Title: Fairness under Noise Perturbation: from the Perspective of Distribution Shift
Venue: NeurIPS 2023
Accepted: no
Keywords: noise-tolerant fairness

distribution shift

fair representation learning
Abstract: Much work on fairness assumes access to clean data during training. In practice, however, due to privacy or legal concern, the collected data can be inaccurate or intentionally perturbed by agents. Under such scenarios, fairness measures on noisy data become a biased estimation of ground-truth discrimination, leading to unfairness for a seemingly fair model during deployment. Current work on noise-tolerant fairness assumes a group-wise universal flip, which can become trivial during training, and requires extra tools for noise rate estimation. In light of existing limitations, in this work, we consider such problem from a novel perspective of distribution shift, where we consider a normalizing flow framework for noise-tolerant fairness without requiring noise rate estimation, which is applicable to both \emph{sensitive attribute noise} and \emph{label noise}. We formulate the noise perturbation as both group- and label-dependent, and we discuss theoretically the connections between fairness measures under noisy and clean data. We prove theoretically the transferability of fairness from noisy to clean data under both types of noise. Experimental results on three datasets show that our method outperforms state-of-the-art alternatives, with better or comparable improvements in group fairness and with relatively small decrease in accuracy under single exposure and the simultaneous presence of two types of noise.

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Abstract

Much work on fairness assumes access to clean data during training. In practice, however, due to privacy or legal concern, the collected data can be inaccurate or intentionally perturbed by agents. Under such scenarios, fairness measures on noisy data become a biased estimation of ground-truth discrimination, leading to unfairness for a seemingly fair model during deployment. Current work on noisetolerant fairness assumes a group-wise universal flip, which can become trivial during training, and requires extra tools for noise rate estimation. In light of existing limitations, in this work, we consider such problem from a novel perspective of distribution shift, where we consider a normalizing flow framework for noisetolerant fairness without requiring noise rate estimation, which is applicable to both sensitive attribute noise and label noise . We formulate the noise perturbation as both group- and label-dependent, and we discuss theoretically the connections between fairness measures under noisy and clean data. We prove theoretically the transferability of fairness from noisy to clean data under both types of noise. Experimental results on three datasets show that our method outperforms stateof-the-art alternatives, with better or comparable improvements in group fairness and with relatively small decrease in accuracy under single exposure and the simultaneous presence of two types of noise.

1 Introduction

As machine learning systems are increasingly used in high-stake social areas, there have been arising 20 concerns that automatic decision-making systems, if not properly regulated or intervened, would 21 perpetuate or amplify existing biases and discrimination in society (Angwin et al., 2016; Dressel 22 and Farid, 2018; De-Arteaga et al., 2022; Ricci Lara et al., 2022). It has been shown that merely 23 removing sensitive information during training is not sufficient to ensure fairness, as there may be 24 correlation or causality between sensitive attributes and other features used in the training process, 25 which could result in discriminatory outcomes (Jackson, 2018; Mehrabi et al., 2021). In response, 26 different metrics and methods on fairness (Hardt et al., 2016; Zafar et al., 2017; Choi et al., 2020; 27 Diana et al., 2022) have been proposed to quantify discrimination and to achieve parity for machine 28 learning models. 29

Current literature on fairness generally assumes access to full and clean sensitive information when 30

imposing fairness intervention. In practice, however, due to privacy or legal concern, it is sometimes 31

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infeasible to collect or use such information, greatly hindering the application of conventional methods

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on fairness (Lahoti et al., 2020; Chai et al., 2022); moreover, the collected sensitive information

can be subject to noisy perturbation, leading to inaccurate estimation of unfairness (Fioretto et al., 34

2022). Despite recent works on proxy sensitive attribute (Yan et al., 2020; Grari et al., 2021), it 35

has been shown that noisy protected information alone, without extra regulation, is not a sufficient 36

substitution for ground-truth sensitive information (Lamy et al., 2019). Therefore, it is crucial to 37 study the problem of fairness under noisy sensitive information. 38

Much of current work on fairness under noisy sensitive information requires access to noise rate 39 or external tools for noise rate estimation and uses group-dependent noise rate to rectify measures 40 of unfairness during training (Wang et al., 2020; Celis et al., 2021; Mehrotra and Celis, 2021). 41 However, the estimation process can be costly and inaccurate up to varied estimation methods, and 42 such formulations may not work well under varying noise rates between training and testing data. 43 Besides, much of current formulation regarding noisy sensitive information assumes uniform flip 44 within different groups, which in return, could lead to trivial modifications of fairness constraints 45 during training, especially in terms of complex neural networks. Instead, we seek to find alternative 46 ways to quantify disparities and to improve fairness under noisy sensitive information, without using 47 extra tools for noise evaluation. 48

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We draw inspirations from fairness under distribution shift, where the goal is to ensure the transferability of fairness and accuracy between source (training) distribution and target (testing) distribution (Rezaei et al., 2021; Singh et al., 2021) for a given classifier. Specifically, in terms of noisy sensitive information, we can readily think of the noisy distribution as source, and clean distribution as target. However, most work on distribution shift requires access to the target distribution, which in return, requires external tools for noise rate evaluation.

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In light of current limitations in both aspects, in this work, we propose a general framework for fairness under noisy sensitive attribute from the perspective of distribution shift. We consider groupand class-dependent noise rates within each subgroup, and we show that under such formulation, fairness metrics under noisy attributes are not necessarily proportional to those under clean attributes. We propose to solve the problem from the perspective of fair representation learning, where the idea is to train a fair encoder such that its latent representation achieves desired fairness and accuracy properties. We quantify disparities between noisy and clean distributions from the perspective of group- and class-dependent distribution shift under our formulation of noisy sensitive information, and we show theoretically that under bounded divergence between noisy distributions of different subgroups, we have the transferability of fairness guarantee between noisy and clean data, where disparities under clean data are upper-bounded by disparities under noisy data up to addictive and multiplicative constants. In this way, we are able to achieve fairness under noisy protected information, without applying extra techniques for noise rate estimation. What's more. we extend our method to fairness under label noise, where we show both theoretically and experimentally that our method improves fairness under group- and label-dependent label noise.

We summarize our contribution as follows:

1. We discuss two types of noise (i.e., sensitive attribute noise and label noise) under group- and label-dependent assumptions, and we derive the theoretical connections between fairness measures under noisy and clean data in the presence of each type of noise.

2. We formulate fairness under sensitive attribute noise through a novel perspective of distribution shift, from which we introduce a representation learning framework without requiring extra techniques for noise rate estimation. Moreover, we extend our framework to address fairness under label noise.

3. We prove theoretically the transferability of fairness between noisy and clean data both under sensitive attribute noise and label noise.

4. We validate the effectiveness of our method in improving fairness through experiments on three benchmark datasets, where we evaluate its performance under both single exposure and simultaneous presence of sensitive attribute and label noise.

2 Related work

Fairness in Machine Learning : Discrepancies in machine learning systems against certain groups 83 or subgroups are generally considered to be originated from biased training data, rather than the 84 training process (Kleinberg et al., 2016). To quantify such disparities, different fairness notions 85 have been proposed, including disparate impact (Willborn, 1984), equal opportunity and equalized 86 odds Hardt et al. (2016), Lipschitz continuity (Dwork et al., 2012; Yurochkin et al., 2019) and 87 calibration(Dwork et al., 2012) for individual fairness. Accordingly, different methods have been 88

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proposed to mitigate bias during the training process. Preprocessing methods (Tan et al., 2020; Li and Liu, 2022; Kleindessner et al., 2023) aims at obtaining a rectified distribution of input features or labels such that the desired fairness measures are satisfied on the training set. Inprocessing methods (Madras et al., 2018; Roh et al., 2020; Chai et al., 2022) aim at reagulating the training process with relaxed fairness constraints. Postprocessing methods aim at adjusting decision thresholds (Hardt et al., 2016; Corbett-Davies et al., 2017; Hsu et al., 2022) for each group or learning a instance-wise mapping of soft labels based on expected fairness measures. However, most of existing work on fairness is formulted without considering the effect of label or attribute noise.

Noise-Tolerant Fairness : Existing work on fairness under attribute noise relies on the estimation of noise rates. Lamy et al. (2019) first proposes a general framework for fairness under groupdependent attribute noise, and propose to rectify unfairness tolerance during training based on noise rate estimation. Celis et al. (2021) considers the problem similarly by rectifying fairness constraints during training with niose transition matrix. Wang et al. (2020) considers the problem from the perspective of distributionally robust optimization and uses soft group assignment to rectify fairness constraint. Mehrotra and Celis (2021) proposes a preprocessing framework based on sample selection with relaxed weight constraints specified by noise rates.

Methods on fairness under label noise generally focuses on rectifying fairness measures based on estimated noise rates. Work including (Wang et al., 2021; Wu et al., 2022) proposes to replace fairness constraints on noisy data with their corresponding surrogate measures on clean data. Zhang et al. (2023) proposes a V AE-based framework to achieve disentanglement between input feature and sensitive information and uses mutual information between noisy and clean label as penalty term.

Fairness under Distribution Shift : Distribution shift has been shown to be non-trivial in fairness and could significantly deteriorate discrimination of a fair classifier (Mishler and Dalmasso, 2022; Schrouff et al., 2022; Chai and Wang, 2023). A general assumption in distribution shift is that labelled source distribution ( X,Y,A ) ∼ P src and unlabelled target distribution ( X,A ) ∼ P trg are accessible during training. Generally, methods on fairness under distribution shift falls into two categories: importance reweighting (Sugiyama et al., 2007; Cortes et al., 2010), where the idea is to reweight instance-wise training loss based on the corresponding ratio between source and target distribution, and robust log loss (Rezaei et al., 2020; Singh et al., 2021; Rezaei et al., 2021; An et al., 2022), where the idea is to formulate training problem as a mini-max optimization problem with robust training loss. Chen et al. (2022) proposes to quantify transferability of fairness under bounded distribution shift represented by group-wise shift vectors, where feature shift and label shift are considered separately.

3 Method

Throughout this section, we use mea to denote measures under clean data, ˆ mea and ˜ mea to denote measures under sensitive attribute noise and under label noise, respectively. For example, we use { A,Y } to denote the random variables of sensitive attribute and label under clean data, { ˆ A,Y } the random variables under attribute noise, and { A, ˜ Y } the random variables under label noise. We use η and β to denote sensitive attribute noise rate and label noise rate, respectively.

3.1 Problem Formulation

Let { ( x i , y i , a i ) , 1 ⩽ i ⩽ N } be the training set where x i ∈ ❘ n is the input feature, y i ∈ { 0 , 1 } the training label and a i ∈ { 0 , 1 } the sensitive attribute, let f be the function of classifier, a general fair classification problem can be formulated as

where l is the classification loss and l f is the fairness constraint specified by designated fairness notions. For example, l f = | ∑ { i | a i = a } ✶ [ f ( x i ) ≥ 0 . 5] |{ i | a i = a }| -∑ { i | a i = a ′ } ✶ [ f ( x i ) ≥ 0 . 5] |{ i | a i = a ′ }| | , where a ′ = | 1 -a | , corresponds to disparate impact (DI), and l f = | ∑ { i | a i = a,y i =0 } ✶ [ f ( x i ) ≥ 0 . 5] |{ i | a i = a,y i =0 }| -∑ { i | a i = a ′ ,y i =0 } ✶ [ f ( x i ) ≥ 0 . 5] |{ i | a i = a ′ ,y i =0 }| | + | ∑ { i | a i = a,y i =1 } ✶ [ f ( x i ) ≥ 0 . 5] |{ i | a i = a,y i =1 }| -∑ { i | a i = a ′ ,y i =1 } ✶ [ f ( x i ) ≥ 0 . 5] |{ i | a i = a ′ ,y i =1 }| | corresponds to equalized odds (EOd).

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̸

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In the presence of sensitive attribute noise, such formulation can result in a biased estimation of 135 discrimination on training data. Previous work (Lamy et al., 2019; Celis et al., 2021) has shown 136 that under group-dependent sensitive attribute noise rate η a := p [ A = ˆ A | ˆ A = a ] , fairness measure 137 under noisy data is proportional to that under clean data: 138

However, such formulation can become trivial during training, especially for deep neural networks, where different noise rates can become ignorable under hyperparameter-tuning due to the proportionality. Instead, we consider a more general version of attribute flip, where noise rates are both group-dependent and label-dependent. Specifically, let P ya and Q ya be the distribution of data and predicted soft labels in the clean subgroup S ya := { i | y i = y, a i = a } respectively, let η ya := p [ A = ˆ A | Y = y, A = a ] be the sensitive attribute noise rate in the corresponding subgroup, we have the following relationship regarding noisy and clean distribution:

Correspondingly, we have the following relationship regarding DI and EOd under clean and noisy data:

Lemma 1. Under group- and label-dependent attribute noise rate η ya , we have

where DTPR (disparate true positive rate) = | TPR 0 -TPR 1 | is the difference in true positive rate (TPR) between the two sensitive groups { i | a i = 0 } and { i | a i = 1 } , DTNR (disparate true negative rate) = | TNR 0 -TNR 1 | , and ˆ α a = |{ i | ˆ a i = a,y i =1 }| |{ i | ˆ a i = a }| is the base rate of noisy data at group { i | ˆ a i = a } . Here we assume η ya + η ya ′ ⩽ 1 ; for η ya + η ya ′ ⩾ 1 , it is easy to come to equivalent expressions due to symmetry. From Lemma 1, we observe that under group- and label-dependent noise, EOd under noisy data can be expressed as a weighted sum of disparate TPR and TNR under clean data, while DI under noisy data takes a more complicated form involving both noisy base rates and noise rates and does not have a similar relationship with DI under clean data due to possible change in base rates. Correspondingly, optimizing over DI or EOd directly on noisy data may not lead to satisfying improvement in fairness, if without noise estimation.

3.2 From the Perspective of Distribution Shift

Estimation of sensitive attribute noise can be inaccurate. Instead, we aim to find a general way for fairness under attribute noise without using extra tools for noise estimation. Note from Lemma 1 that the deviation in fairness measure under noisy data is, in fact, induced by the disparities between noisy and clean distribution, leading to skewed estimation of group-wise utilities. Thus, one direct implication is to consider the problem from the perspective of covariate shift on training set. Specifically, we have the clean distribution of data as weighted subtraction of noisy distributions:

Consider noisy data as the source distribution and clean data as target, we have the KL-divergence 169 between noisy and clean distribution at each subgroup as follows: 170

This indicates that the discrepancy, or shift between noisy and clean distribution are in fact, controlled 171 by the discrepancy between corresponding noisy subgroups. By minimizing the divergence between 172

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data distribution ˆ P ya and ˆ P ya ′ , which, in return, minimizes the divergence between predicted soft label distribution Q ya and ˆ Q ya and thus provides fairness guarantee for noisy data, we are able to minimize the divergence between noisy and clean distribution. Therefore, by minimizing the divergence between ˆ P ya and ˆ P ya ′ we are able to ensure the transferability of fairness improvement between noisy and clean data. Specifically, when ˆ P ya = ˆ P ya ′ , we have D KL ( ˆ P ya || P ya ) = 0 .

3.3 Fair Representation Learning

Inspired by Eq. (3), transferability of fairness between clean and noisy data can be ensured under equalized distribution on noisy data: ˆ P ya = ˆ P ya ′ , ∀ y . Due to disparities on training data, however, such requirement is generally infeasible without applying extra regularization. Therefore, we consider a fair representation learning method for fairness under noisy attribute based on normalizing flow.

Let g ya be the function of bijective encoder for samples in the noisy subgroup ˆ S ya and h be the function of classification head, let z ya = g ya ( x ) be the latent representation of the corresponding subgroup and P z ya be the corresponding density, we can use change of variables formula to calculate the densities of z ya as:

Following Balunovi´ c et al. (2021), we use symmetrized KL-divergence to approximate the statistical 187 distance between subgroups: 188

where B is the batch size. And the overall training objective can be written as 189

arg min g 00 ,g 01 ,g 10 ,g 11 ,h λ 0 L 0 ( g 00 , g 01 ) + λ 1 L 1 ( g 10 , g 11 ) + (1 -λ 0 -λ 1 ) L cls ( g 00 , g 01 , g 10 , g 11 , h ) . (6)

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3.4 Theoretical Analysis

It is easy to see from Eq. (2) that when P ya P ya ′ , we also have P ya = P ya ′ regardless of noise rates, and the classifier achieves perfect EOd on both clean and noisy data. In reality, however, it is hard to achieve prefect fairness. The following theorem states a general relationship between fairness measure under clean and noisy data:

ˆ = ˆ ˆ

̸

Theorem 1. Let Q ya and Q ya be the distribution of predicted soft labels in the clean subgroup S ya and noisy group respectively, let η ya := p [ A = ˆ A | Y = y, ˆ A = a ] be the group- and class-dependent noise rate. For D KL ( ˆ Q ya , ˆ Q ya ′ ) ≤ ϵ y , we have the following upper- and lower-bound regarding EOd under clean distribution and ˆ EOd under noisy distribution:

We defer full proof to appendix. Theorem 1 shows that, despite ˆ EOd itself serves as a biased estimation of ground-truth EOd, by minimizing the KL-divergence between distributions of soft labels in label-wise subgroups, we are able to minimize the upper-bound of clean EOd, which validates the feasibility of our method.

3.5 Fairness under Noisy Labels

̸

We further extent our method to fairness under noisy labels. Following previous work on fairness under label noise (Wang et al., 2021), we consider group- and label-dependent noise rates. Let β ya := p [ Y = ˜ Y | ˜ Y = y, A = a ] be the label noise rate at the subgroup ˜ S ya , we have the following relationship regarding the distribution of clean and noisy data:

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where y ′ = | 1 -y | . Correspondingly, we have the following relationship regarding fairness measures under clean and noisy data:

Lemma 2. Under group- and label-dependent label noise rate β ya , we have

which shows that under label noise, ˜ DI itself serves as an unbiased estimation, while ˜ EOd is not an unbiased estimation of EOd. A natural question here is, does our method also work under label noise? The following lemma shows the connection between ˜ EOd and EOd:

Lemma 3. let β ya be the group- and class-dependent label noise rate, we have the following upper-bound regarding EOd under clean distribution and ˜ EOd under noisy distribution:

We defer full proof to appendix. Therefore, under label noise, optimizing over ˜ EOd can still benefit EOd, which is upper-bounded by ˜ EOd up to an multiplicative constant and an addictive constant determined by the noise rates.

4 Experiments

4.1 Experimental Setup

We validate our method on three benchmark datasets: COMPAS : The COMPAS dataset (Larson et al., 2016) contains 7,215 samples with 11 attributes. Following previous works on fairness (Zafar et al., 2017), we only select black and white defendants in COMPAS dataset, and the modified dataset contains 6,150 samples. The goal is to predict whether a defendant reoffends within two years, and we choose race as sensitive attributes. Adult : The Adult dataset (Dua and Graff, 2017) contains 65,123 samples with 14 attributes. The goal is to predict whether an individual's income exceeds 50 K , and we choose gender as sensitive attributes. CelebA : The CelebA dataset (Liu et al., 2015) contains 202,599 face images, each of resolution 178 × 218 , with 40 binary attributes. We choose gender as labels and age as sensitive attributes.

We implement our method in PyTorch 2.0.0 on one RTX-3090 GPU. We use accuracy as utility measure, DI (Willborn, 1984) and EOd (Hardt et al., 2016) as fairness measure. We use RealNVP (Dinh et al., 2016) to build our models, and network structures for other methods are chosen as MLP for COMPAS and Adult datasets, and ResNet-18 for CelebA dataset. We repeat experiments on each dataset three times and report the average results. In each repetition, we use a 80% -20% training-testing partition of data.

We compare our method with following related methods:

Baseline : Neural network without fairness regularization.

Inprocessing : Neural network with relaxed EOd constraint by (Wang et al., 2022). This is a fairness method without considering noisy data.

DLR : Neural network with fairness constraints rectified by noise transition matrix (Celis et al., 2021). This method focuses on fairness with noisy sensitive attributes.

FairExpec : Neural network with instance-wise reweighing as specified by (Mehrotra and Celis, 2021). This method focuses on fairness with noisy sensitive attributes.

CorScale : Neural network with rectified fairness constraints (Lamy et al., 2019). This method focuses on fairness with noisy sensitive attributes.

SurrogateLoss : Neural network with modified EOd constraint by (Wang et al., 2021). This method focuses on fairness with noisy labels.

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4.2 Fairness with Noisy Protected Attributes

4.2.1 Fairness under given noise rates

Results on fairness under noisy sensitive attributes are shown in Table 1-3. Compared with baseline and inprocessing which also do not require estimation of noise rates our method achieves a better trade-off in terms of fairness and accuracy, with significant improvement in fairness with smaller or comparable sacrifice in accuracy. Compared with methods that require noise estimation (DLR, FairExpec and CorScale), our method achieves better or comparable performance in terms of both fairness and accuracy, which validates the effectiveness of our method.

Table 2: Experimental results on Adult dataset under sensitive attribute noise. The noise rates are set as η 00 = 0 . 15 , η 01 = 0 . 1 , η 10 = 0 . 1 , η 11 = 0 . 3 .

Table 3: Experimental results on CelebA dataset under sensitive attribute noise. The noise rates are set as η 00 = 0 . 1 , η 01 = 0 . 2 , η 10 = 0 . 3 , η 11 = 0 . 1 .

4.2.2 Fairness under Varying Noise Rates

We move on to discuss results on fairness under varying noise rates. Specifically, we use noise rates in previous sections as baseline rates and vary each component within the range of [0 , 0 . 5] . Results under varying noise rates are shown in Fig. 1-3. As shown in the figures, under varying noise rates, our method achieves relatively stable performance for both DI and EOd compared with other methods, which indicates that our method performs robustly under different noise rates.

4.3 Fairness under Noisy Sensitive Attributes and Noisy Labels

As discussed in Lemma 3, apart from sensitive attribute noise, our method can also be generalized to 268 fairness under the exposure of label noise. Therefore, we also validate our method in the presence of 269 both attribute and label noise, and results are shown in Table 4-6. While existing methods typically 270 address one type of noise, our method is capable of handling both types of noise simultaneously, with 271 better or comparable performance in terms of both fairness improvement and accuracy, and without 272 requiring extra tools for noise rate estimation. This also validates our analysis in the previous section. 273

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, EOd

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CorScale

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Ours

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16 -

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Ours

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Ours

) PO3

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24

Baseine

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Bacelin

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Baceine

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5 Conclusion 274

Fairness under noisy perturbation is an important yet less studied problem. In this paper, we formulate 275 noisy perturbation as both group- and label-dependent, and we propose a fair representation learning 276 framework based on normalizing flow to solve the problem without using extra tools for noise 277 estimation. We prove theoretically the transferability of fairness between noisy and clean data under 278 noisy sensitive attributes, and we show theoretically the connection between fairness measures of 279 clean and noisy data under label noise. We validate from experiments that our method performs 280 better or comparably in the improvement of fairness under both label noise and sensitive attributes 281 noise generated under both static and varying noise rates, compared with state-of-the-art alternatives, 282 with relatively small sacrifice in accuracy. Future directions include alternative methods for fair 283 representation learning, and alternative formulations of noise perturbation. 284

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References

An, B., Che, Z., Ding, M., and Huang, F. (2022). Transferring fairness under distribution shifts via fair consistency regularization. arXiv preprint arXiv:2206.12796 .

Angwin, J., Larson, J., Mattu, S., and Kirchner, L. (2016). Machine bias. In Ethics of Data and Analytics , pages 254-264. Auerbach Publications.

Balunovi´ c, M., Ruoss, A., and Vechev, M. (2021). Fair normalizing flows. arXiv preprint arXiv:2106.05937 .

Celis, L. E., Huang, L., Keswani, V., and Vishnoi, N. K. (2021). Fair classification with noisy protected attributes: A framework with provable guarantees. In International Conference on Machine Learning , pages 1349-1361. PMLR.

Chai, J., Jang, T., and Wang, X. (2022). Fairness without demographics through knowledge distillation. Advances in Neural Information Processing Systems , 35:19152-19164.

Chai, J. and Wang, X. (2023). To be robust and to be fair: Aligning fairness with robustness. arXiv preprint arXiv:2304.00061 .

Chen, Y., Raab, R., Wang, J., and Liu, Y. (2022). Fairness transferability subject to bounded distribution shift. arXiv preprint arXiv:2206.00129 .

Choi, Y., Dang, M., and Van den Broeck, G. (2020). Group fairness by probabilistic modeling with latent fair decisions. arXiv preprint arXiv:2009.09031 .

Corbett-Davies, S., Pierson, E., Feller, A., Goel, S., and Huq, A. (2017). Algorithmic decision making and the cost of fairness. In Proceedings of the 23rd acm sigkdd international conference on knowledge discovery and data mining , pages 797-806.

Cortes, C., Mansour, Y., and Mohri, M. (2010). Learning bounds for importance weighting. Advances in neural information processing systems , 23.

De-Arteaga, M., Feuerriegel, S., and Saar-Tsechansky, M. (2022). Algorithmic fairness in business analytics: Directions for research and practice. Production and Operations Management , 31(10):3749-3770.

Diana, E., Gill, W., Kearns, M., Kenthapadi, K., Roth, A., and Sharifi-Malvajerdi, S. (2022). Multiaccurate proxies for downstream fairness. In 2022 ACM Conference on Fairness, Accountability, and Transparency , pages 1207-1239.

Dinh, L., Sohl-Dickstein, J., and Bengio, S. (2016). Density estimation using real nvp. arXiv preprint arXiv:1605.08803 .

Dressel, J. and Farid, H. (2018). The accuracy, fairness, and limits of predicting recidivism. Science advances , 4(1):eaao5580.

Dua, D. and Graff, C. (2017). UCI machine learning repository.

Dwork, C., Hardt, M., Pitassi, T., Reingold, O., and Zemel, R. (2012). Fairness through awareness. In Proceedings of the 3rd innovations in theoretical computer science conference , pages 214-226.

Fioretto, F., Tran, C., Van Hentenryck, P., and Zhu, K. (2022). Differential privacy and fairness in decisions and learning tasks: A survey. arXiv preprint arXiv:2202.08187 .

Grari, V., Lamprier, S., and Detyniecki, M. (2021). Fairness without the sensitive attribute via causal variational autoencoder. arXiv preprint arXiv:2109.04999 .

Hardt, M., Price, E., and Srebro, N. (2016). Equality of opportunity in supervised learning. Advances in neural information processing systems , 29.

Hsu, B., Mazumder, R., Nandy, P., and Basu, K. (2022). Pushing the limits of fairness impossibility: Who's the fairest of them all? arXiv preprint arXiv:2208.12606 .

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372

373

Jackson, J. R. (2018). Algorithmic bias. Journal of Leadership, Accountability and Ethics , 15(4):5565.

Kleinberg, J., Mullainathan, S., and Raghavan, M. (2016). Inherent trade-offs in the fair determination of risk scores. arXiv preprint arXiv:1609.05807 .

Kleindessner, M., Donini, M., Russell, C., and Zafar, M. B. (2023). Efficient fair pca for fair representation learning. In International Conference on Artificial Intelligence and Statistics , pages 5250-5270. PMLR.

Lahoti, P., Beutel, A., Chen, J., Lee, K., Prost, F., Thain, N., Wang, X., and Chi, E. (2020). Fairness without demographics through adversarially reweighted learning. Advances in Neural Information Processing Systems , 33:728-740.

Lamy, A., Zhong, Z., Menon, A. K., and Verma, N. (2019). Noise-tolerant fair classification. Advances in neural information processing systems , 32.

Larson, J., Mattu, S., Kirchner, L., and Angwin, J. (2016). Compas analysis. GitHub, available at: https://github. com/propublica/compas-analysis .

Li, P. and Liu, H. (2022). Achieving fairness at no utility cost via data reweighing with influence. In International Conference on Machine Learning , pages 12917-12930. PMLR.

Liu, Z., Luo, P., Wang, X., and Tang, X. (2015). Deep learning face attributes in the wild. In Proceedings of International Conference on Computer Vision (ICCV) .

Madras, D., Creager, E., Pitassi, T., and Zemel, R. (2018). Learning adversarially fair and transferable representations. In International Conference on Machine Learning , pages 3384-3393. PMLR.

Mehrabi, N., Morstatter, F., Saxena, N., Lerman, K., and Galstyan, A. (2021). A survey on bias and fairness in machine learning. ACM Computing Surveys (CSUR) , 54(6):1-35.

Mehrotra, A. and Celis, L. E. (2021). Mitigating bias in set selection with noisy protected attributes. In Proceedings of the 2021 ACM Conference on Fairness, Accountability, and Transparency , pages 237-248.

Mishler, A. and Dalmasso, N. (2022). Fair when trained, unfair when deployed: Observable fairness measures are unstable in performative prediction settings. arXiv preprint arXiv:2202.05049 .

Rezaei, A., Fathony, R., Memarrast, O., and Ziebart, B. (2020). Fairness for robust log loss classification. In Proceedings of the AAAI Conference on Artificial Intelligence , volume 34, pages 5511-5518.

Rezaei, A., Liu, A., Memarrast, O., and Ziebart, B. D. (2021). Robust fairness under covariate shift. In Proceedings of the AAAI Conference on Artificial Intelligence , volume 35, pages 9419-9427.

Ricci Lara, M. A., Echeveste, R., and Ferrante, E. (2022). Addressing fairness in artificial intelligence for medical imaging. nature communications , 13(1):4581.

Roh, Y., Lee, K., Whang, S. E., and Suh, C. (2020). Fairbatch: Batch selection for model fairness. arXiv preprint arXiv:2012.01696 .

Schrouff, J., Harris, N., Koyejo, S., Alabdulmohsin, I. M., Schnider, E., Opsahl-Ong, K., Brown, A., Roy, S., Mincu, D., Chen, C., et al. (2022). Diagnosing failures of fairness transfer across distribution shift in real-world medical settings. Advances in Neural Information Processing Systems , 35:19304-19318.

Singh, H., Singh, R., Mhasawade, V., and Chunara, R. (2021). Fairness violations and mitigation under covariate shift. In Proceedings of the 2021 ACM Conference on Fairness, Accountability, and Transparency , pages 3-13.

Sugiyama, M., Krauledat, M., and Müller, K.-R. (2007). Covariate shift adaptation by importance weighted cross validation. Journal of Machine Learning Research , 8(5).

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Tan, Z., Yeom, S., Fredrikson, M., and Talwalkar, A. (2020). Learning fair representations for kernel models. In International Conference on Artificial Intelligence and Statistics , pages 155-166. PMLR.

Wang, J., Liu, Y., and Levy, C. (2021). Fair classification with group-dependent label noise. In Proceedings of the 2021 ACM conference on fairness, accountability, and transparency , pages 526-536.

Wang, J., Wang, X. E., and Liu, Y. (2022). Understanding instance-level impact of fairness constraints. In International Conference on Machine Learning , pages 23114-23130. PMLR.

Wang, S., Guo, W., Narasimhan, H., Cotter, A., Gupta, M., and Jordan, M. (2020). Robust optimization for fairness with noisy protected groups. Advances in neural information processing systems , 33:5190-5203.

Willborn, S. L. (1984). The disparate impact model of discrimination: Theory and limits. Am. UL Rev. , 34:799.

Wu, S., Gong, M., Han, B., Liu, Y., and Liu, T. (2022). Fair classification with instance-dependent label noise. In Conference on Causal Learning and Reasoning , pages 927-943. PMLR.

Yan, S., Kao, H.-t., and Ferrara, E. (2020). Fair class balancing: Enhancing model fairness without observing sensitive attributes. In Proceedings of the 29th ACM International Conference on Information & Knowledge Management , pages 1715-1724.

Yurochkin, M., Bower, A., and Sun, Y. (2019). Training individually fair ml models with sensitive subspace robustness. arXiv preprint arXiv:1907.00020 .

Zafar, M. B., Valera, I., Rogriguez, M. G., and Gummadi, K. P. (2017). Fairness constraints: Mechanisms for fair classification. In Artificial Intelligence and Statistics , pages 962-970. PMLR.

Zhang, Y., Zhou, F., Li, Z., Wang, Y ., and Chen, F. (2023). Fair representation learning with unreliable labels. In International Conference on Artificial Intelligence and Statistics , pages 4655-4667. PMLR.

Peer reviews:
{"IS_META_REVIEW": false, "comments": "SUMMARY:\nThe authors introduce an innovative framework that enhances the fairness guarantees of a classifier in the presence of both sensitive attribute noise and label noise, considering them independently as well as in combination. Their approach incorporates theoretical guarantees and involves training a fair encoder to learn a novel data representation that ensures both fairness and accuracy. They demonstrate that by imposing bounded divergence between the noisy and clean distributions, fairness can be effectively transferred from one distribution to another. Notably, their method tackles the problem from a distribution shift perspective, eliminating the need for noise rate estimation typically required by conventional noise tolerant models.\n\nSTRENGTHS:\n- The introduction effectively substantiates all the claims made, including the contributions put forth by the authors. These assertions find validation through a thorough description of the methodology employed and the experiments conducted. The method section elaborates on the techniques and approaches considered, demonstrating how they align with the stated objectives. Furthermore, the experimental results provide empirical evidence that supports the claims made in the introduction. \n- The problem addressed in the paper is well motivated. The authors provide a comprehensive and compelling rationale for the significance and relevance of the problem. They effectively highlight the real-world implications and potential consequences of the existing limitations in the field.  \n- The authors introduce an innovative alternative approach that effectively addresses the limitations of state-of-the-art (SOTA) methods. By identifying and highlighting the drawbacks of existing techniques (noise rate requirements), they demonstrate a clear understanding of the challenges at hand. \n- The methodology is clearly explained and well-organized. The paper includes sub-sections that effectively delineate different aspects of the methodology, ensuring a coherent and structured presentation. \n- The paper demonstrates commendable attention to reproducibility by providing thorough and detailed information regarding the experimental setup.\n- For the experimental evaluation, the authors take into account various types of data, including both tabular and image data.\n- The selection of datasets and the procedure employed to generate synthetic datasets align well with similar approaches found in the existing literature. \n- The evaluation conducted in the paper is both sound and comprehensive. The authors meticulously consider various aspects to ensure a robust evaluation.\n\nWEAKNESSES:\n- (Section 4, Experiments) The authors put forth a proposition to tackle the challenge of ensuring fairness in the presence of noise from a distribution shift perspective. However, in the experimental section, they fail to compare their proposal with methods that specifically address distribution shift in a fairness-aware scenario. It is worth considering that these alternative methods may also yield promising results when handling noisy sensitive and label information. Including such comparisons would provide a more comprehensive understanding of the relative performance and effectiveness of the proposed approach within the context of fairness under distribution shift.\n- (Section 4, Experiments) The paper presents theoretical bounds, but unfortunately, they are not evaluated empirically. While the theoretical analysis offers valuable insights and establishes the potential effectiveness of the proposed approach, the absence of empirical evaluations leaves room for uncertainty regarding its practical applicability. Empirical evaluations would have provided concrete evidence of the proposed method's performance and its ability to meet the expected bounds.\n- (Section 2, Fairness metrics) The discussion of fairness metrics lacks a clear structure, and I would suggest that the authors differentiate between individual and group notions of fairness, providing distinct explanations for each. Additionally, it would be beneficial for the authors to acknowledge the emergence of mini-max fairness notions, which are gaining popularity in the field. \n- (Section 2, Fairness-enhancing interventions)  While describing the pre-, in-, and post-processing methods, the authors primarily focus on specific techniques instead of providing an overview of the general framework. Consequently, it is not accurate to claim that all preprocessing methods aim to rectify the distribution of input features, nor is it true that all in-processing methods incorporate fairness enhancement as relaxed constraints. In reality, regarding the latter, there are variations where fairness is achieved through techniques such as fairness penalizations. While these cases are commonly encountered, it would be preferable for the authors to first describe the overarching objectives of the general workflows before delving into specific specifications. This approach would provide a clearer understanding of the broader goals before examining the specific techniques used. Moreover, the authors fail to explicitly state that their method constitutes an in-processing intervention.\n- (Section 3.2) The authors initially discuss general distribution shift, but in line 167, they assert that they address covariate shift. It is important to note that these two types of shifts have distinct mathematical implications. Covariate shift specifically involves changes in p(x) between the source and target domains, while assuming that the functional form of p(y|x) remains unchanged. It would be beneficial for the authors to clarify which shift they are specifically addressing and how the mathematical characteristics of covariate shift come into play within their approach. Providing further clarity on this matter would help readers understand the specific focus and contributions of the proposed method in addressing the relevant shift.\n- (Section 2, Fairness under distribution shift) In this section, the authors overlook several pertinent works, and some of the works mentioned are not even published. However, there exists a substantial body of literature that specifically addresses the challenge of ensuring fairness guarantees under distribution shift (for a comprehensive survey, the authors can refer to [1]). It is important to differentiate between methods that solely tackle distribution shift and those specifically designed for ensuring fairness under distribution shift. Furthermore, it is worth noting that different methods consider varying levels of data availability in the target domain, and not all of them assume the availability of (X, A) pairs [1]. For instance, the work [2] cited in that section assumes the target data is not available. \n- (Section 2, Related works) The purpose of this section is to not only provide a description of the related works but also to establish the connection between them, elucidate the significance of these relationships, and highlight the novelty of the proposed work or its intended aim to address specific limitations. However, despite providing descriptions of various works, the authors do not explicitly specify the precise position of their work within the broader landscape.\n- Notation issues: After defining the notation at the beginning of Section 3, and Section 3.1, the authors employ symbols that have not been defined, such as, A in line 137, or $\\mathcal{L}_{cls}$  in Eq (6). Regarding the latter, there is no specification regarding its meaning nor its mathematical form. \n- The paper contains several typos: line 67 after more there is a full stop, line 129 after of there should be an 'a', line 217 let should be in uppercase. \n\n[1] Barrainkua, A., Gordaliza, P., Lozano, J. A., & Quadrianto, N. (2022). A Survey on Preserving Fairness Guarantees in Changing Environments. arXiv preprint arXiv:2211.07530.\n\n[2] Rezaei, A., Fathony, R., Memarrast, O., & Ziebart, B. (2020, April). Fairness for robust log loss classification. In Proceedings of the AAAI Conference on Artificial Intelligence (Vol. 34, No. 04, pp. 5511-5518).\n\nQUESTIONS:\n- Theoretical results in the paper are presented in two different contexts: some are with respect to P, while others are with respect to Q. However, the relationship between these two contexts is not clearly established or explained. How are they related?\n- The framework presented in this study focuses on a binary sensitive attribute and a binary label, which may limit its applicability in more complex scenarios commonly encountered in various applications. For example, many SOTA noise tolerant approaches cited in the work can handle those situations. But can this framework be extended to support multiclass Y or multivalue S? Moreover, can it effectively handle scenarios involving multi-dimensional S? Further clarification is needed to assess the flexibility and scalability of the proposed framework in handling these additional complexities.\n- Does your approach primarily consider general distribution shift or does it specifically focus on covariate shift?\n- Why have you only chosen DI and EOd as fairness metrics? Can it be extended to other statistical notions?\n\nLIMITATIONS:\nThe authors do not thoroughly discuss the limitations of their method, which is an important aspect to consider. Taking inspiration from the questions raised concerning the shift type and potential implications beyond binary Y and binary S could be valuable in addressing the limitations and further refining their approach.", "TITLE": "Official Review", "RECOMMENDATION": 4, "REVIEWER_CONFIDENCE": 4, "SOUNDNESS_CORRECTNESS": 3, "DATE": "2023-06-20"}

{"IS_META_REVIEW": false, "comments": "SUMMARY:\nThe paper aims to improve the performances of fair training when the group attributes or labels in the training data have noisy information. The paper views the noisy training data problem as a kind of distribution shift, where the training data is noisy and the test data is clean. To address this issue, the paper proposes a fair representation learning method to reduce the impact of distribution differences. The paper also provides some theoretical analyses to show the relationship between the group fairness results and noisy training data. In the experiment, the paper uses three datasets and compares with several baselines to show the performance gains of the proposed method.\n\nSTRENGTHS:\nS1. The paper solves an important research problem, preserving the performances of fair training under the noisy training data. The paper views this problem as a distribution shift issue.\n\nS2. The paper gives some theoretical analyses on the relationship between the group fairness and noisy data.\n\nS3. The proposed algorithm empirically shows better fairness and accuracy performances compared to the baselines.\n\nWEAKNESSES:\nW1. Many important details are missing in the proposed fair representation learning. \n- In Section 3.3, the final training objective in Eq. (6) has many unexplained important details. For example, what is L_cls, and how are the input arguments (e.g., g_00, h) used in L_cls? Also, it seems the lambda values are the tuning knobs, but there is no explanation on why the loss terms should be connected by two lambda values. Including these details, a clearer rationale for design choices is needed.\n\nW2. In experiments, the proposed algorithm is not clearly analyzed. For example, it would be much better if the paper explains the following.\n- How the lambda values in Equation 6 affect the training performances\n- The computational complexity of the proposed algorithm\n\nW3. Although this work is highly related to the studies on fairness under data distribution shifts, there are no clear comparisons with them. In experiments, all the baselines are from the noisy training literature. Since many algorithms for fair training under distribution shifts have been recently proposed, it would be better to compare with them empirically or at least to be clearly discussed.\n\nQUESTIONS:\nAll questions are included in the above weakness section.\n\nLIMITATIONS:\nThe paper did not discuss the limitations and possible negative societal impacts. As the limitations, this work may discuss which types of data noises cannot be handled by the proposed algorithm.", "TITLE": "Official Review", "RECOMMENDATION": 5, "REVIEWER_CONFIDENCE": 4, "SOUNDNESS_CORRECTNESS": 2, "DATE": "2023-07-07"}

comments: SUMMARY:
The paper studies the fairness problem under noise perturbation on both label and sensitive attributes. In particular, it considers such a problem from the perspective of distribution shift and uses the normalizing flow framework to analyze the problem. Empirically, the proposed methods achieve the best utility and fairness trade-offs under different settings of noise perturbation.

STRENGTHS:
1. The paper presents a method for learning fair representation when there is noise on both sensitive attributes and labels. The method is straightforward and empirically shown to be effective. 
2. The theoretical analysis is sound 
3. Compared to the previous work, this work considers both label and sensitive attribute noise without directly estimation the noise parameter, which is more practical in real-world applications.

WEAKNESSES:
I do not find any obvious weaknesses in the paper. But there are minor points that the author could further improve their paper.
1. The assumption of invertible function in the fair normalizing flow methods might be strong. For example, In ResNet, the default activation function is ReLU, which is not invertible. The authors might need to provide more justification for this.
2. Discussion of limitations. The paper could be improved if there is a discussion of the limitations.

QUESTIONS:
1. Is there a utility-fairness trade-off tuning parameters in your methods? If yes, how does the utility-fairness trade-offs change given different noise rate?

LIMITATIONS:
The authors do not discuss the limitations of the work, which is highly suggested.
TITLE: Official Review
SOUNDNESS_CORRECTNESS: 4
DATE: 2023-07-09

{"IS_META_REVIEW": false, "comments": "SUMMARY:\nThis work studies noise tolerance of fairness from the perspective of subpopulation/subgroup shift, by considering the perturbation of the sensitive attributes as well as the labels _without_ the need for noise-rate estimation - by considering the noisy distribution as the source and clean distribution as the target. This leads to a \"covariate\" shift between the source and the target distributions, with the shift being a consequence of the noise. The work then proposes a fair representation learning method for fairness under noisy attributes based on normalizing flows, and presents a theoretical result showing that this method minimizes the upper-bound of the clean equalized odds. Thorough empirical evaluation is presented for both static and varying noise rates, showing the efficacy of the proposed method.\n\nSTRENGTHS:\nThis work addresses an important setting of achieving fairness when both the label $y$ and sensitive attribute $a$ can be noisy - as traditional metrics can be biased under noisy data. The theoretical analysis presents a comprehensive study of fairness transfer between clean and noisy data and supports the choice of the minimizer in the proposed method. The empirical analysis is thorough - the section 4.2.2 is especially interesting as it considers both static and dynamic noise rates.\n\nWEAKNESSES:\nThe following points should be considered:\n1. The loss function (in Eq. 6) focuses on a binary valued $a$ and $y$. How does this methodology extend to the more general case either/both can be multi-valued? Is it straightforward?\n2. Is there any more intuition on leveraging normalized flows for this setting?\n\nQUESTIONS:\nPlease see Weakness section. \n\nA minor suggestion:\n1. Consider using a bigger text size for the plots as they are unreadable. \n2. Consider using more formal English: e.g. line 67 \"What's more..\"\n\nLIMITATIONS:\nNo limitations of this method are mentioned, and it would be nice if any potential drawbacks can be discussed.", "TITLE": "Official Review", "RECOMMENDATION": 6, "REVIEWER_CONFIDENCE": 3, "SOUNDNESS_CORRECTNESS": 3, "DATE": "2023-07-10"}

{"IS_META_REVIEW": false, "comments": "SUMMARY:\nThis paper targets the problem of ensuring fairness with noises on either sensitive attributes or labels. Specifically, this paper models the noisy data training set and clean test set as a distribution shift and proposes a regularization term to improve the fairness of classifiers.\nThe theoretical analysis indicates that the classifier trained by the proposed framework on the noise data can be bounded when evaluating on the clean data.\n\nSTRENGTHS:\n1. The problem of ensuring fairness when training on noisy data is an important problem.\n\n2. The whole framework makes sense.\n\n3. The experimental results show the advantage of the proposed approach.\n\nWEAKNESSES:\nThe writing is not very friendly to readers without a background in this specific fairness problem. Please check my questions below.\n\nQUESTIONS:\n1. One contribution claimed in this paper is that the proposed framework does not require noise rate estimation. However, if I understand correctly, \\lambda in the objective function (Eq 6) is a function of $\\eta$ and $\\hat{\\alpha}$ defined in Lemma 1. While the $\\eta$ indicates the noise rate in a specific subgroup, I am not convinced that not requiring the noise rate estimation is a contribution. It seems like the proposed framework needs knowledge of the noise rate for each subgroup in advance.\n\n2. As I am not an expert in the fairness issue under the noise data setting, some equations are not very straightforward to me, such as the equation under Line 138 and Eqs 1 and 2. It would be better to give more explanations on those equations. Especially, Eq 2 is important for the conclusion described in Line 177.\n\n3. The proposed framework models the noisy training data and clean testing data from the perspective of distribution shift. The high level idea makes sense to me. However, I do not follow the description between lines 173-174. Why does minimizing the divergence between \\hat{P}_{ya} and \\hat{P}_{ya'} lead to the minimization of  the divergence between $Q_{ya}$ and $\\hat{Q}_{ya}$?\n\nLIMITATIONS:\nPlease check my questions above.", "TITLE": "Official Review", "RECOMMENDATION": 5, "REVIEWER_CONFIDENCE": 1, "SOUNDNESS_CORRECTNESS": 3, "DATE": "2023-07-20"}