Support points [article]

Simon Mak, V. Roshan Joseph
2018 arXiv   pre-print
This paper introduces a new way to compact a continuous probability distribution F into a set of representative points called support points. These points are obtained by minimizing the energy distance, a statistical potential measure initially proposed by Székely and Rizzo (2004) for testing goodness-of-fit. The energy distance has two appealing features. First, its distance-based structure allows us to exploit the duality between powers of the Euclidean distance and its Fourier transform for
more » ... heoretical analysis. Using this duality, we show that support points converge in distribution to F, and enjoy an improved error rate to Monte Carlo for integrating a large class of functions. Second, the minimization of the energy distance can be formulated as a difference-of-convex program, which we manipulate using two algorithms to efficiently generate representative point sets. In simulation studies, support points provide improved integration performance to both Monte Carlo and a specific Quasi-Monte Carlo method. Two important applications of support points are then highlighted: (a) as a way to quantify the propagation of uncertainty in expensive simulations, and (b) as a method to optimally compact Markov chain Monte Carlo (MCMC) samples in Bayesian computation.
arXiv:1609.01811v7 fatcat:a6no2smjyvdh7ln3te2i7lap64