摘要：In this talk, we will survey some of our recent explorations of modern neural networks in problems spanning semiparametric statistics, causal inference, and forward & inverse problems in differential equations. We will discuss the practical performance, some limited theory, and when the theoretical results fall short of guiding practice. Time permitted, we will discuss some potential directions we are working on to narrow the theory-practice gap.

简介：刘林在上海交通大学自然科学研究院、数学科学学院、交大-耶鲁生物统计与数据科学中心任职助理教授，研究方向为非参数半参数统计理论、因果推断、机器学习、及统计学在生物医学中的应用。

摘要：Gaussian mixtures are widely used as a parametric distribution for approximating smooth density function of various, simplifying downstream inference tasks. They find extensive applications in density estimation, belief propagation, and Bayesian filtering. These applications often utilize finite Gaussian mixtures as initial approximations that are recursively updated. A challenge in these recursions is that the order of the Gaussian mixture increases exponentially, and the inference quickly becomes intractable. To overcome the difficulty, the Gaussian mixture reduction, which approximates a high order Gaussian mixture by one with a lower order, can be used. Although existing clustering-based methods are known for their satisfactory performance and computational efficiency, their convergence properties and optimal targets remain unknown. In this work, we propose a novel optimization-based Gaussian mixture reduction method based on composite transportation divergence (CTD). We develop a majorization-minimization algorithm for numerically computing the reduced Gaussian mixture and establish its theoretical convergence under general conditions. Furthermore, we demonstrate that many existing clustering-based methods are special cases of our approach, effectively bridging the gap between optimization-based and clustering-based techniques. Our unified framework empowers users to select the most appropriate cost function in CTD to achieve superior performance in their specific applications. Through extensive empirical experiments, we demonstrate the efficiency and effectiveness of our proposed method, showcasing its potential in various domains.

简介：Pengkun Yang is an assistant professor at the Center for Statistical Science at Tsinghua University. Prior to joining Tsinghua, he was a Postdoctoral Research Associate at the Department of Electrical Engineering at Princeton University. He received a Ph.D. degree (2018) and a master degree (2016) from the Department of Electrical and Computer Engineering at University of Illinois at Urbana-Champaign, and a B.E. degree (2013) from the Department of Electronic Engineering at Tsinghua University. His research interests include statistical inference, learning, optimization, and systems. He is a recipient of Thomas M. Cover Dissertation Award in 2020, and a recipient of Jack Keil Wolf ISIT Student Paper Award at the 2015 IEEE International Symposium on Information Theory (semi-plenary talk).

摘要：With the development of computer technology and the internet, increasingly large amounts of textual data are generated and collected every day. It is a significant challenge to analyze and extract meaningful and actionable information from vast amounts of unstructured textual data. Driven by applications in a wide range of fields, there is an increasing need for developing computationally efficient statistical methods for analyzing a massive amount of textual data with theoretical guarantees. In the presentation, I will discuss supervised topic modeling, which jointly considers a collection of documents and their paired side information. A bias-adjusted algorithm is developed to study the regression coefficients in the supervised topic modeling under the generalized linear model formulation. I will also introduce an approach to constructing valid confidence intervals. Applications of the proposed methods reveal meaningful latent topic structures of textual data.