Inference in Gaussian models with missing data using Equalisation Maximisation

TL;DR

This paper introduces a new perspective on the Equalisation Maximisation (EqM) algorithm, showing it as an approximation of a proximal point method for Gaussian models, and demonstrates its effectiveness in ARMA models with missing data.

Contribution

It generalizes EqM to all Gaussian models and provides a theoretical foundation, improving understanding and application of the algorithm.

Findings

EqM performs comparably to EM in AR processes

EqM has lower computational cost than EM

Numerical simulations validate EqM's effectiveness

Abstract

Equalisation Maximisation (EqM) is an algorithm for estimating parameters in auto-regressive (AR) models where some fraction of the data is missing. It has previously been shown that the EqM algorithm is a competitive alternative to expectation maximisation, estimating models with equal predictive capability at a lower computational cost. The EqM algorithm has previously been motivated as a heuristic. In this paper, we instead show that EqM can be viewed as an approximation of a proximal point algorithm. We also derive the method for the entire class of Gaussian models and exemplify its use for estimation of ARMA models with missing data. The resulting method is evaluated in numerical simulations, resulting in similar results as for the AR processes.