Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Matrix Completion with Nonconvex Regularization: Spectral Operators and
  Scalable Algorithms   In this paper, we study the popularly dubbed matrix completion problem, where
the task is to "fill in" the unobserved entries of a matrix from a small subset
of observed entries, under the assumption that the underlying matrix is of
low-rank. Our contributions herein, enhance our prior work on nuclear norm
regularized problems for matrix completion (Mazumder et al., 2010) by
incorporating a continuum of nonconvex penalty functions between the convex
nuclear norm and nonconvex rank functions. Inspired by SOFT-IMPUTE (Mazumder et
al., 2010; Hastie et al., 2016), we propose NC-IMPUTE- an EM-flavored
algorithmic framework for computing a family of nonconvex penalized matrix
completion problems with warm-starts. We present a systematic study of the
associated spectral thresholding operators, which play an important role in the
overall algorithm. We study convergence properties of the algorithm. Using
structured low-rank SVD computations, we demonstrate the computational
scalability of our proposal for problems up to the Netflix size (approximately,
a $500,000 \times 20, 000$ matrix with $10^8$ observed entries). We demonstrate
that on a wide range of synthetic and real data instances, our proposed
nonconvex regularization framework leads to low-rank solutions with better
predictive performance when compared to those obtained from nuclear norm
problems. Implementations of algorithms proposed herein, written in the R
programming language, are made available on github.

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The categories of this paper are: bayes-an
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The categories of this paper are: ao-sci
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The categories of this paper are: patt-sol
33
The categories of this paper are: plasm-ph
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The categories of this paper are: cs
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The categories of this paper are: q-fin
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The categories of this paper are: hep-th
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The categories of this paper are: q-alg
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The categories of this paper are: adap-org
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The categories of this paper are: chao-dyn
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The categories of this paper are: quant-ph
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The categories of this paper are: dg-ga
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The categories of this paper are: atom-ph
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The categories of this paper are: nucl-ex
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The categories of this paper are: hep-lat
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The categories of this paper are: solv-int