Table of Links Abstract and 1 Introduction 2 Related Works 3 Preliminaries 3.1 Fair Supervised Learning and 3.2 Fairness Criteria 3.3 Dependence Measures for Fair Supervised Learning 4 Inductive Biases of DP-based Fair Supervised Learning 4.1 Extending the Theoretical Results to Randomized Prediction Rule 5 A Distributionally Robust Optimization Approach to DP-based Fair Learning 6 Numerical Results 6.1 Experimental Setup 6.2 Inductive Biases of Models trained in DP-based Fair Learning 6.3 DP-based Fair Classification in Heterogeneous Federated Learning 7 Conclusion and References Appendix A Proofs Appendix B Additional Results for Image Dataset Appendix A Proofs A.1 Proof of Theorem 1 Therefore, for the objective function in Equation (1), we can write the following: Knowing that TV is a metric distance satisfying the triangle inequality, the above equations show that Therefore, A.2 Proof of Theorem 2 A.3 Proof of Theorem 3 Therefore, we can follow the proof of Theorems 1,2 which shows the above inequality leads to the bounds claimed in the theorems. Appendix B Additional Results for Image Dataset This part shows the inductive biases of DP-based fair classifier for CelebA dataset, as well as the visualized plots. For the baselines, two fair classifiers are implemented for image fair classification: KDE proposed by [11] and MI proposed by [6], based on ResNet-18 [28]. This paper is available on arxiv under CC BY-NC-SA 4.0 DEED license. 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). 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 Appendix A Proofs A.1 Proof of Theorem 1 Therefore, for the objective function in Equation (1), we can write the following: Knowing that TV is a metric distance satisfying the triangle inequality, the above equations show that Therefore, A.2 Proof of Theorem 2 A.3 Proof of Theorem 3 Therefore, we can follow the proof of Theorems 1,2 which shows the above inequality leads to the bounds claimed in the theorems. Appendix B Additional Results for Image Dataset This part shows the inductive biases of DP-based fair classifier for CelebA dataset, as well as the visualized plots. For the baselines, two fair classifiers are implemented for image fair classification: KDE proposed by [11] and MI proposed by [6], based on ResNet-18 [28]. 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 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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Mathematical Proofs for Fair AI Bias Analysis

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