K2-ABC: Approximate Bayesian Computation with Infinite Dimensional Summary Statistics via Kernel Embeddings
By Mijung Park, Wittawat Jitkrittum, Dino Sejdinovic. 2015
10 citations recorded by the source corpus.
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 (partial) 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) as a dissimilarity measure between the distributions over observed and simulated data. MMD is easily estimated as the squared difference between their empirical kernel embeddings. Experiments on a simulated scenario and a real-world biological problem illustrate the effectiveness of the proposed algorithm.
Subfields: Artificial Intelligence, Statistics and Probability, Probabilistic & Bayesian Methods, Statistical Learning Theory
How researchers see this paper
The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.
In Artificial Intelligence
- Bharath K. Sriperumbudur
- Krikamol Muandet
- Kenji Fukumizu
- Bernhard Schölkopf
- Arthur Gretton
- David Lopez-Paz
- Dino Sejdinovic
- Jan Peters
In Statistics and Probability
- Krikamol Muandet
- Kenji Fukumizu
- Bharath K. Sriperumbudur
- Bernhard Schölkopf
- Arthur Gretton
- Dino Sejdinovic
- Le Song
- Jan Peters
In Probabilistic & Bayesian Methods
- Krikamol Muandet
- Bharath K. Sriperumbudur
- Kenji Fukumizu
- Bernhard Schölkopf
- Arthur Gretton
- Dino Sejdinovic
- Yu Nishiyama
- Le Song
In Statistical Learning Theory
- Bharath K. Sriperumbudur
- Kenji Fukumizu
- Bernhard Schölkopf
- Krikamol Muandet
- Arthur Gretton
- Dino Sejdinovic
- Le Song
- David Lopez-Paz
Citations in the corpus
- Kernel Mean Embedding of Distributions: A Review and Beyonds (2016, background): “criticism (Lloyd and Ghahramani 2015, Kim et al. 2016), approximate Bayesian computation (Park et al. 2016), and model selection in generative models (Bounliphone et al. 2016), for example.”