Star Discrepancy Subset Selection: Problem Formulation and Efficient Approaches for Low Dimensions

01/19/2021
by   Carola Doerr, et al.
0

Motivated by applications in instance selection, we introduce the star discrepancy subset selection problem, which consists of finding a subset of m out of n points that minimizes the star discrepancy. We introduce two mixed integer linear formulations (MILP) and a combinatorial branch-and-bound (BB) algorithm for this problem and we evaluate our approaches against random subset selection and a greedy construction on different use-cases in dimension two and three. Our results show that one of the MILPs and BB are efficient in dimension two for large and small m/n ratio, respectively, and for not too large n. However, the performance of both approaches decays strongly for larger dimensions and set sizes. As a side effect of our empirical comparisons we obtain point sets of discrepancy values that are much smaller than those of common low-discrepancy sequences, random point sets, and of Latin Hypercube Sampling. This suggests that subset selection could be an interesting approach for generating point sets of small discrepancy value.

READ FULL TEXT

Please sign up or login with your details

Forgot password? Click here to reset