Near-optimal feature selection for large databases

We analyse a new optimization-based approach for feature selection that uses the nested partitions method for combinatorial optimization as a heuristic search procedure to identify good feature subsets. In particular, we show how to improve the performance of the nested partitions method using random sampling of instances. The new approach uses a two-stage sampling scheme that determines the required sample size to guarantee convergence to a near-optimal solution. This approach therefore also has attractive theoretical characteristics. In particular, when the algorithm terminates in finite time, rigorous statements can be made concerning the quality of the final feature subset. Numerical results are reported to illustrate the key results, and show that the new approach is considerably faster than the original nested partitions method and other feature selection methods.