FairCal: Fairness Calibration for Face Verification

1 INTRODUCTION . Face recognition ( FR ) systems are being increasingly deployed worldwide in a variety of contexts , from policing and border control to providing security for everyday consumer electronics . According to Garvie et al . ( 2016 ) , face images of around half of all American adults are searchable in police databases . FR systems have achieved impressive results in maximizing overall accuracy ( Jain et al. , 2016 ) . However , they have also been shown to exhibit significant bias against certain demographic subgroups ( Buolamwini & Gebru , 2018 ; Orcutt , 2016 ; Alvi et al. , 2018 ) , defined by a sensitive attribute such as ethnicity , gender , or age . Many FR systems have much higher false positive rates ( FPRs ) for non-white faces than white faces ( Grother et al. , 2019 ) . Therefore , when FR is employed by law enforcement , non-white individuals may be more likely to be falsely detained ( Allyn , 2020 ) . Thus , it is of utmost importance to devise an easily-implementable solution to mitigate FR bias . Most efforts to mitigate FR bias have been directed towards learning less biased representations ( Liang et al. , 2019 ; Wang et al. , 2019b ; Kortylewski et al. , 2019 ; Yin et al. , 2019 ; Gong et al. , 2020 ; Wang & Deng , 2020 ; Huang et al. , 2020 ; Gong et al. , 2021 ) . These approaches have enjoyed varying degrees of success : though the bias is reduced , is reduced ( Gong et al. , 2020 ) . They often require retraining the models from scratch , which is computationally expensive . Moreover , they often require the sensitive attribute of the face ( such as ethnicity ) ( Gong et al. , 2020 ; Dhar et al. , 2020 ; Terhörst et al. , 2020a ; Dhar et al. , 2021 ; Robinson et al. , 2020 ) , which may not be feasible to obtain . Hence , an approach that improves fairness in existing models without reducing accuracy , or knowing the sensitive attribute , or require retraining , is missing . In this work , we focus on the face verification problem , a major subproblem in FR : determine whether two face images depict the same person . Current state-of-the-art ( SOTA ) classifiers are based on deep neural networks that embed images into a low-dimensional space ( Taigman et al. , 2014 ) . The “ Baseline ” method is one that deems a pair of images is a match if the cosine similarity between their embeddings exceeds a certain threshold . We illustrate and compare the bias of current models in Figure 1 , and compare their characteristics in Table 1 . The fairness of face verification classifiers is typically assessed by three quantities , explained below : ( i ) fairness calibration across subgroups , ( ii ) equal false positive rates ( FPRs ) across subgroups i.e . predictive equality , ( iii ) equal false negative rates ( FNRs ) across subgroups , i.e . equal opportunity . A classifier is said to be globally calibrated if its predicted probability ppred of face matches in a dataset is equal to the fraction ptrue of true matches in the dataset ( Guo et al. , 2017 ) . This requires the classifier to additionally output an estimate of the true probability of a match , i.e . confidence . However , we suggest it is even more crucial for models to be fairly calibrated , i.e. , for calibration to hold conditionally on each subgroup ( see Definition 2 ) . Otherwise , if the same predicted probability is known to carry different meanings for different demographic groups , users including law enforcement officers and judges may be motivated to take sensitive attributes into account when making critical decisions about arrests or sentencing ( Pleiss et al. , 2017 ) . Moreover , previous works such as Canetti et al . ( 2019 ) and Pleiss et al . ( 2017 ) presume the use of a fairly-calibrated model for their success . While global calibration can be achieved with off-the-shelf post-hoc calibration methods ( Platt , 1999 ; Zadrozny & Elkan , 2001 ; Niculescu-Mizil & Caruana , 2005 ; Guo et al. , 2017 ) , they do not achieve fairness-calibration . This is illustrated in Figure 2 . However , achieving all three fairness definitions mentioned above : ( i ) fairness-calibration , ( ii ) equal FPRs , ( iii ) equal FNRs , is impossible in practice as several authors have shown ( Hardt et al. , 2016 ; Chouldechova , 2017 ; Kleinberg et al. , 2017 ; Pleiss et al. , 2017 ) . We elaborate further on this in section 3 , the key takeaway is that we may aim to satisfy at most two of the three fairness notions . In the particular context of policing , equal FPRs i.e . predictive equality is considered more important than equal FNRs , as false positive errors ( false arrests ) risk causing significant harm , especially to members of subgroups already at disproportionate risk for police scrutiny or violence . As a result , our goals are to achieve fairness-calibration and predictive equality across subgroups , while maintaining accuracy , without retraining . We further assume that we do not have access to the sensitive attributes , as this may not be feasible in practice due to ( a ) privacy concerns , ( b ) challenges in defining the sensitive attribute ( e.g . ethnicity can not be neatly divided into discrete categories ) , and ( c ) laborious and expensive to collect . In this paper , we succeed in achieving all of the objectives mentioned above . The main contribution is the introduction of a post-training Fairness Calibration ( FairCal ) method : 1 . Accuracy : FairCal achieves state-of-the-art accuracy ( Table 2 ) for face verification on two large datasets . 2 . Fairness-calibration : Our face verification classifier outputs state-of-the-art fairnesscalibrated probabilities without knowledge of the sensitive attribute ( Table 3 ) . 3 . Predictive equality : Our method reduces the gap in FPRs across sensitive attributes ( Table 4 ) . For example , in Figure 2 , at a Global FPR of 5 % using the baseline method Black people are 15X more likely to false match than white people . Our method reduces this to 1.2X ( while SOTA for post-hoc methods is 1.7X ) . 4 . No sensitive attribute required : Our approach does not require the sensitive attribute , neither at training nor at test time . In fact , it outperforms models that use this knowledge . 5 . No retraining : Our method has no need for retraining or tuning the feature representation model , or training an additional model , since it performs statistical calibration post-hoc . 2 RELATED WORK . Fairness , or Bias mitigation : Work on bias mitigation for deep FR models can be divided into two main camps : ( i ) methods that learn less biased representations , and ( ii ) post-processing approaches that attempt to remove bias from a pre-trained feature representation model by building fairer decision systems ( Srinivas et al. , 2019 ; Dhar et al. , 2020 ; 2021 ; Terhörst et al. , 2020a ; b ; Robinson et al. , 2020 ) . Several approaches have been pursued in ( i ) , including domain adaptation ( Wang et al. , 2019a ) , margin-based losses ( Khan et al. , 2019 ; Huang et al. , 2020 ) , data augmentation ( Kortylewski et al. , 2019 ) , feature augmentation ( Yin et al. , 2019 ; Wang et al. , 2019b ) , reinforcement learning ( Wang & Deng , 2020 ) , adversarial learning ( Liu et al. , 2018 ; Gong et al. , 2020 ) , and attention mechanisms ( Gong et al. , 2021 ) . While these methods mitigate bias , this is often achieved at the expense of recognition accuracy and/or at high computational cost . The work we present in this paper fits into ( ii ) , and thus we focus on reviewing those approaches . For an in-depth literature review of bias mitigation for FR models , see Drozdowski et al . ( 2020 ) . We compare all these methods in Table 1 . Srinivas et al . ( 2019 ) proposed an ensemble approach , exploring different strategies for fusing the scores of multiple models . This work does not directly measure bias reduction , and presents only the results of applying the method to a protected subgroup . Terhörst et al . ( 2020b ) show that while this method is effective in increasing overall accuracy , it fails to reliably mitigate bias . Dhar et al . ( 2020 ) proposed the Adversarial Gender De-biasing algorithm ( AGENDA ) to train a shallow network that removes the gender information of the embeddings of a pre-trained network . Dhar et al . ( 2021 ) extended this work with PASS to deal with any sensitive attribute , and proposed a novel discriminator training strategy . This leads to reduced gender bias in face verification , but at the cost of accuracy . Also , AGENDA and PASS require the sensitive attributes during training . Terhörst et al . ( 2020a ) proposed the Fair Template Comparison ( FTC ) method , which replaces the computation of the cosine similarity score by an additional shallow neural network trained using cross-entropy loss , with a fairness penalization term and an l2 penalty term to prevent overfitting . While this method does indeed reduce a model ’ s bias , it comes at the expense of an overall decrease in accuracy . Moreover , it requires training the shallow neural network and tuning the loss weights . Most importantly , it requires the sensitive attributes during training . Robinson et al . ( 2020 ) proposed GST which uses a group-specific threshold . However , the calibration sets in GST are defined by the sensitive attributes themselves . Terhörst et al . ( 2020b ) proposed the Fair Score Normalization ( FSN ) method , which is essentially GST with unsupervised clusters . FSN normalizes the scores by requiring the model ’ s FPRs across unsupervised clusters to be the same at a predefined global FPR . These methods are not designed to be fairly-calibrated . Moreover , if a different global FPR is desired , the method needs to be recomputed . In contrast , instead of fixing one FPR threshold , our method converts the cosine similarity scores into calibrated probabilities , which can then be used for any choice of fair FPRs . In addition , our approach can be extended to group fairness for K-classification problems , which is not possible with GST or FSN . Calibration : Calibration is closely related to uncertainty estimation for deep networks ( Guo et al. , 2017 ) . Several post-hoc calibration methods have been proposed such as Platt ’ s scaling or temperature scaling ( Platt , 1999 ; Guo et al. , 2017 ) , histogram binning ( Zadrozny & Elkan , 2001 ) , isotonic regression ( Niculescu-Mizil & Caruana , 2005 ) , spline calibration ( Gupta et al. , 2021 ) , and beta calibration ( Kull et al. , 2017 ) , among others . All of these methods involve computing a calibration function . As such , any calibration method can be readily applied , leading to models that are calibrated but not fairly-calibrated . An algorithm to achieve the latter for a binary classifier has been proposed in Hebert-Johnson et al . ( 2018 ) , but the work remains theoretical and no practical implementation is known . Fairly calibrated models are the missing ingredient in the works of Canetti et al . ( 2019 ) and Pleiss et al . ( 2017 ) , since they work with the presumption that a fairly calibrated model exists .

Summary: The paper proposes an approach, called FairCal, for fairly calibrating face verification models. The method does not require access to sensitive attributes for calibrating, instead the paper uses k-means algorithm to find clusters of data and applies beta-calibrating algorithm on each cluster. The authors show that after calibrating with FairCal the model still achieves good accuracy and outputs more fairness-calibrated probabilities. Also, the method reduces the FPR gap across sensitive attributes.