Wenliang, LK;
Sutherland, DJ;
Strathmann, H;
Gretton, A;
(2019)
Learning deep kernels for exponential family densities.
In:
Proceedings of the 36th International Conference on Machine Learning.
(pp. pp. 11693-11710).
Proceedings of Machine Learning Research (PMLR): Long Beach, CA, USA.
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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 features of the local 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, deep maximum-likelihood models can yield higher likelihoods, while our approach gives better estimates of the gradient of the log density, the score, which describes the distribution's shape.
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