Matrix Factorisation with Linear Filters

TL;DR

This paper introduces a probabilistic framework linking matrix factorisation and recursive linear filters, deriving a new high-dimensional matrix factorisation algorithm that can be interpreted as a stochastic gradient method, with applications in image restoration.

Contribution

It presents a novel probabilistic model connecting matrix factorisation with recursive linear filters, leading to an efficient high-dimensional algorithm.

Findings

Effective matrix factorisation via recursive linear filters

Interpretation as stochastic gradient algorithm

Successful application to image restoration

Abstract

This text investigates relations between two well-known family of algorithms, matrix factorisations and recursive linear filters, by describing a probabilistic model in which approximate inference corresponds to a matrix factorisation algorithm. Using the probabilistic model, we derive a matrix factorisation algorithm as a recursive linear filter. More precisely, we derive a matrix-variate recursive linear filter in order to perform efficient inference in high dimensions. We also show that it is possible to interpret our algorithm as a nontrivial stochastic gradient algorithm. Demonstrations and comparisons on an image restoration task are given.