Subset Selection by Pareto Optimization

Selecting the optimal subset from a large set of variables is a fundamental problem in various learning tasks such as feature selection, sparse regression, dictionary learning, etc. In this paper, we propose the POSS approach which employs evolutionary Pareto optimization to find a small-sized subset with good performance. We prove that for sparse regression, POSS is able to achieve the best-so-far theoretically guaranteed approximation performance efficiently. Particularly, for the Exponential Decay subclass, POSS is proven to achieve an optimal solution. Empirical study verifies the theoretical results, and exhibits the superior performance of POSS to greedy and convex relaxation methods.