On the complexity of switching linear regression

TL;DR

This paper investigates the computational complexity of switching linear regression, proving it is NP-hard but also providing a polynomial-time algorithm for fixed data dimensions and modes, advancing understanding of its computational limits.

Contribution

It extends previous complexity results to switching linear regression, showing NP-hardness and offering a polynomial-time solution under fixed parameters.

Findings

Switching linear regression is NP-hard.

A polynomial-time algorithm exists for fixed data dimensions and modes.

The results clarify the computational boundaries of the problem.

Abstract

This technical note extends recent results on the computational complexity of globally minimizing the error of piecewise-affine models to the related problem of minimizing the error of switching linear regression models. In particular, we show that, on the one hand the problem is NP-hard, but on the other hand, it admits a polynomial-time algorithm with respect to the number of data points for any fixed data dimension and number of modes.