Unifying Orthogonal Monte Carlo Methods

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Krzysztof Choromanski, Mark Rowland, Wenyu Chen, Adrian Weller ;
Proceedings of the 36th International Conference on Machine Learning, PMLR 97:1203-1212, 2019.

Abstract

Many machine learning methods making use of Monte Carlo sampling in vector spaces have been shown to be improved by conditioning samples to be mutually orthogonal. Exact orthogonal coupling of samples is computationally intensive, hence approximate methods have been of great interest. In this paper, we present a unifying perspective of many approximate methods by considering Givens transformations, propose new approximate methods based on this framework, and demonstrate the first statistical guarantees for families of approximate methods in kernel approximation. We provide extensive empirical evaluations with guidance for practitioners.

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