A Convex Program for Mixed Linear Regression with a Recovery Guarantee for Well-Separated Data

Abstract

We introduce a convex approach for mixed linear regression over d features. This approach is a second-order cone program, based on L1 minimization, which assigns an estimate regression coefficient in R^d for each data point. These estimates can then be clustered using, for example, k-means. For problems with two or more mixture classes, we prove that the convex program exactly recovers all of the mixture components in the noiseless setting under technical conditions that include a well-separation assumption on the data. Under these assumptions, recovery is possible if each class has at least d independent measurements. We also explore an iteratively reweighted least squares implementation of this method on real and synthetic data.

Tasks

Reproductions