Details
| Original language | English |
|---|---|
| Pages (from-to) | 1411-1456 |
| Number of pages | 46 |
| Journal | Electronic journal of statistics |
| Volume | 17 |
| Issue number | 1 |
| Publication status | Published - 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.
Keywords
- approximate Bayesian computation, discrepancy, generative models, intractable models infer-ence, minimum distance estimation, Quasi-Monte Carlo, sample complexity
ASJC Scopus subject areas
- Mathematics(all)
- Statistics and Probability
- Decision Sciences(all)
- Statistics, Probability and Uncertainty
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In: Electronic journal of statistics, Vol. 17, No. 1, 2023, p. 1411-1456.
Research output: Contribution to journal › Article › Research › peer review
}
TY - JOUR
T1 - Discrepancy-based inference for intractable generative models using Quasi-Monte Carlo
AU - Niu, Ziang
AU - Meier, Johanna
AU - Briol, François Xavier
N1 - Funding Information: arXiv: 2106.11561 ∗FXB was supported by the Lloyd’s Register Foundation programme on data-centric engineering at The Alan Turing Institute under the EPSRC grant [EP/N510129/1]. †Contributed equally. ‡Corresponding author.
PY - 2023
Y1 - 2023
N2 - 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.
AB - 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.
KW - approximate Bayesian computation
KW - discrepancy
KW - generative models
KW - intractable models infer-ence
KW - minimum distance estimation
KW - Quasi-Monte Carlo
KW - sample complexity
UR - http://www.scopus.com/inward/record.url?scp=85160224507&partnerID=8YFLogxK
U2 - 10.1214/23-EJS2131
DO - 10.1214/23-EJS2131
M3 - Article
AN - SCOPUS:85160224507
VL - 17
SP - 1411
EP - 1456
JO - Electronic journal of statistics
JF - Electronic journal of statistics
SN - 1935-7524
IS - 1
ER -