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Bayesian Methods for Low-Rank Matrix Estimation: Short Survey and Theoretical Study

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Algorithmic Learning Theory (ALT 2013)

Part of the book series: Lecture Notes in Computer Science ((LNAI,volume 8139))

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Abstract

The problem of low-rank matrix estimation recently received a lot of attention due to challenging applications. A lot of work has been done on rank-penalized methods [1] and convex relaxation [2], both on the theoretical and applied sides. However, only a few papers considered Bayesian estimation. In this paper, we review the different type of priors considered on matrices to favour low-rank. We also prove that the obtained Bayesian estimators, under suitable assumptions, enjoys the same optimality properties as the ones based on penalization.

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Alquier, P. (2013). Bayesian Methods for Low-Rank Matrix Estimation: Short Survey and Theoretical Study. In: Jain, S., Munos, R., Stephan, F., Zeugmann, T. (eds) Algorithmic Learning Theory. ALT 2013. Lecture Notes in Computer Science(), vol 8139. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-40935-6_22

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  • DOI: https://doi.org/10.1007/978-3-642-40935-6_22

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-40934-9

  • Online ISBN: 978-3-642-40935-6

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