Optimally-weighted Estimators of the Maximum Mean Discrepancy for Likelihood-Free Inference

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Conference article in proceedings
Date
2023-07
Major/Subject
Mcode
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Language
en
Pages
24
2289-2312
Series
Proceedings of the 40th International Conference on Machine Learning, Proceedings of Machine Learning Research, Volume 202
Abstract
Likelihood-free inference methods typically make use of a distance between simulated and real data. A common example is the maximum mean discrepancy (MMD), which has previously been used for approximate Bayesian computation, minimum distance estimation, generalised Bayesian inference, and within the nonparametric learning framework. The MMD is commonly estimated at a root-m rate, where m is the number of simulated samples. This can lead to significant computational challenges since a large m is required to obtain an accurate estimate, which is crucial for parameter estimation. In this paper, we propose a novel estimator for the MMD with significantly improved sample complexity. The estimator is particularly well suited for computationally expensive smooth simulators with low- to mid-dimensional inputs. This claim is supported through both theoretical results and an extensive simulation study on benchmark simulators.
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Citation
Bharti , A , Naslidnyk , M , Key , O , Kaski , S & Briol , F X 2023 , Optimally-weighted Estimators of the Maximum Mean Discrepancy for Likelihood-Free Inference . in A Krause , E Brunskill , K Cho , B Engelhardt , S Sabato & J Scarlett (eds) , Proceedings of the 40th International Conference on Machine Learning . Proceedings of Machine Learning Research , vol. 202 , JMLR , pp. 2289-2312 , International Conference on Machine Learning , Honolulu , Hawaii , United States , 23/07/2023 . < https://proceedings.mlr.press/v202/bharti23a.html >