Source separation as an exercise in logical induction

Abstract

We examine the relationship between the Bayesian and information-theoretic formulations of source separation algorithms. This work makes use of the relationship between the work of Claude E. Shannon and the "Recent Contributions" by Warren Weaver (Shannon & Weaver 1949) as clarified by Richard T. Cox (1979) and expounded upon by Robert L. Fry (1996) as a duality between a logic of assertions and a logic of questions. Working with the logic of assertions requires the use of probability as a measure of degree of implication. This leads to a Bayesian formulation of the problem. Whereas, working with the logic of questions requires the use of entropy as a measure of the bearing of a question on an issue leading to an information-theoretic formulation of the problem.