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Short Course

TIME:July 8 - July 10, 2023

PLACE:Science Building, Room No.207, Peking University



Jiming Jiang


University of California, Davis, USA




An Introduction to Martingale Limit Theory and Its Application in Asymptotic Analysis of Linear Mixed Models


This short course offers an introduction to martingale limit theory and selected topics of its applications. We begin with an overview of the classical limit theorems for sum of independent random variables. We then introduce the basic concepts of martingales, and the fundamental theorem on martingale convergence. For the martingale limit theory, we shall focus on the martingale strong law of large numbers (SLNN) and a martingale central limit theory (CLT). There are many applications of the martingale limit theory but here we shall focus on its application in the analysis of linear mixed models, where the restricted maximum likelihood (REML) method is widely used. This is a 200-minute lecture divided in four parts. The specific topics are listed below:

Part I: A review of classical limit theorems for sum of independent random variables

Part II: An introduction to martingales (examples and the martingale convergence theorem)

Part III: Some martingale limit theorems (SLLN and CLT)

Part IV: Application to asymptotic analysis of linear mixed models

Main Reference:

Jiang, J. (2022), Large Sample Techniques for Statistics, 2nd ed., Springer, New York (chapters 6 and 8).



Jiashun Jin


Carnegie Mellon University




Analysis of social networks


This short course is for those who are new to social network analysis and are interested in this area. It will cover topics such as data resources, network modeling, recent approaches in network community detection, nonnegative matrix factorization, degree matching techniques and finally recent approaches in network testing. The course will cover a variety of methods and theory (eg., SCORE, Mixed-SCORE, a self normalizing cycle count statistics) and especially with applications to the MADStat dataset on the publications of statisticians.



Tracy Ke

Associate professor

Harvard University




An introduction to statistical methods for text analysis


This short course aims to introduce some recent developments of statistical methods for text analysis. After an overview of the history, mainstream methods, and available data sets, I will delve into the problem of Topic Modeling. This part covers the Hoffman’s topic model, the anchor word assumption, a fast spectral method, and the minimax results for topic modeling. Next, I will discuss some inference problems related to text analysis, including but not limited global detection of topics, authorship attribution, and detection of variability of online text reviews. This part focuses on a self-normalizing statistical, called DELVE, as well as how it yields optimal inference in the aforementioned problems. The last part of this course will cover applications of these methods on the MADStat data sets (text abstracts of 83K statistical papers) and Dow Jones Newswire (2.5M financial news articles).


1. Overview of text analysis (0.5 hour): History, mainstream methods, and available data sets

2. Topic modeling (1.5 hour): 2.1 A spectral method Topic-SCORE, 2.2 Analysis of error rates, 2.3 The random matrix theory basics, 2.4 Estimation of the weight vectors, 2.5 Other methods including LDA, EM, and NMF algorithms

3. Application in MADStat (0.5 hour): 3.1 Major topics in the statistical literature, 3.2 Topic interests of journals and authors, 3.2 Ranking of the citation impacts of topics

4. Detection of within-group variability in text (1 hour): 3.1 A testing framework, 3.2 Application to global detection of topic modeling, 3.3 Application to authorship attribution



Linglong Kong


University of Alberta, Canada




Distributional Reinforcement Learning


The distributional reinforcement learning models the full distribution of discounted long term reward instead of the expected value. Its analysis has recently emerged as part of rapidly evolving field of machine learning. Many classic methods from traditional reinforcement learning can be inherited with some adaption but the complexity of tracing to full distribution also poses new challenges. In this course, we will first give an overview of the reinforcement learning, deep reinforcement learning, and distributional reinforcement learning. We discuss some prominent examples like the representation of reward distribution, the optimal algorithm of action selection and finding theoretical guarantees. By the end, we will point out some statistical directions on using alternative expectiles, exploration and theoretical developments.



Annie Qu


University of California, Irvine




Deep Learning from Statistics Perspective


This short course is for those who are new to machine learning and interested in understanding deep learning models. It is for those who want to become familiar with the core concepts behind these learning algorithms and their successful applications. It is for those who want to start thinking about how machine learning and deep learning might be useful in their research, business or career development. This half-day short course will provide an overview of deep learning methods. Topics include deep neural networks, computational algorithms and software of deep learning, and various applications in deep learning.


The course does not require any prior knowledge on machine learning or deep learning.

The following topics will be covered

(i) Brief Overview

 a. Machine learning and deep learning overview

 b. Supervised versus Unsupervised Learning

(ii) Supervised Learning

 a. Deep feedforward neural networks

 b. Convolutional neural networks

(iii) Unsupervised Learning

 a. Variational autoencoders

 b. Generative adversarial networks

 c. RNN and LSTM

(vi) Connections between Deep Learning Models and Statistical Models