会场介绍 | 第15届中国 R 会（北京）——机器学习专场

西安交通大学管理学院，教授、博士生导师。研究方向为函数逼近论、分布式学习理论、深度学习理论及强化学习理论。在应用数学顶级期刊ACHA、SINUM、CA及机器学习顶级期刊JMLR，TPAMI，TIT等发表论文70余篇。主持或以核心骨干参与国家级课题11项。 

深度学习在诸如图像处理、自然语言处理、运筹、博弈等领域取得了巨大的成功。但其成功的原因依然缺乏严格的理论解释与验证。在这种未知性下，学术界与业界掀起了深度学习浪潮， 试图用深度神经网络去处理所有学习问题。很显然，在某些应用上，效果不如预期。该报告将从数学上（统计学习的角度）揭露深度神经网络的学习能力并在一定程度阐明深度学习的适用范围。特别地，该报告聚焦如下四个基本问题：

1.深度网是否一定比单层网好?

2.在什么情况下用深度学习会更有效？

3.为什么深度网在大数据时代取得这么大成功？

4.过参数化深度神经网络为何可规避过拟合现象?

杨文昊，北京大学前沿交叉学科研究院数据科学（统计学）专业的博士研究生。其于2018年获得北京大学统计学学士学位。主要的研究兴趣包括统计学习和机器学习理论，目前集中在强化学习的理论研究上。其研究成果发表在NeurIPS, ICLR, AISTATS等国际会议和Annals of Statistics国际杂志上。

Robust MDPs are proposed to handle the sensitive estimation errors in value estimation of MDPs, where the transition probability is allowed to take values in an uncertainty set. In recent years, many works have proposed computationally efficient learning algorithms to solve robust MDPs and obtained the near-optimal robust policy and value function. However, the statistical performances of the optimal robust policy and value function are less studied. In this talk, we will introduce the basic theories and algorithms of robust MDPs and figure out two questions: (a) How many samples are sufficient to guarantee the accuracy of the robust estimators; (b) whether it is possible to make statistical inferences from the robust estimators. We will answer these questions from both non-asymptotic and asymptotic viewpoints.

李赛，中国人民大学统计与大数据研究院准聘副教授，博士生导师。2018年毕业于罗格斯新泽西州立大学，获得统计博士学位，后于宾夕法尼亚大学生物统计系和统计系进行博士后研究，目前的研究方向包括高维数据分析、迁移学习、因果推断的统计方法及理论和在遗传学、流行病学和机器学习中的应用。

We consider Q-learning with knowledge transfer, using samples from a target reinforcement learning (RL) task as well as source samples from different but related RL tasks. We propose transfer learning algorithms for both batch and online Q-learning with offline source studies. The proposed transferred Q-learning algorithm contains a novel re-targeting step that enables vertical information-cascading along multiple steps in an RL task, besides the usual horizontal information-gathering as transfer learning (TL) for supervised learning. We establish the first theoretical justifications of TL in RL tasks by showing a faster rate of convergence of the Q-function estimation in the offline RL transfer, and a lower regret bound in the offline-to-online RL transfer under certain similarity assumptions. Empirical evidences from both synthetic and real datasets are presented to back up the proposed algorithm and our theoretical results.

赵俊龙，北京师范大学统计学院教授。主要从事统计学和机器学习相关研究，包括：高维数据分析、统计机器学习、稳健统计等。在统计学各类期刊发表SCI论文四十余篇，部分结果发表在统计学国际顶级期刊JRSSB，AOS、JASA，Biometrika等。主持多项国家自然科学基金项目，参与国家自然科学基金重点项目。任中国现场统计学会高维数据分会理事，北京应用统计学会理事、北京大数据学会常务理事等。

A problem of major interest in network data analysis is to explain the strength of connections using context information. To achieve this, we introduce a novel approach, called network supervised dimension reduction, in which covariates are projected onto low-dimensional spaces to reveal the linkage pattern without assuming a model. We propose a new loss function for estimating the parameters in the resulting linear projection, based on the notion that closer proximity in the low-dimension projection corresponds to stronger connections. Interestingly, the convergence rate of our estimator is found to depend on a network effect factor, which is the smallest number that can partition a graph in a manner similar to the graph colouring problem. Our method has interesting connections to principal component analysis and linear discriminant analysis, which we exploit for clustering and community detection. The proposed approach is further illustrated by numerical experiments and analysis of a pulsar candidates dataset from astronomy.