Faster Maximum Feasible Subsystem Solutions for Dense Constraint Matrices
This work addresses the computational bottleneck in solving MAX FS for dense matrices, which is crucial for applications like machine learning and compressive sensing, but it is incremental as it builds on existing heuristics.
The paper tackled the slow heuristic algorithms for the Maximum Feasible Subsystem (MAX FS) problem with dense constraint matrices by extending existing methods to increase speed while maintaining solution quality, achieving significant speed improvements without accuracy loss in binary classification and compressive sensing applications.
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.