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Recently a new adaptive path interpolation method has been developed as asimple and versatile scheme to calculate exactly the asymptotic mutualinformation of Bayesian inference problems defined on dense factor graphs.These include random linear and generalized estimation, sparse superpositioncodes, or low-rank matrix and tensor estimation. For all these systems, theadaptive interpolation method directly proves that the replica symmetricprediction is exact, in a simple and unified manner. When the underlying factorgraph of the inference problem is sparse the replica prediction is considerablymore complicated, and rigorous results are often lacking or obtained by rathercomplicated methods. In this work we show how to extend the adaptive pathinterpolation method to sparse systems. We concentrate on a Censored BlockModel, where hidden variables are measured through a binary erasure channel,for which we fully prove the replica prediction.

Adaptive Path Interpolation for Sparse Systems: Application to a Simple Censored Block Model