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K2-ABC: Approximate Bayesian Computation with Kernel Embeddings

Park, M; Jitkrittum, W; Sejdinovic, D; (2016) K2-ABC: Approximate Bayesian Computation with Kernel Embeddings. In: Gretton, A and Robert, CC, (eds.) Proceedings of the 19th International Conference on Artificial Intelligence and Statistics. (pp. pp. 398-407). Journal of Machine Learning Research (JMLR): Cadiz, Spain. Green open access

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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.

Type: Proceedings paper
Title: K2-ABC: Approximate Bayesian Computation with Kernel Embeddings
Event: 19th International Conference on Artificial Intelligence and Statistics
Open access status: An open access version is available from UCL Discovery
Publisher version: http://www.jmlr.org/proceedings/papers/v51/park16....
Language: English
Additional information: Copyright © The Authors 2016.
UCL classification: UCL
UCL > Provost and Vice Provost Offices > UCL BEAMS
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
URI: https://discovery.ucl.ac.uk/id/eprint/1474173
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