Asymptotics of MAP Inference in Deep Networks

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Asymptotics of MAP Inference in Deep Networks

Creation Date: Jul 07, 2019

Published In: Jul 2019

Paper Type: Conference Paper

Book Title: Proceedings of the 2019 IEEE International Symposium on Information Theory

Address: Paris, France

Abstract:

Deep generative priors are a powerful tool for reconstruction problems with complex data such as images and text. Inverse problems using such models require solving an inference problem of estimating the input and hidden units of the multi-layer network from its output. Maximum a priori (MAP) estimation is a widely-used inference method as it is straightforward to implement, and has been successful in practice. However, rigorous analysis of MAP inference in multi-layer networks is difficult. This work considers a recently-developed method, multilayer vector approximate message passing (ML-VAMP), to study MAP inference in deep networks. It is shown that the mean squared error of the ML-VAMP estimate can be exactly and rigorously characterized in a certain high-dimensional random limit. The proposed method thus provides a tractable method for MAP inference with exact performance guarantees.

IEEE Explore link: https://ieeexplore.ieee.org/document/8849316

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