报告人：何志坚（华南理工大学）

时间：2024年04月20日 16：00-

地点：数统学院LD402

摘要：Sequential neural posterior estimation (SNPE) techniques have been recently proposed for dealing with simulation-based models with intractable likelihoods. They are devoted to learning the posterior from adaptively proposed simulations using neural network-based conditional density estimators. As a SNPE technique, the automatic posterior transformation (APT) method proposed by Greenberg et al. (2019) performs notably and scales to high dimensional data. However, the APT method bears the computation of an expectation of the logarithm of an intractable normalizing constant, i.e., a nested expectation. Although atomic APT was proposed to solve this by discretizing the normalizing constant, it remains challenging to analyze the convergence of learning. In this paper, we propose a nested APT method to estimate the involved nested expectation instead. This facilitates establishing the convergence analysis. Since the nested estimators for the loss function and its gradient are biased, we make use of unbiased multi-level Monte Carlo (MLMC) estimators for debiasing. To further reduce the excessive variance of the unbiased estimators, we also develop some truncated MLMC estimators by taking account of the trade-off between the bias and the average cost. Numerical experiments for approximating complex posteriors with multimodal in moderate dimensions are provided. This is joint work with Xiliang Yang and Yifei Xiong.

简介：何志坚，华南理工大学数学学院教授、博导、副经理，国家级青年人才计划获得者，广东省计算数学学会副理事长，广东省现场统计学会理事。于2015年7月在清华大学获得理学博士学位。研究兴趣为随机计算方法与不确定性量化，特别是拟蒙特卡罗方法的理论和应用研究。目前发表SCI论文近20篇，其中10篇发表在统计学和计算科学的国际著名刊物Journal of the Royal Statistical Society: Series B，SIAM Journal on Numerical Analysis，SIAM Journal on Scientific Computing，Mathematics of Computation。博士论文获得新世界数学奖（ICCM毕业论文奖）银奖。主持两项国家自然科学基金项目以及三项省部级项目。

邀请人：张志民

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