Geometrically Coupled Monte Carlo Sampling

Part of Advances in Neural Information Processing Systems 31 (NeurIPS 2018)

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Authors

Mark Rowland, Krzysztof M. Choromanski, Fran├žois Chalus, Aldo Pacchiano, Tamas Sarlos, Richard E. Turner, Adrian Weller

Abstract

<p>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.</p>