Learning deep kernels for exponential family densities

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Li Wenliang, Dougal Sutherland, Heiko Strathmann, Arthur Gretton ;
Proceedings of the 36th International Conference on Machine Learning, PMLR 97:6737-6746, 2019.

Abstract

The kernel exponential family is a rich class of distributions, which can be fit efficiently and with statistical guarantees by score matching. Being required to choose a priori a simple kernel such as the Gaussian, however, limits its practical applicability. We provide a scheme for learning a kernel parameterized by a deep network, which can find complex location-dependent local features of the data geometry. This gives a very rich class of density models, capable of fitting complex structures on moderate-dimensional problems. Compared to deep density models fit via maximum likelihood, our approach provides a complementary set of strengths and tradeoffs: in empirical studies, the former can yield higher likelihoods, whereas the latter gives better estimates of the gradient of the log density, the score, which describes the distribution’s shape.

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