Sparse trace norm regularization

J Chen, J Ye - Computational Statistics, 2014 - Springer
Computational Statistics, 2014Springer
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 ℓ _1 ℓ 1-norm simultaneously. We propose to solve the convex program using …
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 -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.
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