Bayesian linear models with unknown design over finite alphabets

Abstract

AbstractOur topic is the reconstruction of the unknown matricesSandωfor the multivariate linear modelY=Sω+εunder the assumption that the entries ofSare drawn from the finite alphabet 𝔄 = 0, 1 andωis a weight matrix. While a frequentist method has recently been proposed for this purpose, a Bayesian approach seems also desirable. We therefore provide a new hierarchical Bayesian method for this inferential task. Our approach provides estimates of the posterior that may be used to quantify uncertainty. Since matching permutations in bothSandωlead to the same reconstructionSω, we introduce an order-preserving shrinkage prior to establish identifiability with respect to permutations.