Original: GroupMixNorm Layer for Learning Fair Models
Revised: GroupMixNorm Layer for Learning Fair Models

Original: Anonymous Author(s)

Original: AffiliationAddress email

Original: Abstract
Revised: Abstract

Original: Recent research has focused on proposing algorithms for bias mitigation fromautomated prediction algorithms.
Revised: Recent research has focused on proposing algorithms for bias mitigation from automated prediction algorithms.

Original: Most of the techniques include convex surrogatesof fairness metrics such as demographic parity or equalized odds in the loss function, which are not easy to estimate.
Revised: Most of the techniques include convex surrogates of fairness metrics such as demographic parity or equalized odds in the loss function, which are not easy to estimate.

Original: Further, these fairness constraints are mostlydata-dependent and aim to minimize the disparity among the protected groupsduring the training.
Revised: Further, these fairness constraints are mostly data-dependent and aim to minimize the disparity among the protected groups during the training.

Original: However, they may not achieve similar performance on thetest set.
Revised: However, they may not achieve similar performance on the test set.

Original: In order to address the above limitations, this research proposes a novel
Revised: In order to address the above limitations, this research proposes a novel

Original: GroupMixNorm layer for bias mitigation from deep learning models.
Revised: GroupMixNorm layer for bias mitigation from deep learning models.

Original: As an alternative to solving constraint optimization separately for each fairness metric, we haveformulated bias mitigation as a problem of distribution alignment of several groupsidentified through the protected attributes.
Revised: As an alternative to solving constraint optimization separately for each fairness metric, we have formulated bias mitigation as a problem of distribution alignment of several groups identified through the protected attributes.

Original: To this effect, the GroupMixNorm layerprobabilistically mixes group-level feature statistics of samples across differentgroups based on the protected attribute.
Revised: To this effect, the GroupMixNorm layer probabilistically mixes group-level feature statistics of samples across different groups based on the protected attribute.

Original: The proposed method improves uponseveral fairness metrics with minimal impact on accuracy.
Revised: The proposed method improves upon several fairness metrics with minimal impact on accuracy.

Original: Experimental evaluationand extensive analysis on benchmark tabular and image datasets demonstrate theefficacy of the proposed method to achieve state-of-the-art performance.
Revised: Experimental evaluation and extensive analysis on benchmark tabular and image datasets demonstrate the efficacy of the proposed method to achieve state-of-the-art performance.

Original:  Introduction
Revised:  Introduction

Original: Adoption of AI systems is increasing at a rapid rate to deliver seamless consumer experience acrossvarious domains such as travel time prediction, health monitoring, authentication etc Mehrabi et al.(2021);
Revised: Adoption of AI systems is increasing at a rapid rate to deliver seamless consumer experience across various domains such as travel time prediction, health monitoring, authentication etc Mehrabi et al.

Original:  Du et al. (2021b) ; Bellamy et al.
Revised: ; Du et al. (2021b); Bellamy et al.

Original: Such pipelines are mostly automated in naturewithout any human intervention, owing to the large data processing, high efficiency and highaccuracy.
Revised: Such pipelines are mostly automated in nature without any human intervention, owing to the large data processing, high efficiency and high accuracy.

Original: Despite the benefits of automated processing, current AI systems are marred with thechallenge of biased predictions resulting in unfavourable outcomes.
Revised: Despite the benefits of automated processing, current AI systems are marred with the challenge of biased predictions resulting in unfavourable outcomes.

Original: In order to rectify such biasesand advance in the society, we need models that generate fair results without any discrimination orfavouritism towards certain individual or groups of society.
Revised: In order to rectify such biases and advance in the society, we need models that generate fair results without any discrimination or favouritism towards certain individual or groups of society.

Original: To this effect, this research proposesa novel GroupMixNorm layer for learning an unbiased model from the given data ensuring fairoutcomes across different groups.
Revised: To this effect, this research proposes a novel GroupMixNorm layer for learning an unbiased model from the given data ensuring fair outcomes across different groups.

Revised: Lower protected attributed based distinction enables a

Original: Existing in-processing techniques mostly aim to solve a constraint optimization problem to ensure fairness Woodworth et al
Revised: Existing in-processing techniques mostly aim to solve a constraint optimization problem to ensure fairness Woodworth et al.

Original:  Zafar et al
Revised: (2017); Zafar et al.

Original:  Kamishima et al
Revised: ; Kamishima et al.

Original:  Wu et al
Revised: ; Wu et al.

Original: Wilson et al.
Revised: Wilson et al.

Original:  Zhang et al.
Revised: ; Zhang et al.

Original: by introducing a penalty term in the loss function corre- sponding to the convex surrogates of the fairness objective like demographic parity or equalized odds 
Revised: by introducing a penalty term in the loss function corresponding to the convex surrogates of the fairness objective like demographic parity or equalized odds .

Original: However, as has been observed in literature, it is challenging to formulate surrogates for differentfairness constraints that is a reasonable estimate of the original constraint Manisha and Gujar (2020).
Revised: However, as has been observed in literature, it is challenging to formulate surrogates for different fairness constraints that is a reasonable estimate of the original constraint Manisha and Gujar (2020).

Original: The proposed GroupMixNorm layer is applied at the in-processing stage which promotes the model to learn bias invariant features for classification by modeling the data distribution during training.
Revised: The proposed GroupMixNorm layer is applied at the in-processing stage which promotes the model to learn bias invariant features for classification by modeling the data distribution during training.

Original: In this research, we formulate the problem of bias mitigation as distribution alignment of severalgroups identified through the protected attributes (Figure 1).
Revised: In this research, we formulate the problem of bias mitigation as distribution alignment of several groups identified through the protected attributes (Figure 1).

Original: Our formulation is motivated by the observation that Deep Learning based algorithms tend to explore the difference in the distributionLower protected attributed-based distinction enables the generation of a fairer classification model among the groups of the protected attributes (for example, male and female with similar featureslike age and education may have different salaries, thus resulting in different distributions) to lift theoverall performance and in the process may result in bias being exhibited towards certain groups.
Revised: Our formulation is motivated by the observation that Deep Learning based algorithms tend to explore the difference in the distribution among the groups of the protected attributes (for example, male and female with similar features like age and education may have different salaries, thus resulting in different distributions) to lift the overall performance and in the process may result in bias being exhibited towards certain groups.

Original: The proposed method, termed GroupMixNorm, mixes the group-level feature statistics and furthertransforms all the features in a training batch based on the interpolated group statistics.
Revised: The proposed method, termed GroupMixNorm, mixes the group-level feature statistics and further transforms all the features in a training batch based on the interpolated group statistics.

Original: This enablesthe classifier to learn invariant features pertaining to protected attributes during training.
Revised: This enables the classifier to learn invariant features pertaining to protected attributes during training.

Original: Keyhighlights of this research are as follows:
Revised: Key highlights of this research are as follows:

Original: • This research proposes a novel GroupMixNorm layer for learning fairer classification models.
Revised: • This research proposes a novel GroupMixNorm layer for learning fairer classification models.

Original: The proposed layer is applied at the architectural level, and is an in-processing techniquewhich focuses on distribution alignment of different groups during model training.• GroupMixNorm operates at the feature level, thus making it flexible to be placed acrossvarious layers of a neural network and fits well into the mini-batch gradient-based training.• The efficacy of the proposed approach has been demonstrated on different datasets (structuredand unstructured), where it achieves improved performance while enforcing multiple fairnessconstraints such as demographic parity, equal opportunity and equalized odds.
Revised: The proposed layer is applied at the architectural level, and is an in-processing technique which focuses on distribution alignment of different groups during model training. • GroupMixNorm operates at the feature level, thus making it flexible to be placed across various layers of a neural network and fits well into the mini-batch gradient-based training. • The efficacy of the proposed approach has been demonstrated on different datasets (structured and unstructured), where it achieves improved performance while enforcing multiple fairness constraints such as demographic parity, equal opportunity and equalized odds.

Original:  Proposed GroupMixNorm Layer
Revised:  Proposed GroupMixNorm Layer

Original: The proposed GroupMixNorm layer focuses on achieving group fairness across different sensitivegroups within a protected attribute by eliminating the difference between the group features/statisticsduring training.
Revised: The proposed GroupMixNorm layer focuses on achieving group fairness across different sensitive groups within a protected attribute by eliminating the difference between the group features/statistics during training.

Original: As part of the GroupMixNorm layer, we normalize each group of a protected attributein a batch separately to collect group specific statistics (i.e. for the gender attribute, normalize allmale samples and female samples in a batch separately) and further take a probabilistic convexcombination between the group-level statistics and apply across all the samples in a batch.
Revised: As part of the GroupMixNorm layer, we normalize each group of a protected attribute in a batch separately to collect group specific statistics (i.e. for the gender attribute, normalize all male samples and female samples in a batch separately) and further take a probabilistic convex combination between the group-level statistics and apply across all the samples in a batch.

Original: Thisprocess ensures that any protected group related diversity is removed from the internal representationof a neural network and doesn’t allow the network to explore this information to lift the overallperformance.
Revised: This process ensures that any protected group related diversity is removed from the internal representation of a neural network and doesn’t allow the network to explore this information to lift the overall performance.

Original: The introduction of additional inductive bias in the network structure enforces it tolearn invariant features pertaining to protected attributes while training the network.
Revised: The introduction of additional inductive bias in the network structure enforces it to learn invariant features pertaining to protected attributes while training the network.

Original: The GroupMixNorm layer is implemented as a plug-and-play module.
Revised: The GroupMixNorm layer is implemented as a plug-and-play module.

Original: It can be inserted betweenfully connected layers of a neural network-based classifier during training.
Revised: It can be inserted between fully connected layers of a neural network-based classifier during training.

Original: Let X, Y and S be theinput features, class labels and protected attribute labels in a training batch respectively.
Revised: Let X, Y and S be the input features, class labels and protected attribute labels in a training batch respectively.

Original: As illustratedin Figure 2 consider Z be an n dimensional hidden representation obtained from the previous layerand A i represent feature along dimension i .
Revised: As illustrated in Figure 2 consider Z be an n dimensional hidden representation obtained from the previous layer and A i represent feature along dimension i .

Original: We identify the groups G j in a batch based on theprotected attribute labels S , and calculate their respective mean ( µ G j ,i ) and variance ( σ G j ,i ) alongeach dimension, as shown in the step-1 of Figure 2.
Revised: We identify the groups G j in a batch based on the protected attribute labels S , and calculate their respective mean ( µ G j ,i ) and variance ( σ G j ,i ) along each dimension, as shown in the step-1 of Figure 2.

Original: Next we calculate weighted average of meanγ mix,i and variance β mix,i along each dimension (Equation 1).
Revised: Next we calculate weighted average of mean γ mix,i and variance β mix,i along each dimension (Equation 1).

Original: We mix group level statistics bycalculating a weighted average of mean γ mix i and variance β mix i along each dimension (Equation1).
Revised: We mix group level statistics by calculating a weighted average of mean γ mix i and variance β mix i along each dimension (Equation 1).

Original: As we mix statistics of two groups, the mixing coefficient λ is sampled from a symmetric Betadistribution Beta ( α, α ) , for α ∈ (0 , ∞ ) .
Revised: As we mix statistics of two groups, the mixing coefficient λ is sampled from a symmetric Beta distribution Beta ( α, α ) , for α ∈ (0 , ∞ ) .

Original: The hyper-parameter α controls the interpolation strength.
Revised: The hyper-parameter α controls the interpolation strength.

Original: [Figure] Finally, we normalize all the samples by applying the calculated γ mix and β mix to each sample asshown in Equation 3.
Revised: Finally, we normalize all the samples by applying the calculated γ mix and β mix to each sample as shown in Equation 3.

Original: For the ease of notation, we have considered two groups i.e. binary protectedattributes.
Revised: For the ease of notation, we have considered two groups i.e. binary protected attributes.

Original: Nevertheless, the proposed solution can be easily applied to non-binary protected attributes.
Revised: Nevertheless, the proposed solution can be easily applied to non-binary protected attributes.

Original: The three step approach is shown in Figure 2.
Revised: The three step approach is shown in Figure 2.

Original: [Equation]

Original: [Equation]

Original: [Equation]
Revised: [Equation]

Original: The updated features ˆ Z =
Revised: The updated features ˆ Z =

Original: [ ˆ Z G 1 , ˆ Z G 2 ] are then provided as input to the following layer of the neuralnetwork for further processing.
Revised: [ ˆ Z G 1 , ˆ Z G 2 ] are then provided as input to the following layer of the neural network for further processing.

Original: The process of mixing group level statistics in a GroupMixNormlayer occurs in the feature space and has no learnable parameters.
Revised: The process of mixing group level statistics in a GroupMixNorm layer occurs in the feature space and has no learnable parameters.

Original: The GroupMixNorm layer is easyto implement and fits perfectly into mini-batch training.
Revised: The GroupMixNorm layer is easy to implement and fits perfectly into mini-batch training.

Original: We train the entire neural network end-to-endfor the classification task on Binary cross-entropy loss.
Revised: We train the entire neural network end-to-end for the classification task on Binary cross-entropy loss.

Original: However, GroupMixNorm layer is turned offduring inference, hence we don’t need protected attribute information during inference time.
Revised: However, GroupMixNorm layer is turned off during inference, hence we don’t need protected attribute information during inference time.

Original:  Results
Revised:  Results

Original: Since the proposed technique focuses on mitigating bias during the training process, comparisonshave been performed with algorithms that optimize fairness constraints during training.
Revised: Since the proposed technique focuses on mitigating bias during the training process, comparisons have been performed with algorithms that optimize fairness constraints during training.

Original: In particular,we have compared with a (i) Plain Classifier, (ii) Adversarial Debiasing Zhang et al.
Revised: In particular, we have compared with a (i) Plain Classifier, (ii) Adversarial Debiasing Zhang et al.

Original: (2018), (iii)
Revised: (2018), (iii)

Original: Fair Mixup: Fairness via Interpolation (Fair Mixup)
Revised: Fair Mixup: Fairness via Interpolation (Fair Mixup)

Original: Chuang and Mroueh (2021), and (iv) Fairnessvia Representation Neutralization (RNF)
Revised: Chuang and Mroueh (2021), and (iv) Fairness via Representation Neutralization (RNF)

Original: Du et al.
Revised: Du et al.

Original: (2021a).
Revised: (2021a).

Original: The Fair Mixup technique uses twoseparate regularizing terms for optimizing the fairness metrics of Demographic Parity(DP) and Equal
Revised: The Fair Mixup technique uses two separate regularizing terms for optimizing the fairness metrics of Demographic Parity(DP) and Equal

Original: [Figure]

Original: Opportunity (EO), and thus can solve for either DP or EO at a time.
Revised: Opportunity (EO), and thus can solve for either DP or EO at a time.

Original: In this paper, we refer to thesetwo variants of Fair Mixup as Fair Mixup DP and Fair Mixup EO. 
Revised: In this paper, we refer to these two variants of Fair Mixup as Fair Mixup DP and Fair Mixup EO. [Figure] [Figure]

Original: For a fair comparison, we evaluate all the models under the same setting.
Revised: For a fair comparison, we evaluate all the models under the same setting.

Original: We have reported the classification performance on Average Precision (AP) and fairness on standard metrics like Demographic
Revised: We have reported the classification performance on Average Precision (AP) and fairness on standard metrics like Demographic

Original: Parity Difference (DPD), Equalized Odds Difference (EOD), and Equal Opportunity Difference(EOD).
Revised: Parity Difference (DPD), Equalized Odds Difference (EOD), and Equal Opportunity Difference (EOD).

Original: For the Adult dataset, we follow the defined pre-processing Chuang and Mroueh (2021) forall the experiments.
Revised: For the Adult dataset, we follow the defined pre-processing Chuang and Mroueh (2021) for all the experiments.

Original: We report the average results of 10 independent runs with different seeds.
Revised: We report the average results of 10 independent runs with different seeds.

Original: Further,techniques such as Adversarial Debiasing, Fair Mixup and RNF introduce a regularization term inthe loss function to improve fairness, via a hyper-parameter α that controls the trade-off between theaverage precision (AP) and fairness metrics (DPD, EOD, and EOP).
Revised: Further, techniques such as Adversarial Debiasing, Fair Mixup and RNF introduce a regularization term in the loss function to improve fairness, via a hyper-parameter α that controls the trade-off between the average precision (AP) and fairness metrics (DPD, EOD, and EOP).

Original: We have reported the results onvarying values of α as suggested in their respective papers.
Revised: We have reported the results on varying values of α as suggested in their respective papers.

Original: In our case, the GroupMixNorm layeris proposed towards architecture design and not the loss function, thus there is no such trade-off.
Revised: In our case, the GroupMixNorm layer is proposed towards architecture design and not the loss function, thus there is no such trade-off.

Original: Performance analysis on different datasets is as follows:
Revised: Performance analysis on different datasets is as follows:

Original: Comparison on the UCI Adult Income Dataset: Figure 3 shows the performance comparison onthe UCI Adult dataset, where we observe that the proposed GroupMixNorm method produces fairerresults as compared to other techniques across all the three fairness metrics (DPD, EOP, EOD) withminimal impact on average precision (AP).
Revised: Comparison on the UCI Adult Income Dataset: Figure 3 shows the performance comparison on the UCI Adult dataset, where we observe that the proposed GroupMixNorm method produces fairer results as compared to other techniques across all the three fairness metrics (DPD, EOP, EOD) with minimal impact on average precision (AP).

Original: Fair Mixup solves separate constraint optimizations toachieve lower Demographic Parity and Equalized Odds, thus minimizing either DP or EO at a time.
Revised: Fair Mixup solves separate constraint optimizations to achieve lower Demographic Parity and Equalized Odds, thus minimizing either DP or EO at a time.

Original: This is evident from Figure 3(a), where Fair Mixup EO doesn’t work well for DP and the DPD valuesare greater than 0.1 throughout.
Revised: This is evident from Figure 3(a), where Fair Mixup EO doesn’t work well for DP and the DPD values are greater than 0.1 throughout.

Original: In terms of fairness metrics, RNF produces fair results however theaverage precision is relatively much lower, thus making it unsuitable for the classification task.
Revised: In terms of fairness metrics, RNF produces fair results however the average precision is relatively much lower, thus making it unsuitable for the classification task.

Original: Comparison on the CelebA Dataset: Figure 4 presents the experimental results on the CelebAdataset.
Revised: Comparison on the CelebA Dataset: Figure 4 presents the experimental results on the CelebA dataset.

Original: For Fair Mixup, comparison has been performed with the combination of manifold mixup
Revised: For Fair Mixup, comparison has been performed with the combination of manifold mixup

Original: Verma et al.
Revised: Verma et al.

Original: (2019) which has shown to achieve improved results in the published manuscript Chuangand Mroueh (2021)
Revised: (2019) which has shown to achieve improved results in the published manuscript Chuang and Mroueh (2021)

Original: (Fair M Mixup DP and Fair M Mixup EO).
Revised: (Fair M Mixup DP and Fair M Mixup EO).

Original: Similar to the previous experiments,it is observed that either Fair M Mixup DP or Fair M Mixup EO achieves optimal performance at atime for a fairness metric.
Revised: Similar to the previous experiments, it is observed that either Fair M Mixup DP or Fair M Mixup EO achieves optimal performance at a time for a fairness metric.

Original: Further, the RNF model produces fair results across all the fairness metrics,however achieves low average precision (classification performance).
Revised: Further, the RNF model produces fair results across all the fairness metrics, however achieves low average precision (classification performance).

Original: The proposed GroupMixNormachieves comparable performance to the best performing model across all the metrics, while obtaininghigh average precision as well, thus suggesting high applicability in real-world setups.
Revised: The proposed GroupMixNorm achieves comparable performance to the best performing model across all the metrics, while obtaining high average precision as well, thus suggesting high applicability in real-world setups.

Original:  Conclusion
Revised:  Conclusion

Original: Learning bias-invariant models are the need of the hour for the research community.
Revised: Learning bias-invariant models are the need of the hour for the research community.

Original: While existingresearch has focused on proposing novel solutions for learning unbiased classifiers, most of thetechniques incorporate an additional term in the loss function for modeling the model fairness.
Revised: While existing research has focused on proposing novel solutions for learning unbiased classifiers, most of the techniques incorporate an additional term in the loss function for modeling the model fairness.

Original: Webelieve that it is often difficult to extrapolate the learnings of such an optimization function to the testset.
Revised: We believe that it is often difficult to extrapolate the learnings of such an optimization function to the test set.

Original: To this effect, this research proposes a novel GroupMixNorm layer, which promotes learning fairermodels at the architectural level.
Revised: To this effect, this research proposes a novel GroupMixNorm layer, which promotes learning fairer models at the architectural level.

Original: GroupMixNorm is a distribution alignment strategy operating acrossthe different groups identified in a protected attribute, enabling attribute-invariant feature learning.
Revised: GroupMixNorm is a distribution alignment strategy operating across the different groups identified in a protected attribute, enabling attribute-invariant feature learning.

Original: Experimental evaluation has been performed on two datasets containing tabular and image data,respectively for the classification task.
Revised: Experimental evaluation has been performed on two datasets containing tabular and image data, respectively for the classification task.

Original: Across multiple experiments, GroupMixNorm demonstratesimproved fairness metrics while maintaining the highest average precision level.
Revised: Across multiple experiments, GroupMixNorm demonstrates improved fairness metrics while maintaining the highest average precision level.