Covariate-moderated Empirical Bayes Matrix Factorization
William Denault, Karl Tayeb, Peter Carbonetto, Jason Willwerscheid, Matthew Stephens
Matrix factorization is a fundamental method in statistics and machinelearning for inferring and summarizing structure in multivariatedata. Modern data sets often come with ``side information'' of variousforms (images, text, graphs) that can be leveraged to improveestimation of the underlying structure. However, existing methods thatleverage side information are limited in the types of data they canincorporate, and they assume specific parametric models. Here, weintroduce a novel method for this problem, {\em covariate-moderated  empirical Bayes matrix factorization} (cEBMF). cEBMF is a modularframework that accepts any type of side information that isprocessable by a probabilistic model or neural network.The cEBMF framework can accommodate different assumptions andconstraints on the factors through the use of different priors, and itadapts these priors to the data. We demonstrate the benefits of cEBMFin simulations and in analyses of spatial transcriptomics andMovieLens data.