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Discrepancy-based inference for intractable generative models using Quasi-Monte Carlo

Publikation: Beitrag in FachzeitschriftArtikelForschungPeer-Review

Autoren

  • Ziang Niu
  • Johanna Meier
  • François Xavier Briol

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Externe Organisationen

  • University of Pennsylvania
  • University College London (UCL)
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OriginalspracheEnglisch
Seiten (von - bis)1411-1456
Seitenumfang46
FachzeitschriftElectronic journal of statistics
Jahrgang17
Ausgabenummer1
PublikationsstatusVeröffentlicht - 2023

Abstract

Intractable generative models, or simulators, 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 simulating a high number of realisations from the model for different parameter values, which can be a significant challenge when simulating is an expensive operation. In this paper, 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. Our 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 an improved accuracy is sometimes also possible in some settings which are not covered by the theory.

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Discrepancy-based inference for intractable generative models using Quasi-Monte Carlo. / Niu, Ziang; Meier, Johanna; Briol, François Xavier.
in: Electronic journal of statistics, Jahrgang 17, Nr. 1, 2023, S. 1411-1456.

Publikation: Beitrag in FachzeitschriftArtikelForschungPeer-Review

Niu, Ziang ; Meier, Johanna ; Briol, François Xavier. / Discrepancy-based inference for intractable generative models using Quasi-Monte Carlo. in: Electronic journal of statistics. 2023 ; Jahrgang 17, Nr. 1. S. 1411-1456.
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