Mixed Regression via Approximate Message Passing

We study the problem of regression in a generalized linear model (GLM) with multiple signals and latent variables. This model, which we call a matrix GLM, covers many widely studied problems in statistical learning, including mixed linear regression, max-affine regression, and mixture-of-experts. The goal in all these problems is to estimate the signals, and possibly some of the latent variables, from the observations. We propose a novel approximate message passing (AMP) algorithm for estimation in a matrix GLM and rigorously …

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