第二届丝绸之路青年学者研讨会(西安交通大学，2016)

数学与统计学院系列学术讲座

时间：2016年12月22日下午2:30-5:00

地点：中心一楼2124会议室

1.赵悦博士后研究员讲座

题目：Estimation of Elliptical Copula Correlation Matrix

摘要：This talk addresses aspects of the non-asymptotic statistical inference problem for the semiparametric elliptical copula model.  The semiparametric elliptical copula model is the family of distributions whose dependence structures are specified by parametric elliptical copulas but whose marginal distributions are left unspecified.  An elliptical copula is uniquely characterized by a characteristic generator and a copula correlation matrix Sigma.  In this talk, we will consider the estimation of Sigma by the natural plug-in estimator Sigmahat formed thorugh rank-based Kendall's tau statistic.  I will exhibit (reasonably) sharp bounds on the operator norm of Sigmahat - Sigma via either matrix concentration inequalities or Gaussian concentration inequalities.  If time permits I will also present applications of these bounds.

讲座人简介：

赵悦，比利时（荷语）鲁汶大学博士后本科毕业于斯坦福大学；博士先后毕业于普林斯顿大学物理学专业和康奈尔大学统计学专业。博士毕业后曾在麦吉尔大学担任加拿大统计科学研究所的博士后。现主要从事数理统计方面的研究，具体研究方向为多元变量统计的关联结构，高维统计，经验过程等。曾在超导转变边缘传感器以及椭圆分布关联结构的关联矩阵的估算等方向发表多篇论文。

2.张一乐博士后研究员讲座

题目：Machine Learning Algorithms for Mode-of-action Classification in Toxicity Assessment

摘要：We present machine learning approaches for MOA assessment. Computational tools based on artificial neural network (ANN) and support vector machine (SVM) are developed to analyze the time-concentration response curves (TCRCs) of human cell lines responding to tested chemicals. The techniques are capable of learning data from given TCRCs with known MOA information and then making MOA classification for the unknown toxicity. A novel data processing step based on wavelet transform is introduced to extract important features from the original TCRC data. From the dose response curves, time interval leading to higher classification success rate can be selected as input to enhance the performance of the machine learning algorithm. This is particularly helpful when handling cases with limited and imbalanced data. The validation of the proposed method is demonstrated by the supervised learning algorithm applied to the exposure data of HepG2 cell line to 63 chemicals with 11 concentrations in each test case. Classification success rate in the range of 85 to 95 % are obtained using SVM for MOA classification with two clusters to cases up to four clusters.

讲座人简介：

张一乐，加拿大阿尔伯塔大学博士后。本科和硕士毕业于东北大学；博士毕业于加拿大阿尔伯塔大学应用数学专业。博士及博后期间共发表学术论文七篇，承担了两项加拿大自然科学基金研究课题，四次获得院校奖学金。同时参与了多个横向课题，承担了与Alberta Health在内的四家加拿大企业的科研项目，并有一项专利在申请中。目前的研究课题包括数值计算，数据挖掘，生物信息学等。

3.马舒洁助理教授讲座

题目：Estimating Subgroup-specific Treatment Effects via Concave Fusion

摘要：Understanding treatment heterogeneity is essential to the development of precision medicine, which seeks to tailor medical treatments to subgroups of patients with similar characteristics. One of the challenges to achieve this goal is that we usually do not have a priori knowledge of the grouping information of patients with respect to treatment. To address this problem, we consider a heterogeneous regression model by assuming that the coefficients for treatment variables are subject-dependent and belong to different subgroups with unknown grouping information. We develop a concave fusion penalized method and derive an alternating direction method of multipliers algorithm for its implementation. The method is able to automatically estimate the grouping structure and the subgroup-specific treatment effects. We show that under suitable conditions the oracle least squares estimator with a priori knowledge of the true grouping information is a local minimizer of the objective function with high probability. This provides a theoretical justification for the statistical inference about the subgroup structure and treatment effects. We evaluate the performance of the proposed method by simulation studies and illustrate its application by analyzing the data from the AIDS Clinical Trials Group Study.

讲座人简介：

马舒洁，University of California, Riverside，Assistant Professor, Department of Statistics。本科毕业于西安交通大学；硕士毕业于Michigan State大学；博士毕业于美国Michigan State大学统计学专业。主要研究方向：Precision (personalized) medicine, factor models, large-scale data analysis；Inference of high-dimensional data, functional data and nonlinear time series data；Asymptotic theory, stochastic processes, extreme value theory; Applications to gene-environment interaction, environmental risk assessment, medicine and financial dat；已经发表22篇文章，其中包括7篇顶级文章。研究得到NSF和NIH的资助。曾获得过Hellman Fellowship和国家优秀自费留学生的奖励。

4.田源副教授讲座

题目：害虫治理与半连续动力系统理论

摘要：农业害虫治理问题一直以来备受人们的关注，对害虫所采取的控制手段也随之成为学者们的一个研究热点。喷洒杀虫剂是传统而有效的治理手段，但广泛使用杀虫剂不仅会给人类和环境带来一定的风险，还会大量毁灭可提供生物防治服务的天敌物种。害虫综合治理以最小的使用有害农药和其他不受欢迎的措施可有效地实现对害虫的治理效果。本报告主要结合基于状态反馈的害虫综合治理手段，介绍几类基于状态反馈控制的害虫综合治理模型，同时借助于半连续动力系统理论对模型进行动力学性态分析，以期为实际害虫综合治理过程提供理论参考和依据。

讲座人简介：

田源，大连大学副教授。本科毕业于辽宁师范大学；硕士毕业于北京师范大学；博士毕业于中国大连理工大学应用数学专业。目前主要从事生物数学方向半连续动力系统及其应用方面的研究，已发表论文30余篇，其中SCI检索近20篇，主持国家自然科学基金青年基金一项。

5.薄立军教授讲座

题目：Risk Sensitive Control and Cascading Defaults

摘要：We consider an optimal risk-sensitive portfolio allocation problem accounting for the possibility of cascading defaults. Default events have an impact on the distress state of the surviving stocks in the portfolio. We study the recursive system of non-Lipschitz quasi-linear parabolic HJB-PDEs associated with the value function of the control problem in the different default states of the economy. We show the existence of a classical solution to this system via super-sub solution techniques and give an explicit characterization of the optimal feedback strategy in terms of the value function. We prove a verification theorem establishing the uniqueness of the solution. A numerical analysis indicates that the investor accounts for contagion effects when making investment decisions, reduces his risk exposure as he becomes more sensitive to risk, and that his strategy depends non-monotonically on the aggregate risk level. This is a joint work with J. Birge (Chicago) and A. Capponi (Columbia).

讲座人简介：

薄立军，中国科学技术大学数学科学学院教授。本科毕业于西安电子科技大学硕士；毕业于南开大学；博士毕业于南开大学概率论与数理统计专业。2012年入选教育部新世纪优秀人才支持计划, 美国数学会《Mathematical Reviews》特邀评论员, 国家自然科学基金通讯评审专家, 中国工程概率统计学会常务理事。目前主要从事随机(偏)微分方程、随机分析和数理金融的研究, 具体工作包括物理化学中随机偏微分方程解的刻画、受控信用市场的建模与定价以及金融随机网络的稳定性与随机控制。主要研究成果已发表在Adv. Appl. Probab., J. Theor. Probab., Electron. J. Probab., J. Diff. Eqn., Appl. Math. Optim., Queueing Syst.等概率论、金融数学和管理运筹领域国际权威学术期刊上。

6.冼军教授讲座

题目: Random sampling and reconstruction algorithm

摘要: We consider random sampling in finitely generated shift-invariant spaces $V(\Phi) \subset {\rm L}^2(\mathbb{R}^n)$ generated by a vector $\Phi (\varphi_1,\ldots,\varphi_r) \in {\rm L}^2(\mathbb{R}^n)^r$. Following the approach introduced by Bass and Gr\"ochenig, we consider certain relatively compact subsets $V_{R,\delta}(\Phi)$ of such a space, defined in terms of a concentration inequality with respect to a cube with side lengths $R$. Under very mild assumptions on the generators, we show that for $R$ sufficiently large, taking $O(R^n log(R^{n^2/\alpha'}))$ many random samples (taken independently uniformly distributed within $C_R$) yields a sampling set for $V_{R,\delta}(\Phi)$ with high probability. Here $\alpha' \le n$ is a suitable constant. We give explicit estimates of all involved constants in terms of the generators $\varphi_1, \ldots, \varphi_r$.

讲座人简介：

冼军，中山大学教授。本科毕业于湖北师范大学；硕士毕业于湖北大学；博士毕业于中山大学基础数学专业。国家自然科学基金优秀青年基金获得者，国家自然科学基金重点项目主要参加者。主要研究领域分别涉及采样理论、小波分析理论与应用等方面，并且在这些领域当中近五年已完成十余篇学术论文。函数的采样与重构是信号处理里两个重要的研究方向，研究成果是小波分析理论、采样理论以及函数逼近论的实质性扩充，而且在信号处理及电子信息工程等领域中均有重要的应用。

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