Zen and the Science of Pattern Identification: An Inquiry into Bayesian Skepticism

Abstract

Finding patterns in data is one of the most challenging open questions in information science. The number of possible relationships scales combinatorially with the size of the dataset, overwhelming the exponential increase in availability of computational resources. Physical insights have been instrumental in developing efficient computational heuristics. Using quantum field theory methods and rethinking three centuries of Bayesian inference, we formulated the problem in terms of finding landscapes of patterns and solved this problem exactly. The generality of our calculus is illustrated by applying it to handwritten digit images and to finding structural features in proteins from sequence alignments without any presumptions about model priors suited to specific datasets. Landscapes of patterns can be uncovered on a desktop computer in minutes.