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Poster
Matrix Inference and Estimation in MultiLayer Models
Parthe Pandit · Mojtaba Sahraee Ardakan · Sundeep Rangan · Philip Schniter · Alyson Fletcher
We consider the problem of estimating the input and hidden variables of a stochastic multilayer neural network from an observation of the output. The hidden variables in each layer are represented as matrices with statistical interactions along both rows as well as columns. This problem applies to matrix imputation, signal recovery via deep generative prior models, multitask and mixed regression, and learning certain classes of twolayer neural networks. We extend a recentlydeveloped algorithm  MultiLayer Vector Approximate Message Passing (MLVAMP), for this matrixvalued inference problem. It is shown that the performance of the proposed MultiLayer Matrix VAMP (MLMatVAMP) algorithm can be exactly predicted in a certain random largesystem limit, where the dimensions $N\times d$ of the unknown quantities grow as $N\rightarrow\infty$ with $d$ fixed. In the twolayer neuralnetwork learning problem, this scaling corresponds to the case where the number of input features, as well as training samples, grow to infinity but the number of hidden nodes stays fixed. The analysis enables a precise prediction of the parameter and test error of the learning.
Author Information
Parthe Pandit (University of California, Los Angeles)
Parthe is a Postdoc at the Halicioglu Data Science Institute at UCSD. He is interested in highdimensional optimization problems in machine learning and signal processing.
Mojtaba Sahraee Ardakan (UCLA)
Sundeep Rangan (NYU)
Philip Schniter (The Ohio State University)
Alyson Fletcher (UCLA)
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