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Optimally-weighted Estimators of the Maximum Mean Discrepancy for Likelihood-Free Inference
Ayush Bharti · Masha Naslidnyk · Oscar Key · Samuel Kaski · Francois-Xavier Briol

Thu Jul 27 01:30 PM -- 03:00 PM (PDT) @ Exhibit Hall 1 #726
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.

Author Information

Ayush Bharti (Aalto University)
Masha Naslidnyk (University College London, University of London)
Oscar Key (UCL)
Samuel Kaski (Aalto University and University of Manchester)
Francois-Xavier Briol (University of Cambridge)

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