K2-ABC: Approximate Bayesian Computation with Kernel Embeddings

Mijung Park, Wittawat Jitkrittum, Dino Sejdinovic
Proceedings of the 19th International Conference on Artificial Intelligence and Statistics, PMLR 51:398-407, 2016.

Abstract

Complicated generative models often result in a situation where computing the likelihood of observed data is intractable, while simulating from the conditional density given a parameter value is relatively easy. Approximate Bayesian Computation (ABC) is a paradigm that enables simulation-based posterior inference in such cases by measuring the similarity between simulated and observed data in terms of a chosen set of summary statistics. However, there is no general rule to construct sufficient summary statistics for complex models. Insufficient summary statistics will leak information, which leads to ABC algorithms yielding samples from an incorrect posterior. In this paper, we propose a fully nonparametric ABC paradigm which circumvents the need for manually selecting summary statistics. Our approach, K2-ABC, uses maximum mean discrepancy (MMD) to construct a dissimilarity measure between the observed and simulated data. The embedding of an empirical distribution of the data into a reproducing kernel Hilbert space plays a role of the summary statistic and is sufficient whenever the corresponding kernels are characteristic. Experiments on a simulated scenario and a real-world biological problem illustrate the effectiveness of the proposed algorithm.

Cite this Paper

BibTeX
@InProceedings{pmlr-v51-park16, title = {K2-ABC: Approximate Bayesian Computation with Kernel Embeddings}, author = {Park, Mijung and Jitkrittum, Wittawat and Sejdinovic, Dino}, booktitle = {Proceedings of the 19th International Conference on Artificial Intelligence and Statistics}, pages = {398--407}, year = {2016}, editor = {Gretton, Arthur and Robert, Christian C.}, volume = {51}, series = {Proceedings of Machine Learning Research}, address = {Cadiz, Spain}, month = {09--11 May}, publisher = {PMLR}, pdf = {http://proceedings.mlr.press/v51/park16.pdf}, url = {https://proceedings.mlr.press/v51/park16.html}, abstract = {Complicated generative models often result in a situation where computing the likelihood of observed data is intractable, while simulating from the conditional density given a parameter value is relatively easy. Approximate Bayesian Computation (ABC) is a paradigm that enables simulation-based posterior inference in such cases by measuring the similarity between simulated and observed data in terms of a chosen set of summary statistics. However, there is no general rule to construct sufficient summary statistics for complex models. Insufficient summary statistics will leak information, which leads to ABC algorithms yielding samples from an incorrect posterior. In this paper, we propose a fully nonparametric ABC paradigm which circumvents the need for manually selecting summary statistics. Our approach, K2-ABC, uses maximum mean discrepancy (MMD) to construct a dissimilarity measure between the observed and simulated data. The embedding of an empirical distribution of the data into a reproducing kernel Hilbert space plays a role of the summary statistic and is sufficient whenever the corresponding kernels are characteristic. Experiments on a simulated scenario and a real-world biological problem illustrate the effectiveness of the proposed algorithm.} }
Endnote
%0 Conference Paper %T K2-ABC: Approximate Bayesian Computation with Kernel Embeddings %A Mijung Park %A Wittawat Jitkrittum %A Dino Sejdinovic %B Proceedings of the 19th International Conference on Artificial Intelligence and Statistics %C Proceedings of Machine Learning Research %D 2016 %E Arthur Gretton %E Christian C. Robert %F pmlr-v51-park16 %I PMLR %P 398--407 %U https://proceedings.mlr.press/v51/park16.html %V 51 %X Complicated generative models often result in a situation where computing the likelihood of observed data is intractable, while simulating from the conditional density given a parameter value is relatively easy. Approximate Bayesian Computation (ABC) is a paradigm that enables simulation-based posterior inference in such cases by measuring the similarity between simulated and observed data in terms of a chosen set of summary statistics. However, there is no general rule to construct sufficient summary statistics for complex models. Insufficient summary statistics will leak information, which leads to ABC algorithms yielding samples from an incorrect posterior. In this paper, we propose a fully nonparametric ABC paradigm which circumvents the need for manually selecting summary statistics. Our approach, K2-ABC, uses maximum mean discrepancy (MMD) to construct a dissimilarity measure between the observed and simulated data. The embedding of an empirical distribution of the data into a reproducing kernel Hilbert space plays a role of the summary statistic and is sufficient whenever the corresponding kernels are characteristic. Experiments on a simulated scenario and a real-world biological problem illustrate the effectiveness of the proposed algorithm.
RIS
TY - CPAPER TI - K2-ABC: Approximate Bayesian Computation with Kernel Embeddings AU - Mijung Park AU - Wittawat Jitkrittum AU - Dino Sejdinovic BT - Proceedings of the 19th International Conference on Artificial Intelligence and Statistics DA - 2016/05/02 ED - Arthur Gretton ED - Christian C. Robert ID - pmlr-v51-park16 PB - PMLR DP - Proceedings of Machine Learning Research VL - 51 SP - 398 EP - 407 L1 - http://proceedings.mlr.press/v51/park16.pdf UR - https://proceedings.mlr.press/v51/park16.html AB - Complicated generative models often result in a situation where computing the likelihood of observed data is intractable, while simulating from the conditional density given a parameter value is relatively easy. Approximate Bayesian Computation (ABC) is a paradigm that enables simulation-based posterior inference in such cases by measuring the similarity between simulated and observed data in terms of a chosen set of summary statistics. However, there is no general rule to construct sufficient summary statistics for complex models. Insufficient summary statistics will leak information, which leads to ABC algorithms yielding samples from an incorrect posterior. In this paper, we propose a fully nonparametric ABC paradigm which circumvents the need for manually selecting summary statistics. Our approach, K2-ABC, uses maximum mean discrepancy (MMD) to construct a dissimilarity measure between the observed and simulated data. The embedding of an empirical distribution of the data into a reproducing kernel Hilbert space plays a role of the summary statistic and is sufficient whenever the corresponding kernels are characteristic. Experiments on a simulated scenario and a real-world biological problem illustrate the effectiveness of the proposed algorithm. ER -
APA
Park, M., Jitkrittum, W. & Sejdinovic, D.. (2016). K2-ABC: Approximate Bayesian Computation with Kernel Embeddings. Proceedings of the 19th International Conference on Artificial Intelligence and Statistics, in Proceedings of Machine Learning Research 51:398-407 Available from https://proceedings.mlr.press/v51/park16.html.

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