PAC-Bayesian Matrix Completion with a Spectral Scaled Student Prior. (arXiv:2104.08191v2 [stat.ML] UPDATED)

We study the problem of matrix completion in this paper. A spectral scaled
Student prior is exploited to favour the underlying low-rank structure of the
data matrix. We provide a thorough theoretical investigation for our approach
through PAC-Bayesian bounds. More precisely, our PAC-Bayesian approach enjoys a
minimax-optimal oracle inequality which guarantees that our method works well
under model misspecification and under general sampling distribution.
Interestingly, we also provide efficient gradient-based sampling
implementations for our approach by using Langevin Monte Carlo. …

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