Table of Links Abstract and 1 Introduction Abstract and 1 Introduction 2 Related Works 2 Related Works 3 Preliminaries 3.1 Fair Supervised Learning and 3.2 Fairness Criteria 3.1 Fair Supervised Learning and 3.2 Fairness Criteria 3.3 Dependence Measures for Fair Supervised Learning 3.3 Dependence Measures for Fair Supervised Learning 4 Inductive Biases of DP-based Fair Supervised Learning 4 Inductive Biases of DP-based Fair Supervised Learning 4.1 Extending the Theoretical Results to Randomized Prediction Rule 4.1 Extending the Theoretical Results to Randomized Prediction Rule 5 A Distributionally Robust Optimization Approach to DP-based Fair Learning 5 A Distributionally Robust Optimization Approach to DP-based Fair Learning 6 Numerical Results 6.1 Experimental Setup 6.1 Experimental Setup 6.2 Inductive Biases of Models trained in DP-based Fair Learning 6.2 Inductive Biases of Models trained in DP-based Fair Learning 6.3 DP-based Fair Classification in Heterogeneous Federated Learning 6.3 DP-based Fair Classification in Heterogeneous Federated Learning 7 Conclusion and References 7 Conclusion and References Appendix A Proofs Appendix A Proofs Appendix B Additional Results for Image Dataset Appendix B Additional Results for Image Dataset 6.1 Experimental Setup Datasets. In our experiments, we attempted the following standard datasets in the machine learning litera Datasets 1. COMPAS dataset with 12 features and a binary label on whether a subject has recidivism in two years, where the sensitive attribute is the binary race feature[1]. To simulate a setting with imbalanced sensitive attribute distribution, we considered 2500 training and 750 test samples, in both of which 80% are from Z = 0 "non-Caucasian" and 20% of the samples are from Z = 1 "Caucasian”. COMPAS 2. Adult dataset with 64 binary features and a binary label indicating whether a person has more than 50K annual income. In this case, gender is considered as the sensitive attribute[2]. In our experiments, we used 15k training and 5k test samples, where, to simulate an imbalanced distribution on the sensitive attribute, 80% of the data have male gender and 20% of the samples are females. 3. CelebA Proposed by [27], containing the pictures of celebrities with 40 attribute annotations, where we considered "gender" as a binary label, and the sensitive attribute is the binary variable on blond/non-blond hair. In the experiments, we used 5k training samples and 2k test samples. To simulate an imbalanced sensitive attribute distribution, 80% of both training and test samples are marked with Blond hair and 20% samples are marked with non-blond hair. CelebA DP-based Learning Methods: We performed the experiments using the following DP-based fair classification methods: 1) DDP-based KDE method [6] and FACL [12], 2) the mutual information-based fair classifier [11], 3) the maximal Correlation-based RFI classifier [13], to learn binary classification models on COMPAS and Adult datasets. For CelebA experiments, we used the following two DP-based fair classification methods: KDE method [6], and mutual information (MI) fair classifier [11]. DP-based Learning Methods: In the experiments, we attempted both a logistic regression classifier with a linear prediction model and a neural net classifier. The neural net architecture was 1) for the COMPAS case, a multi-layer perceptron (MLP) with 4 hidden layers with 64 neurons per layer, 2) for the Adult case, an MLP with 4 hidden layers with 512 neurons per layer, 3) for the CelebA case, the ResNet-18 [28] architecture suited for the image input in the experiments. This paper is available on arxiv under CC BY-NC-SA 4.0 DEED license. This paper is available on arxiv under CC BY-NC-SA 4.0 DEED license. available on arxiv [1] https://github.com/propublica/compas-analysis https://github.com/propublica/compas-analysis [2] https://archive.ics.uci.edu/dataset/2/adult https://archive.ics.uci.edu/dataset/2/adult Authors:
(1) Haoyu LEI, Department of Computer Science and Engineering, The Chinese University of Hong Kong (hylei22@cse.cuhk.edu.hk);
(2) Amin Gohari, Department of Information Engineering, The Chinese University of Hong Kong (agohari@ie.cuhk.edu.hk);
(3) Farzan Farnia, Department of Computer Science and Engineering, The Chinese University of Hong Kong (farnia@cse.cuhk.edu.hk). Authors: Authors: (1) Haoyu LEI, Department of Computer Science and Engineering, The Chinese University of Hong Kong (hylei22@cse.cuhk.edu.hk); (2) Amin Gohari, Department of Information Engineering, The Chinese University of Hong Kong (agohari@ie.cuhk.edu.hk); (3) Farzan Farnia, Department of Computer Science and Engineering, The Chinese University of Hong Kong (farnia@cse.cuhk.edu.hk).

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