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Bayesian methods for low-rank matrix estimation: short survey and theoretical study. (English) Zbl 1411.62136

Jain, Sanjay (ed.) et al., Algorithmic learning theory. 24th international conference, ALT 2013, Singapore, October 6–9, 2013. Proceedings. Berlin: Springer. Lect. Notes Comput. Sci. 8139, 309-323 (2013).
Summary: 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 [F. Bunea et al., Ann. Stat. 39, No. 2, 1282–1309 (2011; Zbl 1216.62086)] and convex relaxation [E. J. Candès and T. Tao, IEEE Trans. Inf. Theory 56, No. 5, 2053–2080 (2010; Zbl 1366.15021)], 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.
For the entire collection see [Zbl 1272.68024].

MSC:

62H12 Estimation in multivariate analysis
62F15 Bayesian inference
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