Natural Gradients in Practice: Non-Conjugate Variational Inference in Gaussian Process Models

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Hugh Salimbeni, Stefanos Eleftheriadis, James Hensman ;
Proceedings of the Twenty-First International Conference on Artificial Intelligence and Statistics, PMLR 84:689-697, 2018.

Abstract

The natural gradient method has been used effectively in conjugate Gaussian process models, but the non-conjugate case has been largely unexplored. We examine how natural gradients can be used in non-conjugate stochastic settings, together with hyperparameter learning. We conclude that the natural gradient can significantly improve performance in terms of wall-clock time. For ill-conditioned posteriors the benefit of the natural gradient method is especially pronounced, and we demonstrate a practical setting where ordinary gradients are unusable. We show how natural gradients can be computed efficiently and automatically in any parameterization, using automatic differentiation.

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