# Convolutional Imputation of Matrix Networks

A matrix network is a family of matrices, where the relationship between them is modeled as a weighted graph. Each node represents a matrix, and the weight on each edge represents the similarity between the two matrices. Suppose that we observe a few entries of each matrix with noise, and the fraction of entries we observe varies from matrix to matrix. Even worse, a subset of matrices in this family may be completely unobserved. How can we recover the entire matrix network from noisy and incomplete observations? One motivating example is the cold start problem, where we need to do inference on new users or items that come with no information. To recover this network of matrices, we propose a structural assumption that the matrix network can be approximated by generalized convolution of low rank matrices living on the same network. We propose an iterative imputation algorithm to complete the matrix network. This algorithm is efficient for large scale applications and is guaranteed to accurately recover all matrices, as long as there are enough observations accumulated over the network.

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