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The adaptive interpolation method for proving replica formulas. Applications to the Curie-Weiss and Wigner spike models (1901.06516v2)
Published 19 Jan 2019 in cond-mat.dis-nn, cs.IT, math-ph, math.IT, math.MP, and math.PR
Abstract: In this contribution we give a pedagogic introduction to the newly introduced adaptive interpolation method to prove in a simple and unified way replica formulas for Bayesian optimal inference problems. Many aspects of this method can already be explained at the level of the simple Curie-Weiss spin system. This provides a new method of solution for this model which does not appear to be known. We then generalize this analysis to a paradigmatic inference problem, namely rank-one matrix estimation, also refered to as the Wigner spike model in statistics. We give many pointers to the recent literature where the method has been succesfully applied.