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JMLR
2010

Spectral Regularization Algorithms for Learning Large Incomplete Matrices

8 years 1 months ago
Spectral Regularization Algorithms for Learning Large Incomplete Matrices
We use convex relaxation techniques to provide a sequence of regularized low-rank solutions for large-scale matrix completion problems. Using the nuclear norm as a regularizer, we provide a simple and very efficient convex algorithm for minimizing the reconstruction error subject to a bound on the nuclear norm. Our algorithm SOFT-IMPUTE iteratively replaces the missing elements with those obtained from a soft-thresholded SVD. With warm starts this allows us to efficiently compute an entire regularization path of solutions on a grid of values of the regularization parameter. The computationally intensive part of our algorithm is in computing a low-rank SVD of a dense matrix. Exploiting the problem structure, we show that the task can be performed with a complexity of order linear in the matrix dimensions. Our semidefinite-programming algorithm is readily scalable to large matrices; for example SOFT-IMPUTE takes a few hours to compute low-rank approximations of a 106
Rahul Mazumder, Trevor Hastie, Robert Tibshirani
Added 19 May 2011
Updated 19 May 2011
Type Journal
Year 2010
Where JMLR
Authors Rahul Mazumder, Trevor Hastie, Robert Tibshirani
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