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Regression under demographic parity constraints via unlabeled post-processing

Evgenii Chzhen, Mohamed Hebiri, Gayane Taturyan

TL;DR

A general-purpose post-processing algorithm that, using accurate estimates of the regression function and a sensitive attribute predictor, generates predictions that meet the demographic parity constraint, involves discretization and stochastic minimization of a smooth convex function.

Abstract

We address the problem of performing regression while ensuring demographic parity, even without access to sensitive attributes during inference. We present a general-purpose post-processing algorithm that, using accurate estimates of the regression function and a sensitive attribute predictor, generates predictions that meet the demographic parity constraint. Our method involves discretization and stochastic minimization of a smooth convex function. It is suitable for online post-processing and multi-class classification tasks only involving unlabeled data for the post-processing. Unlike prior methods, our approach is fully theory-driven. We require precise control over the gradient norm of the convex function, and thus, we rely on more advanced techniques than standard stochastic gradient descent. Our algorithm is backed by finite-sample analysis and post-processing bounds, with experimental results validating our theoretical findings.

Regression under demographic parity constraints via unlabeled post-processing

TL;DR

A general-purpose post-processing algorithm that, using accurate estimates of the regression function and a sensitive attribute predictor, generates predictions that meet the demographic parity constraint, involves discretization and stochastic minimization of a smooth convex function.

Abstract

We address the problem of performing regression while ensuring demographic parity, even without access to sensitive attributes during inference. We present a general-purpose post-processing algorithm that, using accurate estimates of the regression function and a sensitive attribute predictor, generates predictions that meet the demographic parity constraint. Our method involves discretization and stochastic minimization of a smooth convex function. It is suitable for online post-processing and multi-class classification tasks only involving unlabeled data for the post-processing. Unlike prior methods, our approach is fully theory-driven. We require precise control over the gradient norm of the convex function, and thus, we rely on more advanced techniques than standard stochastic gradient descent. Our algorithm is backed by finite-sample analysis and post-processing bounds, with experimental results validating our theoretical findings.
Paper Structure (36 sections, 22 theorems, 127 equations, 5 figures, 1 table, 4 algorithms)

This paper contains 36 sections, 22 theorems, 127 equations, 5 figures, 1 table, 4 algorithms.

Table of Contents

  1. Introduction
  2. Contributions
  3. Organization.
  4. Notation.
  5. Problem setup
  6. Our methodology
  7. Introducing discretization.
  8. Properties of $F$ and $\pi_{{\mathbf{\Lambda}}^\star,{\mathbf{V}}^\star}$.
  9. Gradient of $F$ is crucial.
  10. Summary of our approach and why is it different from others.
  11. Proposed algorithm
  12. Theoretical guarantees.
  13. Extension to unknown $\eta$ and $\tau$.
  14. Numerical illustration
  15. Comparison with agarwal2019fair.
  16. ...and 21 more sections

Key Result

Lemma 3.1

Let $L \in \mathbb{N}$ and $\beta > 0$. Let ${\mathbf{\Lambda}}^\star = (\lambda^\star_{\ell s})_{\ell \in [\![ L ]\!], s \in [K]}$ and ${\mathbf{V}}^\star = (\nu^\star_{\ell s})_{\ell \in [\![ L ]\!], s \in [K]}$ be two matrices that are solutions to where $\boldsymbol{t}({\boldsymbol x}) \stackrel{\hbox{\scriptsize \rm def}}{=} 1-\frac{\boldsymbol{\tau}({\boldsymbol x})}{{\boldsymbol p}}$, $r_\

Figures (5)

  • Figure 1: Risk and unfairness of our estimator on Communities and Crime and Law School datasets.
  • Figure 2: Comparison with ADW model on Communitites and Crime and Law School datasets.
  • Figure 3: Comparison of SDG, ACSA, ACSA2, SDG3+ACSA and SDG3+ACSA2 algorithms on Communitites and Crime and Law School datasets.
  • Figure 4: Experiment on Adult dataset: risk convergence, unfairness convergence and comparison with ADW.
  • Figure 5: The distributions of the (scaled) predictions of the fair and base models.

Theorems & Definitions (45)

  • Remark 2.1
  • Remark 2.2
  • Remark 3.1: On abuse of notation
  • Lemma 3.1
  • Lemma 3.2: Fairness quantification
  • Lemma 3.3: Risk gain
  • Lemma 3.4: Regularity of $F$
  • Lemma 3.5
  • Remark 3.2: On the dynamic of algorithm
  • Lemma 4.1
  • ...and 35 more