Niu, Ziang;
Meier, Johanna;
Briol, François-Xavier;
(2021)
Discrepancy-based Inference for Intractable Generative Models using
Quasi-Monte Carlo.
arXiv: Ithaca, NY, USA.
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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. 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.
Type: | Working / discussion paper |
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Title: | Discrepancy-based Inference for Intractable Generative Models using Quasi-Monte Carlo |
Open access status: | An open access version is available from UCL Discovery |
Publisher version: | https://doi.org/10.48550/arXiv.2106.11561 |
Language: | English |
Additional information: | This version is the version of record. For information on re-use, please refer to the publisher’s terms and conditions. |
UCL classification: | UCL > Provost and Vice Provost Offices > UCL BEAMS > Faculty of Maths and Physical Sciences UCL > Provost and Vice Provost Offices > UCL BEAMS > Faculty of Maths and Physical Sciences > Dept of Statistical Science UCL > Provost and Vice Provost Offices > UCL BEAMS UCL |
URI: | https://discovery.ucl.ac.uk/id/eprint/10158245 |
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