Active Learning of Conditional Mean Embeddings via Bayesian Optimisation

Sayak Ray Chowdhury, Rafael Oliveira, Fabio Ramos
Proceedings of the 36th Conference on Uncertainty in Artificial Intelligence (UAI), PMLR 124:1119-1128, 2020.

Abstract

We consider the problem of sequentially optimising the conditional expectation of an objective function, with both the conditional distribution and the objective function assumed to be fixed but unknown. Assuming that the objective function belongs to a reproducing kernel Hilbert space (RKHS), we provide a novel upper confidence bound (UCB) based algorithm CME-UCB via estimation of the conditional mean embeddings (CME), and derive its regret bound. Along the way, we derive novel approximation guarantees for the CME estimates. Finally, experiments are carried out in a synthetic example and in a likelihood-free inference application that highlight the useful insights of the proposed method.

Cite this Paper


BibTeX
@InProceedings{pmlr-v124-ray-chowdhury20a, title = {Active Learning of Conditional Mean Embeddings via Bayesian Optimisation}, author = {Ray Chowdhury, Sayak and Oliveira, Rafael and Ramos, Fabio}, booktitle = {Proceedings of the 36th Conference on Uncertainty in Artificial Intelligence (UAI)}, pages = {1119--1128}, year = {2020}, editor = {Jonas Peters and David Sontag}, volume = {124}, series = {Proceedings of Machine Learning Research}, month = {03--06 Aug}, publisher = {PMLR}, pdf = {http://proceedings.mlr.press/v124/ray-chowdhury20a/ray-chowdhury20a.pdf}, url = { http://proceedings.mlr.press/v124/ray-chowdhury20a.html }, abstract = {We consider the problem of sequentially optimising the conditional expectation of an objective function, with both the conditional distribution and the objective function assumed to be fixed but unknown. Assuming that the objective function belongs to a reproducing kernel Hilbert space (RKHS), we provide a novel upper confidence bound (UCB) based algorithm CME-UCB via estimation of the conditional mean embeddings (CME), and derive its regret bound. Along the way, we derive novel approximation guarantees for the CME estimates. Finally, experiments are carried out in a synthetic example and in a likelihood-free inference application that highlight the useful insights of the proposed method.} }
Endnote
%0 Conference Paper %T Active Learning of Conditional Mean Embeddings via Bayesian Optimisation %A Sayak Ray Chowdhury %A Rafael Oliveira %A Fabio Ramos %B Proceedings of the 36th Conference on Uncertainty in Artificial Intelligence (UAI) %C Proceedings of Machine Learning Research %D 2020 %E Jonas Peters %E David Sontag %F pmlr-v124-ray-chowdhury20a %I PMLR %P 1119--1128 %U http://proceedings.mlr.press/v124/ray-chowdhury20a.html %V 124 %X We consider the problem of sequentially optimising the conditional expectation of an objective function, with both the conditional distribution and the objective function assumed to be fixed but unknown. Assuming that the objective function belongs to a reproducing kernel Hilbert space (RKHS), we provide a novel upper confidence bound (UCB) based algorithm CME-UCB via estimation of the conditional mean embeddings (CME), and derive its regret bound. Along the way, we derive novel approximation guarantees for the CME estimates. Finally, experiments are carried out in a synthetic example and in a likelihood-free inference application that highlight the useful insights of the proposed method.
APA
Ray Chowdhury, S., Oliveira, R. & Ramos, F.. (2020). Active Learning of Conditional Mean Embeddings via Bayesian Optimisation. Proceedings of the 36th Conference on Uncertainty in Artificial Intelligence (UAI), in Proceedings of Machine Learning Research 124:1119-1128 Available from http://proceedings.mlr.press/v124/ray-chowdhury20a.html .

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