Geometrically Coupled Monte Carlo Sampling
Mark Rowland, Krzysztof M Choromanski, François Chalus, Aldo Pacchiano, Tamas Sarlos, Richard E Turner, Adrian Weller
Abstract
Monte Carlo sampling in high-dimensional, low-sample settings is important in many machine learning tasks. We improve current methods for sampling in Euclidean spaces by avoiding independence, and instead consider ways to couple samples. We show fundamental connections to optimal transport theory, leading to novel sampling algorithms, and providing new theoretical grounding for existing strategies. We compare our new strategies against prior methods for improving sample efficiency, including QMC, by studying discrepancy. We explore our findings empirically, and observe benefits of our sampling schemes for reinforcement learning and generative modelling.
BibTeX
@inproceedings{NEURIPS2018_b3e3e393,
author = {Rowland, Mark and Choromanski, Krzysztof M and Chalus, Fran\c{c}ois and Pacchiano, Aldo and Sarlos, Tamas and Turner, Richard E and Weller, Adrian},
booktitle = {Advances in Neural Information Processing Systems},
editor = {S. Bengio and H. Wallach and H. Larochelle and K. Grauman and N. Cesa-Bianchi and R. Garnett},
pages = {},
publisher = {Curran Associates, Inc.},
title = {Geometrically Coupled Monte Carlo Sampling},
url = {https://proceedings.neurips.cc/paper_files/paper/2018/file/b3e3e393c77e35a4a3f3cbd1e429b5dc-Paper.pdf},
volume = {31},
year = {2018}
}