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Poster
Importance Weighted Kernel Bayes' Rule
Liyuan Xu · Yutian Chen · Arnaud Doucet · Arthur Gretton

Thu Jul 21 03:00 PM -- 05:00 PM (PDT) @ Hall E #515
in Poster Session 3 »

We study a nonparametric approach to Bayesian computation via feature means, where the expectation of prior features is updated to yield expected posterior features, based on regression from kernel or neural net features of the observations. All quantities involved in the Bayesian update are learned from observed data, making the method entirely model-free. The resulting algorithm is a novel instance of a kernel Bayes' rule (KBR). Our approach is based on importance weighting, which results in superior numerical stability to the existing approach to KBR, which requires operator inversion. We show the convergence of the estimator using a novel consistency analysis on the importance weighting estimator in the infinity norm. We evaluate our KBR on challenging synthetic benchmarks, including a filtering problem with a state-space model involving high dimensional image observations. The proposed method yields uniformly better empirical performance than the existing KBR, and competitive performance with other competing methods.We evaluate our KBR on challenging synthetic benchmarks, including a filtering problem with a state-space model involving high dimensional image observations. The proposed method yields uniformly better empirical performance than the existing KBR, and competitive performance with other competing methods.

Keywords: PM: Bayesian Models and Methods · T: Learning Theory · MISC: Kernel methods
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Author Information

Liyuan Xu (Gatsby Computational Neuralscience Unit)
Yutian Chen (DeepMind)
Arnaud Doucet (Google DeepMind)
Arthur Gretton (Gatsby Computational Neuroscience Unit)

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