Fair Matrix Completion: Objectives and Optimization

Presenter

Anish Mitagar

Campus

UMass Amherst

Sponsor

Yair Zick, Department of Computer Science, UMass Amherst

Schedule

Session 2, 11:30 AM - 12:15 PM [Schedule by Time][Poster Grid for Time/Location]

Location

Poster Board A50, Campus Center Auditorium, Row 3 (A41-A60) [Poster Location Map]

Abstract

Current Matrix Factorization Systems attempt to complete a matrix from incomplete observations. Generally such systems minimize a loss over all observed cells, which incentives accuracy, but does not incorporate fairness. We introduce a framework for fair matrix completion which optimizes group fair objectives. We consider the case where rows represent people and columns represent objects, and the case where both columns and rows are people. Each person belongs to some group and we optimize some fair objective over the average loss for each group. For example minimizing a weighted average is equivalent to standard loss minimization, but minimizing the maximum loss over all groups is a fair variant of this approach. Our framework considers a broad family of both fairness criteria of loss functions and classes of matrices that are useful for real world applications ranging from movie recommendations to dating and other matching problems. Crucially we address the often neglected human element in these tasks in both one sided and two sided matching problems. We show that, under mild conditions, these fair matrix optimization tasks can be posed as convex optimization problems. We implement this framework using the cvxpy optimization library and show that optimizing our fair objectives leads to better outcomes for minority groups.

Keywords

Matrix Factorization, Convex Optimization, Fair Algorithms

Research Area

Probability, Statistics, and Machine Learning

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