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Title: Discrepancy-based inference for intractable generative models using quasi-Monte Carlo Authors:  Ziang Niu - Renmin University of China (China)
Johanna Meier - Leibniz University Hannover (Germany) [presenting]
Francois-Xavier Briol - University College London (United Kingdom)
Abstract: Intractable generative models are models for which the likelihood is unavailable but sampling is possible. Most approaches to parameter inference in this setting require the computation of some discrepancy between the data and the generative model. This is, for example, the case for minimum distance estimation and approximate Bayesian computation. These approaches require sampling a high number of realisations from the model for different parameter values, which can be a significant challenge when simulating is an expensive operation. We propose to enhance this approach by enforcing ``sample diversity'' in simulations of our models. This will be implemented through the use of quasi-Monte Carlo (QMC) point sets. The key results are sample complexity bounds which demonstrate that, under smoothness conditions on the generator, QMC can significantly reduce the number of samples required to obtain a given level of accuracy when using three of the most common discrepancies: the maximum mean discrepancy, the Wasserstein distance, and the Sinkhorn divergence. This is complemented by a simulation study which highlights that improved accuracy is sometimes also possible in some settings which are not covered by the theory.