Jo, Ritsugen;
Chen, Yutian;
Doucet, Arnaud;
Gretton, Arthur;
(2022)
Importance Weighting Approach in Kernel Bayes' Rule.
In:
Proceedings of Machine Learning Research.
(pp. pp. 24524-24538).
PMLR: Baltimore, Maryland, USA.
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Abstract
We study a nonparametric approach to Bayesian computation via feature means, where the expectation of prior features is updated to yield expected kernel posterior features, based on regression from learned neural net or kernel 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.
| Type: | Proceedings paper |
|---|---|
| Title: | Importance Weighting Approach in Kernel Bayes' Rule |
| Event: | International Conference on Machine Learning and Cybernetics 2022 |
| Open access status: | An open access version is available from UCL Discovery |
| Publisher version: | https://proceedings.mlr.press/v162/xu22a.html |
| Language: | English |
| Additional information: | This version is the author accepted manuscript. For information on re-use, please refer to the publisher’s terms and conditions. |
| UCL classification: | UCL > Provost and Vice Provost Offices > UCL BEAMS > Faculty of Engineering Science UCL > Provost and Vice Provost Offices > UCL BEAMS > Faculty of Engineering Science > Dept of Computer Science UCL > Provost and Vice Provost Offices > UCL BEAMS UCL |
| URI: | https://discovery.ucl.ac.uk/id/eprint/10151138 |
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