Binary Classification with the Maximum Score Model and Linear Programming

TL;DR

This paper introduces a linear programming-based method for binary classification under Manski's maximum score model, offering computational efficiency and robustness with discrete and continuous covariates, supported by simulations and empirical tests.

Contribution

It develops a new linear programming approach for maximum score estimation that is computationally efficient and applicable to both discrete and continuous covariates, with theoretical and empirical validation.

Findings

Method is minimax optimal under certain conditions.

Reformulation as linear programs reduces computational complexity.

Demonstrated effectiveness through simulations and real data.

Abstract

This paper presents a computationally efficient method for binary classification using Manski's (1975,1985) maximum score model when covariates are discretely distributed and parameters are partially but not point identified. We establish conditions under which it is minimax optimal to allow for either non-classification or random classification and derive finite-sample and asymptotic lower bounds on the probability of correct classification. We also describe an extension of our method to continuous covariates. Our approach avoids the computational difficulty of maximum score estimation by reformulating the problem as two linear programs. Compared to parametric and nonparametric methods, our method balances extrapolation ability with minimal distributional assumptions. Monte Carlo simulations and empirical applications demonstrate its effectiveness and practical relevance.