A Convergence Analysis of Approximate Message Passing with Non-Separable Functions and Applications to Multi-Class Classification

TL;DR

This paper provides a convergence analysis of approximate message passing algorithms with non-separable functions, extending their theoretical understanding and applying it to multi-class classification problems.

Contribution

It offers the first convergence analysis of AMP with non-separable multivariate nonlinearities and applies this to analyze convex optimization in multi-class classification.

Findings

Convergence guarantees for AMP with non-separable functions

Application to multi-class classification optimization

Enhanced theoretical understanding of AMP dynamics

Abstract

Motivated by the recent application of approximate message passing (AMP) to the analysis of convex optimizations in multi-class classifications [Loureiro, et. al., 2021], we present a convergence analysis of AMP dynamics with non-separable multivariate nonlinearities. As an application, we present a complete (and independent) analysis of the motivated convex optimization problem.