DeepAI AI Chat
Log In Sign Up

Asymptotics of MAP Inference in Deep Networks

by   Parthe Pandit, et al.
NYU college

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, multi-layer 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.


page 1

page 2

page 3

page 4


Inference with Deep Generative Priors in High Dimensions

Deep generative priors offer powerful models for complex-structured data...

Inference in Deep Networks in High Dimensions

Deep generative networks provide a powerful tool for modeling complex da...

Plug-in Estimation in High-Dimensional Linear Inverse Problems: A Rigorous Analysis

Estimating a vector x from noisy linear measurements Ax+w often requires...

Inference in Multi-Layer Networks with Matrix-Valued Unknowns

We consider the problem of inferring the input and hidden variables of a...

Estimation for High-Dimensional Multi-Layer Generalized Linear Model – Part I: The Exact MMSE Estimator

This two-part work considers the minimum means square error (MMSE) estim...

Towards Building Deep Networks with Bayesian Factor Graphs

We propose a Multi-Layer Network based on the Bayesian framework of the ...

Multi-layer State Evolution Under Random Convolutional Design

Signal recovery under generative neural network priors has emerged as a ...