paper is currently not good enough to accept.", "strength_and_weaknesses": "", "limitations_and_societal_impact": "", "review_text": "", "extra_scores": {"correctness": "3: Some of the paper’s claims have minor issues. A few statements are not well-supported, or require small changes to be made correct.", "technical_novelty_and_significance": "2: The contributions are only marginally significant or novel.", "empirical_novelty_and_significance": "2: The contributions are only marginally significant or novel."}, "extra_text": {}}, {"review_id": "NuSfYBTsIIM", "reviewer": "Reviewer_vzpf", "summary": "", "questions": "", "limitations": "", "rating": 5, "confidence": 3, "soundness": null, "presentation": null, "contribution": null, "strengths": "", "weaknesses": "", "quality": null, "clarity": null, "significance": null, "originality": null, "strengths_and_weaknesses": "", "was_revised": false, "final_justification": "", "rebuttal": "", "claims_and_evidence": "", "methods_and_evaluation_criteria": "", "theoretical_claims": "", "experimental_designs_or_analyses": "", "relation_to_broader_scientific_literature": "", "essential_references_not_discussed": "", "other_strengths_and_weaknesses": "", "other_comments_or_suggestions": "", "questions_for_authors": "", "summary_of_paper": "", "summary_of_recommendation": "", "technical_quality": "", "clarity_of_presentation": "", "potential_impact": "", "robotics_focus": "", "quality_of_limitations": "", "questions_for_rebuttal": "", "reasons_to_accept": "", "reasons_to_reject": "", "questions_to_authors": "", "main_review": "Strengths\n- The introduced idea to use the von Mises-Fisher loss as the training objective to effectively control the space allocated to each protected subgroup in latent space is insightful and useful for the ML ethics community. Including the maximum likelihood interpretation was also a good choice as it also helps to illustrate a different perspective of thinking about it.\n- The motivation of BFRR and BFAR is well explained by situating it relative to other fairness metrics\n\nWeaknesses\n- The citation style does not follow ICLR conventions\n- Glaringly missing analysis in Section 4.2\n- Lack of connection between BFAR and BFRR (see below)\n- Lack of comparison to other post-processing methods (see below)\n- The results shown in Section 4.1 do not seem to be clearly analysed (see below)\n\nQuestions\n- Why exactly is a balanced dataset not enough to mitigate bias? It is good to explain in related work to more strongly motivate your approach of post-processing.\n- Under BFRR and BFAR, we do not compare across multiple sensitive attributes, only the worst performing class and the best performing class. Why is this appropriate in your view?\n- Under Section 4, how long did it take to train the MLP? On what hardware? It would be good to give such figures if you are claiming it is a fast post-processing method.\n- Table 1 seems misleading to compare because FRR@FAR is a %, but BFRR and BFAR are ratios. It might be helpful to remind the reader in the caption\n- In Section 4.1, I am not able to see the relationship between increasing $\\kappa_1$ and $FRR_1 / FRR_0$ or $FAR_1 / FAR_0$ because the trend is different at each fixed value of $\\kappa_0$. Similarly for $\\kappa_0$ at each fixed value of $\\kappa_1$. Could you help me understand this more clearly? Also, can you provide an intuitive explanation for the role of $\\kappa_0$ and $\\kappa_1$ with respect to the ratios?\n- Can the BFAR and BFRR discussion be applied to Ethical Module other than a grid search (which suggests a weak link if this is the only use)? How so?\n- I also find it surprising that the authors did not compare with other post-processing methods in the experiments. How would you compare your approach to others, given that experiments were not run?\n\nTypo\n- Right above section 4: NLL not \"NNL is in fact the...\"\n", "summary_of_the_paper": "The paper introduces a post-processing method they call an Ethical Module, which is composed of a shallow multi-layer perceptron trained with a von Mises-Fisher loss. The authors also introduce two new fairness metrics BFRR and BFAR, which are more security demanding and  interpretable.\n\nThe author's claimed contributions are the following:\n- 2 fairness metrics: BFRR, BFAR\n- The Ethical Module\n", "summary_of_the_review": "Overall, I think this paper is marginally below the acceptance threshold. I appreciate the novel approach of the von Mises-Fisher loss for post-processing, and the discussion surrounding how to think about it. My concern is in regard to a more intuitive explanation of the behaviour of the hyperparameters governing the von Mises-Fisher loss, and missing analysis with regard to some experiments or comparisons. Without them, the paper in the current state is difficult to accept even though the idea is technically interesting.", "strength_and_weaknesses": "", "limitations_and_societal_impact": "", "review_text": "", "extra_scores": {"correctness": "3: Some of the paper’s claims have minor issues. A few statements are not well-supported, or require small changes to be made correct.", "technical_novelty_and_significance": "4: The contributions are significant, and do not exist in prior works.", "empirical_novelty_and_significance": "4: The contributions are significant, and do not exist in prior works."}, "extra_text": {}}, {"review_id": "Kpl6KfsoFQc", "reviewer": "Reviewer_7eUe", "summary": "", "questions": "", "limitations": "", "rating": 5, "confidence": 3, "soundness": null, "presentation": null, "contribution": null, "strengths": "", "weaknesses": "", "quality": null, "clarity": null, "significance": null, "originality": null, "strengths_and_weaknesses": "", "was_revised": false, "final_justification": "", "rebuttal": "", "claims_and_evidence": "", "methods_and_evaluation_criteria": "", "theoretical_claims": "", "experimental_designs_or_analyses": "", "relation_to_broader_scientific_literature": "", "essential_references_not_discussed": "", "other_strengths_and_weaknesses": "", "other_comments_or_suggestions": "", "questions_for_authors": "", "summary_of_paper": "", "summary_of_recommendation": "", "technical_quality": "", "clarity_of_presentation": "", "potential_impact": "", "robotics_focus": "", "quality_of_limitations": "", "questions_for_rebuttal": "", "reasons_to_accept": "", "reasons_to_reject": "", "questions_to_authors": "", "main_review": "I find the adaptation of face recognition metrics to the fairness\ndomain interesting. My main concerns are related to the evaluation of\nthe model. If I understood correctly, the few values for K0 and K1 are\nchosen through grid search. The evaluation presents results for three\nsuch combination of K0,K1. I'm guessing the results are for a test\nsplit of the datasets. I'm curious to understand, if the evaluation\nwould involve a \"deployment scenario\", in which a dev/eval split set\nis used to choose a particular combination for K0, K1, how would the\nresults look for the test set. The reason I'm asking this is that the\nresults are not improved overall for all combinations of K0,K1 and it\nis not clear what would happen in a realistic setting.\n\nIf I understand correctly, the results obtained for IJB-B dataset\nseemed to be inferior to the ones of the original model (Table\n3). There is no comment on these results in the paper and I wonder if\nthere is any intuition why these results are different.\n", "summary_of_the_paper": "This paper proposes introducing a shallow network used as a\npost-processing stage for face recognition models. The newly\nintroduced module operates on the encodings generated by the main\nmodule and its main goal is to reduce the bias of the original model\nas measured by fairness metrics. The fairness metrics used in this\npaper are inspired by equalized odds and adapted to the face\nrecognition scenarios. Instead of using differences, the metrics\nintroduced employ the ratios of FRRs and FARs (False Rejection and\nFalse Acceptance Rates, similar to false negatives and false positive\nrates). The new module is referred to as \"the ethical module\". The\nethical module is trained using a loss based on the Von Mises-Fisher\ndistribution.\n\nThe ethical model is evaluated in conjunction with Arcface, which is a\nstate of the art model for face recognition. The ethical model is used\nto mitigate gender bias. Gender labels are generated by an in-house\nclassifier that assigns gender to each image.\n\nThe performance of the model is also verified on several image datasets. \n\n", "summary_of_the_review": "The adaptation of fairness metrics to the face recognition setting is\ninteresting. The evaluation of the method proposed has some gaps that\nlowers the quality of the paper.", "strength_and_weaknesses": "", "limitations_and_societal_impact": "", "review_text": "", "extra_scores": {"correctness": "3: Some of the paper’s claims have minor issues. A few statements are not well-supported, or require small changes to be made correct.", "technical_novelty_and_significance": "3: The contributions are significant and somewhat new. Aspects of the contributions exist in prior work.", "empirical_novelty_and_significance": "3: The contributions are significant and somewhat new. Aspects of the contributions exist in prior work."}, "extra_text": {}}, {"review_id": "5vcSRy2ksON", "reviewer": "Reviewer_u2Cg", "summary": "", "questions": "", "limitations": "", "rating": 5, "confidence": 4, "soundness": null, "presentation": null, "contribution": null, "strengths": "", "weaknesses": "", "quality": null, "clarity": null, "significance": null, "originality": null, "strengths_and_weaknesses": "", "was_revised": false, "final_justification": "", "rebuttal": "", "claims_and_evidence": "", "methods_and_evaluation_criteria": "", "theoretical_claims": "", "experimental_designs_or_analyses": "", "relation_to_broader_scientific_literature": "", "essential_references_not_discussed": "", "other_strengths_and_weaknesses": "", "other_comments_or_suggestions": "", "questions_for_authors": "", "summary_of_paper": "", "summary_of_recommendation": "", "technical_quality": "", "clarity_of_presentation": "", "potential_impact": "", "robotics_focus": "", "quality_of_limitations": "", "questions_for_rebuttal": "", "reasons_to_accept": "", "reasons_to_reject": "", "questions_to_authors": "", "main_review": "**Advantages**:\n1. It is well written, and I enjoyed reading it.\n2. The proposed post-processing module is simple, yet effective.\n3. Two new metrics are proposed to help evaluate the fairness of Face Recognition systems.\n\n\n**I have some minor concerns and questions**:\n\n1. There is no comparing baselines. It is thus difficult to evaluate the relative effectiveness of the proposed model.\n2. Experiments section only provides quantitative evaluation results. There is no analysis of what has been learned by the Ethical Module. It would be great if the authors could provide some explainability analysis, to provide insights into the transformation that has been conducted by the Ethical Module.\n3. Only gender bias is considered. Could the proposed module be adapted to address other categories of bias, such as race and age bias? In addition, the authors mentioned that the current gender classifiers are used to generate proxy gender labels. If the race bias is considered, whether current race classifiers could be used to generate proxy race labels?\n4. For the pre-trained model, only Arcface is considered. It would be interesting to know the mitigation performance for other pretrained models.\n\n\n=========\n\nI did not see the authors' response. Also considering other reviewers' comments, I have adjusted my rating to 5.\n", "summary_of_the_paper": "This paper proposes a post-processing mitigation method, termed as the Ethical Module, to mitigate gender bias of Face Recognition models. The ethical module is a three-layer shallow MLP built on top of a frozen pretrained model, with the goal to correct the biases that could exist in the embedding space of the pretrained model. The module is trained using the proposed von Mises-Fisher loss. Despite being very simple, experimental results on benchmark face recognition datasets have validated the effectiveness of the proposed post-processing mitigation module.\n", "summary_of_the_review": "The proposed ethical module and the way to train it is novel. Besides the paper is well written. The experimental evaluation part could be strengthened, to better validate the effectiveness of the proposed method.", "strength_and_weaknesses": "", "limitations_and_societal_impact": "", "review_text": "", "extra_scores": {"correctness": "4: All of the claims and statements are well-supported and correct.", "technical_novelty_and_significance": "4: The contributions are significant, and do not exist in prior works.", "empirical_novelty_and_significance": "4: The contributions are significant, and do not exist in prior works."}, "extra_text": {}}]

Author rebuttal:

Meta-review: The paper proposes a novel post-processing method technique that can mitigate the model bias, called the Ethical Module. It transforms the deep embeddings of a given model to give more representation power to the disadvantaged subgroups. 

The idea of ​​resolving discrimination against a specific group through effective post processing is promising, and proposing new metrics for fairness is also a very important and relevant issue.

However, the connection between the technique proposed in this paper and the newly proposed fairness metric is not clear, so the focus of the paper is somewhat lowered. Moreover, several design choices are somewhat unclear and ad-hoc. In particular, although there was a lot of improvement through the rebuttal period, it is difficult to verify the superiority of the proposed method via the experiments in the paper; Direct comparisons with existing methods for fairness is essential, and it seems necessary to consider a hyperparameter selection strategy that can be taken in a practical scenario rather than simply choosing the best performing hyperparameter for the test set.
Decision: Reject