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.
翻译:可吸引的基因变现模型是不可能找到的模型,但抽样是可能的。在这个设置中,参数推断的多数方法要求计算数据和基因变现模型之间的某些差异。例如,最低距离估计和近似巴伊西亚计算的情况就是如此。这些方法要求从不同参数值模型中抽样大量实现,如果模拟操作费用昂贵,这可能是一个重大挑战。在本文中,我们提议通过在模拟模型时执行“抽样多样性”来加强这一方法。这将通过使用准蒙特卡洛(QMC)点数据集来实施。我们的关键结果为样本复杂性界限,表明在生成器的平稳条件下,QMC可以大量减少在使用三种最常见的差异时获得一定准确度所需的样品数量:最大平均差异、瓦塞斯坦距离和辛克霍恩差异。这得到模拟研究的补充,该研究强调,在某些理论没有覆盖的环境中,有时还可以提高准确度。