概率统计及交叉领域学术论坛

**概率统计及交叉领域****学术论坛**

报告题目：An optimal control problem for mean-field FBSDE with partial information

报告人：王光臣 山东大学

报告时间：2017年12月9日08:40-09:20 地点：数学院144教室

摘要：This talk is concerned with an optimal control problem of mean-field FBSDE under partial information. The control problem is different from the existing literature about optimal control for mean-field stochastic systems, and has more applications in mathematical finance. Using a backward separation method with a decomposition technique, two optimality conditions and two coupled forward-backward optimal filters are derived. Several LQ optimal control problems for mean-field FBSDEs are studied. Closed-form optimal solutions are obtained in detailed situations.

报告题目：Risk-sensitive semi-Markov decision processes with multiple constraints

报告人：黄永辉 中山大学

报告时间：2017年12月9日09:20-10:00 地点：数学院144教室

摘要：In this talk, we investigate risk-sensitive semi-Markov control processes with a Borel state space, unbounded cost rates, and general utility functions. The performance criteria are several expected utilities of the total reward in a finite horizon. Unlike those in the literature, our analysis is based on a type of finite-horizon occupation measure. We have succeeded in expressing the distribution of finite-horizon reward in terms of the occupation measure for each policy, wherein the discount is needless (unlike in the previous study where the discount was indispensable). For the multiple-constraint problem, we have established the existence and computation of optimal policies. In particular, a linear program and its dual program for the constrained problem were developed, and moreover, the strong duality between the two programs was established.

报告题目：Study on brain structural and functional abnormality

based on magnetic resonance imaging

报告人：郭水霞 湖南师范大学

报告时间：2017年12月9日10:20-11:00 地点：数学院144教室

摘要：The human brain is a complex system with dynamic interactions among various brain regions that operate in a large-scale network. Magnetic resonance imaging (MRI), which has been applied widely in understanding the interworking of the brain, has provided an unprecedented opportunity to study various brain disorders, such as depression, Alzheimer’s disease, and schizophrenia, and may represent the key to the early diagnosis of such diseases. In this talk, we present some results on detecting the structural and functional abnormality of mental patients, which may be the biomarker of such diseases.

报告题目：Statistical identification of Markov chain

报告人：向绪言 湖南文理学院

报告时间：2017年12月9日11:00-11:40 地点：数学院144教室

摘要：The theoretical study of continuous time homogeneous Markov chains is usually based a natural assumption on a known transition rate matrix (TRM). However TRM of a Markov chain in realistic systems might be unknown and even need be identified by partially observable data. Thus an issue how to identify the TRM of the underlying Mrakov chain by partially observable information is derived from the great significance in applications. That is what we call the statistical identification of Markov chain. Markov chain inversion approach has been derived for most of reversible Markov chains by partial observation at few states. Such approach has obvious advantages over others in that it can identify the most of reversible Markov chain without the requirement of bivariate distributions of subsequent sojourn time and hitting time, and in that the computation is accurate based on the accurate sojourn time PDFs and the prior information about the underlying topological structure of Markov chain. Hence the work opens up the possibility of carrying out the statistical identification for all reversible Markov chains.

报告题目：Asymptotic variability analysis for queues with feedbacks based on strong approximation

报告人：郭永江 北京邮电大学

报告时间：2017年12月9日14:00-14:40 地点：数学院144教室

摘要：In this talk, we analyze the asymptotic variability for queues by the functional law of the iterated logarithm (LIL) and its corresponding LIL using an approach based on strong approximation. The functional LIL and the LIL limits quantify the magnitude of asymptotic stochastic fluctuations of stochastic processes compensated by their deterministic fluid limits in two forms: the functional and numerical, respectively. The earliest functional LIL and LIL concerned are both developed for Brownian motion by Volker Strassen and Lévy respectively. We establish the functional LILs and their corresponding LILs covering three regimes divided by the traffic intensity: the underloaded, critically loaded and overloaded, for five processes: the queue length, workload, busy, idle and departure processes. By the primitive data of the first and second moments of the interarrival and service times, all the functional LILs are expressed into some compact sets of continuous functions and all the corresponding LILs are some analytic functions. The proofs are based on the fluid approximation and the strong approximation of the queueing system, with the fluid approximation characterizing the expected values of the performance functions and the strong approximation approximating discrete performance processes with reflected Brownian motions.

报告题目：Robust optimal investment and reinsurance of an insurer under a CEV model with generalized mean-variance premium principle and default risk

报告人：周杰明 湖南师范大学

报告时间：2017年12月9日14:40-15:20 地点：数学院144教室

In this paper, we analyze a robust optimal investment and reinsurance problem in a defaultable market. The insurer can trade in a money account, a stock and a defaultable corporate. The price process of the risky asset is described by a constant elasticity of variance (CEV) model. In particular, the reinsurance premium is calculated according to the generalized mean-variance premium principle. Using the dynamic programming approach, we study the pre-default case and a post-default case respectively, and then derive the optimal strategies and the corresponding value function under the worst-case scenario. Finally, we give some numerical examples to illustrate our main results.

报告题目：Optimal dividends and reinsurance: review and some recent progress

报告人： 郭军义 南开大学

报告时间：2017年12月9日15:40-16:20 地点：数学院144教室

摘要：A brief review of optimal reinsurance and dividends problems will be given in this talk. Also, some recent progress in this field will be presented

报告题目： Equivalence relations and Borel reduction

报告人： 丁龙云 南开大学

报告时间：2017年12月9日16:20-17:00 地点：数学院144教室

摘要：In Descriptive Set Theory, Borel reduction is a useful tool to characterize the relative complexity of equivalence relations from vary branches in mathematics. In recent years, many logicians worked on this topic and many interesting results were founded. In this talk, we will give a survey on this topic, from the beginning to some brand new results.

报告题目： Time-Inconsistent Recursive Stochastic Optimal Control Problems

报告人： 于志勇 山东大学

报告时间：2017年12月9日17:00-17:40 地点：数学院144教室

摘要：In this talk, a time-inconsistent stochastic optimal control problem with a recursive cost functional is studied. Equilibrium strategy is introduced, which is time-consistent and locally approximately optimal. By means of multi-person hierarchical differential games associated with partitions of the time interval, a family of approximate equilibrium strategy is constructed and by sending the mesh size of the time interval partition to zero, an equilibrium Hamilton-Jacobi-Bellman (HJB, for short) equation is derived through which the equilibrium value function can be identified and the equilibrium strategy can be obtained. Moreover, a well-posedness result of the equilibrium HJB equation is established under certain conditions, and a verification theorem is proved. This talk is based a joint work with Dr. Qingmeng Wei and Prof. Jiongmin Yong.

报告题目：在线学习（Online learning from data）

报告人：贺文武 福建工程学院

报告时间：2017年12月9日14:00-14:40 地点：数学院143教室

摘要：在线学习即学即用，实时更新学习模型、发布学习结果，其学习效率高而存储成本低。在线学习有其自身适用的特殊场景，比如基于流式数据的学习，也是大数据问题中实现大规模学习的重要途径。大数据体系中，流式数据是一种广泛存在的重要形式，通常产生和应用于金融服务、智能交通、互联网、传感器网络和航空航天等领域，具有在线、实时和动态特性。在诸如coupon设计、投资组合和广告设置等问题中，甚至具有互动、博弈特点，经典批学习模式难以直接适用。通行做法是引入并行批处理或微批处理模式，比如Spark、Storm分布式系统，对算力普遍要求高，需要学习算法另行对接。在线学习模式，能直接从流数据中学习，算力允许条件下亦可自然地引入并行模式，而大规模批量数据学习问题亦可自然转化进而以在线学习模式施行高效学习。因此，在线学习具有深入研究与推广应用的重要价值。本报告主要就在线学习背景、适用情景、基本学习框架，时下研究热点话与大家进行交流。

报告题目：Inference using a differential private bi-degree sequence of directed graphs

报告人：晏挺 华中师范大学

报告时间：2017年12月9日14:40-15:20 地点：数学院143教室

摘要：In this talk, we release the bi-degree sequence of a directed graph using a discrete Laplace mechanism and propose an efficient algorithm for finding a maximum likelihood estimate of the bi-degree sequence, which is equivalent to projecting the noisy bi-degree sequence on the set of all graphical bi-degree sequences with the $L_1$ distance. Along the way, our algorithm also outputs a synthetic directed graph. By using the outputs, we present a differentially private estimator of the parameter in the $p_0$ model. We show that the estimator is asymptotically consistent and normally distributed, whose rate of convergence is the same as as the non private estimator. Numerical studies demonstrate our theoretical findings.

报告题目：Deep learning for chat and QA

报告人：黄浩军 微软中国

报告时间：2017年12月9日15:40-16:20 地点：数学院143教室

摘要：Chatbot/QA system is vibrant topic both in machine learning and natural language processing. Deviate from sophisticated method proposed by linguist, we are rethinking those topics with the assistant of deep learning(seq2seq) methods. And the good news is that this technique can our time from cumbersome hand-craft feature engineering.

This deck will cover following topics:

1. Sequence to Sequence model for chat

2.How to leverage context in Sequence to Sequence model

3.Knowledge Base empowered chatbot.

4.QnA in summarization.

报告题目：非线性脉冲微分系统解的变分方法应用

报告人：刘健 山东财经大学

报告时间：2017年12月9日16:20-17:00 地点：数学院143教室

摘要：针对脉冲微分系统（微分方程和哈密顿系统）建立变分结构（构造整体或分解的泛函），利用相应的临界点理论，加上精确的分析，得到古典解或弱解至少一个、两个、至少三个、无穷多个的存在性。

报告题目：A Combined Association Test for Genes Using Summary Statistics

报告人：黄健飞 扬州大学

报告时间：2017年12月9日17:00-17:40 地点：数学院143教室

摘要：We propose a combined association test (COMBAT) for genes, which incorporates strengths from existing gene-based tests and shows higher overall performance than any individual test. Our method does not require raw genotype or phenotype data, but needs only SNP-level P-values and correlations between SNPs from ancestry-matched samples. Extensive simulations showed that COMBAT has an appropriate type I error rate, maintains higher power across a wide range of genetic models, and is more robust than any individual gene-based test. We further demonstrated the superior performance of COMBAT over several other gene-based tests through reanalysis of the meta-analytic results of GWAS for bipolar disorder. Our method allows for the more powerful application of gene-based analysis to complex diseases, which will have broad use given that GWAS summary results are increasingly publicly available.