Linear Program Method for Multiclass

Note

Learning tasks: Multiclassification.

Introduction

A previous linear programming technique is extended to accommodate a theoretically arbitrarily large number of discrete outcomes and levels of a protected attribute. This method aims to achieve fairness in multiclass settings by adjusting the predictions of a blackbox classifier to reduce disparity across different protected groups.

Description

• Problem definition

  The primary goal is to adjust the predictions of a blackbox classifier to ensure fairness across different protected groups while maintaining as much predictive performance as possible. The method focuses on reducing post-adjustment disparity in multiclass classification problems.

• Main features

  • Extends the linear programming technique to handle multiple discrete outcomes and protected attribute levels.

  • Evaluates the tradeoff between fairness and discrimination.

• Step-by-step description of the approach

  1. Initial Setup:

     • Train a classifier to predict the multiclass outcome.

     • Obtain the initial predictions \(\hat{Y}\).

  2. Linear Program Formulation:

     • Define the fairness constraints based on the type of fairness desired (e.g., equalized odds, equal opportunity, demographic parity).

     • Formulate the linear program to adjust the predictions \(Y_{\text{adj}}\) such that the fairness constraints are satisfied.

  3. Solving the Linear Program:

     • Solve the linear program on the entire dataset to obtain the adjusted probabilities \(P_a\).

     • Use these probabilities to generate the adjusted predictions \(Y_{\text{adj}}\).

Basic Usage

You can find an example of using the Linear Program Method for Multiclass in the following demo.

Read more about the class attributes and methods in the API reference: LPDebiaserMulticlass.

References

1. Putzel, Preston, and Scott Lee. “Blackbox Post-Processing for Multiclass Fairness.”arXiv preprint arXiv:2201.04461 (2022);.