Sparse trace norm regularization

Jianhui Chen () and Jieping Ye ()

Computational Statistics, 2014, vol. 29, issue 3, 623-639

Abstract: We study the problem of estimating multiple predictive functions from a dictionary of basis functions in the nonparametric regression setting. Our estimation scheme assumes that each predictive function can be estimated in the form of a linear combination of the basis functions. By assuming that the coefficient matrix admits a sparse low-rank structure, we formulate the function estimation problem as a convex program regularized by the trace norm and the $$\ell _1$$ ℓ 1 -norm simultaneously. We propose to solve the convex program using the accelerated gradient (AG) method; we also develop efficient algorithms to solve the key components in AG. In addition, we conduct theoretical analysis on the proposed function estimation scheme: we derive a key property of the optimal solution to the convex program; based on an assumption on the basis functions, we establish a performance bound of the proposed function estimation scheme (via the composite regularization). Simulation studies demonstrate the effectiveness and efficiency of the proposed algorithms. Copyright Springer-Verlag Berlin Heidelberg 2014

Keywords: Low Rank; Regression; Gradient method; Performance bound (search for similar items in EconPapers)
Date: 2014
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Citations: View citations in EconPapers (3)

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Persistent link: https://EconPapers.repec.org/RePEc:spr:compst:v:29:y:2014:i:3:p:623-639

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DOI: 10.1007/s00180-013-0440-7

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