Faster Maximum Feasible Subsystem Solutions for Dense Constraint Matrices

TL;DR

This paper enhances heuristic algorithms for the Maximum Feasible Subsystem problem with dense matrices, significantly increasing their speed while maintaining or improving solution quality, benefiting applications like machine learning and compressive sensing.

Contribution

It extends existing heuristics for dense matrices, achieving faster solutions without sacrificing accuracy in MAX FS problems.

Findings

Speed of heuristics greatly increased for dense matrices

Solution quality preserved or improved

Effective in applications like binary classification and compressive sensing

Abstract

Finding the largest cardinality feasible subset of an infeasible set of linear constraints is the Maximum Feasible Subsystem problem (MAX FS). Solving this problem is crucial in a wide range of applications such as machine learning and compressive sensing. Although MAX FS is NP-hard, useful heuristic algorithms exist, but these can be slow for large problems. We extend the existing heuristics for the case of dense constraint matrices to greatly increase their speed while preserving or improving solution quality. We test the extended algorithms on two applications that have dense constraint matrices: binary classification, and sparse recovery in compressive sensing. In both cases, speed is greatly increased with no loss of accuracy.