（1）主题：Structure Learning for High Dimensional Partially Varying-Coefficient Model
Partially varying coefficient models (PVCM) provide a useful class of tools for modelling complex data by incorporating a combination of constant and time-varying covariate effects. One natural question is that how to decide which covariates correspond to constant coefficients and which correspond to time-dependent coefficient functions. The structure selection problem is fundamentally important, since tackling this problem enhances model interpretation and avoids over fitting, as well as keeps the model flexibility. To address this issue, this paper proposes a new approach to estimation and structure selection for PVCM. Within a high-dimensional framework, we derive convergence rates for the prediction risk of the proposed method when each unknown time-dependent coefficient lies in a reproducing kernel Hilbert space. Our upper bounds in $\|\cdot\|_2$ and $\|\cdot\|_n$ norms are established under two different kinds of settings, and are shown to be the optimality of our method under their individual settings. Under certain regularity conditions, we also show that the proposed estimator is able to identify the underlying structure correctly with high probability.
吕绍高副教授，2011年毕业于中国科大-香港城大联合培养博士项目，获得理学博士。现为西南财大统计学院副教授，博士生导师。主要研究兴趣：统计机器学习与数据挖掘，高维统计与网络模型的推断。在《journal of machine learning research》《neural computation》《Annals of institution of Statistical mathematics》等计算机或统计类国际杂志发表论文10余篇。
（1）主题：Learning Dynamical Systems
In this presentation, I will report our recent work on some learning problems in the dynamical system context. We consider a family of measure-preserving and ergodic dynamical systems. Several typical examples of the measure-preserving and ergodic dynamical systems include Gauss map, Logistic map, and beta map. Here, we are interested in estimating the chaotic maps in dynamical systems. This is done by applying the classic kernel smoothing technique from nonparametric statistics. On the other hand, by assuming that the considered dynamical system admits a unique underlying invariant density function, we are also concerned with the estimation problem of this density. The purpose is achieved by adopting the Parzen-Rosenblatt estimator. Our main results are the consistency and convergence rates of the considered estimators which are derived by employing capacity-dependent arguments and concentration inequalities developed recently in the literature.
Yunlong Feng received his Ph.D. degree in mathematics from the University of Science and Technology of China and a joint Ph.D. degree from the City University of Hong Kong in 2012. Currently, he is a postdoc researcher in the Department of Electrical Engineering, KU Leuven. His research interests include theory and methodologies in machine learning, with the current emphasis on robust learning and nonparametric learning in dynamical systems.
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