Bayesian Learning for Low-Rank matrix reconstruction

Martin Sundin; Cristian R. Rojas; Magnus Jansson; Saikat Chatterjee

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arXiv · 1501.05740

Bayesian Learning for Low-Rank matrix reconstruction

Martin Sundin·Cristian R. Rojas·Magnus Jansson·Saikat Chatterjee

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Abstract

We develop latent variable models for Bayesian learning based low-rank matrix completion and reconstruction from linear measurements. For under-determined systems, the developed methods are shown to reconstruct low-rank matrices when neither the rank nor the noise power is known a-priori. We derive relations between the latent variable models and several low-rank promoting penalty functions. The relations justify the use of Kronecker structured covariance matrices in a Gaussian based prior. In the methods, we use evidence approximation and expectation-maximization to learn the model parameters. The performance of the methods is evaluated through extensive numerical simulations.

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BibTeX RIS

Martin Sundin, Cristian R. Rojas, Magnus Jansson, Saikat Chatterjee. 2015-01-23. Bayesian Learning for Low-Rank matrix reconstruction. https://arxiv.org/abs/1501.05740

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