On Sparsity by NUV-EM, Gaussian Message Passing, and Kalman Smoothing

TL;DR

This paper explores the use of NUV priors with EM in linear state space models, enhancing sparsity and robustness for applications like impulsive signal estimation and outlier detection through Gaussian message passing algorithms related to Kalman smoothing.

Contribution

It introduces improved Gaussian message passing algorithms for NUV-EM in linear state space models, facilitating sparse and robust estimation tasks.

Findings

Enhanced Gaussian message passing algorithms derived

Two preferred algorithms identified for practical use

Applications include impulsive signals and outlier removal

Abstract

Normal priors with unknown variance (NUV) have long been known to promote sparsity and to blend well with parameter learning by expectation maximization (EM). In this paper, we advocate this approach for linear state space models for applications such as the estimation of impulsive signals, the detection of localized events, smoothing with occasional jumps in the state space, and the detection and removal of outliers. The actual computations boil down to multivariate-Gaussian message passing algorithms that are closely related to Kalman smoothing. We give improved tables of Gaussian-message computations from which such algorithms are easily synthesized, and we point out two preferred such algorithms.