# Structured Monte Carlo Sampling for Nonisotropic Distributions via Determinantal Point Processes

arXiv: https://arxiv.org/abs/1905.12667 · HTML: https://mlsanity.com/paper/1905.12667/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 29 May 2019.

## Built on by (most cited first, 1 of 1)

- [Langevin Quasi-Monte Carlo](https://mlsanity.com/paper/2309.12664/) (2023)

## Abstract (arXiv)

We propose a new class of structured methods for Monte Carlo (MC) sampling, called DPPMC, designed for high-dimensional nonisotropic distributions where samples are correlated to reduce the variance of the estimator via determinantal point processes. We successfully apply DPPMCs to problems involving nonisotropic distributions arising in guided evolution strategy (GES) methods for RL, CMA-ES techniques and trust region algorithms for blackbox optimization, improving state-of-the-art in all these settings. In particular, we show that DPPMCs drastically improve exploration profiles of the existing evolution strategy algorithms. We further confirm our results, analyzing random feature map estimators for Gaussian mixture kernels. We provide theoretical justification of our empirical results, showing a connection between DPPMCs and structured orthogonal MC methods for isotropic distributions.