Approximate Bayesian Computation with the Sliced-Wasserstein Distance

Approximate Bayesian Computation (ABC) is a popular method for approximate inference in generative models with intractable but easy-to-sample likelihood. It constructs an approximate posterior distribution by finding parameters for which the simulated data are close to the observations in terms of s...

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Bibliographic Details
Main Authors: Nadjahi, Kimia, Bortoli, Valentin De, Durmus, Alain, Badeau, Roland, Simsekli, Umut
Format: Conference Proceeding
Language:English
Subjects:
Approximate Bayesian Computation
Bayes methods
Conferences
Convergence
Image denoising
Likelihood-free inference
Optimal transport
Signal processing
Sliced-Wasserstein distance
Speech processing
Task analysis
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Summary:Approximate Bayesian Computation (ABC) is a popular method for approximate inference in generative models with intractable but easy-to-sample likelihood. It constructs an approximate posterior distribution by finding parameters for which the simulated data are close to the observations in terms of summary statistics. These statistics are defined beforehand and might induce a loss of information, which has been shown to deteriorate the quality of the approximation. To overcome this problem, Wasserstein-ABC has been recently proposed, and compares the datasets via the Wasserstein distance between their empirical distributions, but does not scale well to the dimension or the number of samples. We propose a new ABC technique, called Sliced-Wasserstein ABC and based on the Sliced-Wasserstein distance, which has better computational and statistical properties. We derive two theoretical results showing the asymptotical consistency of our approach, and we illustrate its advantages on synthetic data and an image denoising task.
ISSN:2379-190X
DOI:10.1109/ICASSP40776.2020.9054735