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The approximation of a high-dimensional vector by a small combination ofcolumn vectors selected from a fixed matrix has been actively debated inseveral different disciplines. In this paper, a sampling approach based on theMonte Carlo method is presented as an efficient solver for such problems.Especially, the use of simulated annealing (SA), a metaheuristic optimizationalgorithm, for determining degrees of freedom (the number of used columns) bycross validation is focused on and tested. Test on a synthetic model indicatesthat our SA-based approach can find a nearly optimal solution for theapproximation problem and, when combined with the CV framework, it can optimizethe generalization ability. Its utility is also confirmed by application to areal-world supernova data set.

Sampling approach to sparse approximation problem: determining degrees of freedom by simulated annealing