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 authors propose a simple cluster-conditional post-hoc strategy to calibrate the similarity scores obtained using a pre-trained network. In essence, this work proposes to use a cluster-specific (or group-specific in case of Oracle) calibration function (\mu), which results in improving the scores pertaining to verification of a x1-x2 pair (where both x1 and x2 belong to the same demographic group) mapping function. This is similar to choosing group-specific threshold demonstrated in the BFW paper (Robinson et al, CVPRW 2020). Unlike existing methods such as AGENDA, FTC etc. FairCal does not require the protected attribute labels during training and testing.