  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.
