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Event(s) on June 2016
- Thursday, 2nd June, 2016
Title: Adjoint Methods and Symplectic Adjoint Methods - A Simple Way to Construct High-order Runge-Kutta Methods Speaker: Prof. SUN Geng, Institute of Mathematics, Chinese Academy of Sciences, China Time/Place: 15:00 - 16:00
FSC1217, Fong Shu Chuen Library, HSH Campus, Hong Kong Baptist UniversityAbstract: This talk deals with studying properties of Runge-Kutta (RK) methods. First, some properties of adjoint RK methods are obtained. By the properties, construction of certain RK methods becomes easier. Second, definition of symplectic adjoint methods is introduced and properties of symplectic adjoint methods are discussed. By the aforementioned properties, a novel and simple way to construct high-order RK methods will be provided. - Friday, 3rd June, 2016
Title: Pairwise Learning Algorithms in Machine Learning Speaker: Dr. YING Yiming , Department of Mathematics and Statistics, State University of New York at Albany, USA Time/Place: 10:30 - 11:30
FSC1217, Fong Shu Chuen Library, HSH Campus, Hong Kong Baptist UniversityAbstract: Recently, a new paradigm of learning from data called pairwise learning has attracted much attention in machine learning, among which the most notable ones are bipartite ranking, metric learning and AUC maximization. In contrast to the standard classification problem, the objective function in pairwise learning involves statistically dependent pairs of instances, which are usually quadratic in the number of training examples. This learning setting poses new challenges and opportunities for designing efficient optimization algorithms. In this talk, I will present some of our contributions to this research direction. In the first part of the talk, I will present a novel online AUC maximization algorithm for large-scale streaming data, which only needs space and time complexity of one datum at each iteration. A key idea is to formulate AUC maximization as a stochastic saddle point problem. In the second part, I will introduce a novel metric learning approach (DML-eig) which is shown to be equivalent to a well- known eigenvalue optimization problem. This new formulation facilitates the development of efficient metric learning algorithms for high-dimensional data. The main theme behind these studies is the active interplay between machine learning and optimization. - Tuesday, 7th June, 2016
Title: Review of XVA Calculation Framework Speaker: Dr. YANG Chao, TD Securities, Canada Time/Place: 15:00 - 16:00
FSC1217, Fong Shu Chuen Library, HSH Campus, Hong Kong Baptist UniversityAbstract: In this talk, we will introduce one of the hot topics in the current financial industry: XVA calculation. We introduce the commonly used collateralized multiple curves model. We will discuss the possible schemes for the future exposure calculation. Further, we show the scheme for margin period of risk, wrong way risk and collateral process simulation. Afterwards, we give the formula for CVA, FVA and CollVA calculations and present how the banks manage the trade from XVA perspective. Finally, we will propose some interesting mathematical problems in this area for future research. - Wednesday, 8th June, 2016
Title: Laguerre calculus on nilpotent Lie groups of step 2 and its applications Speaker: Prof. CHANG Der-Chen , Department of Mathematics and Statistics, Georgetown University, USA Time/Place: 15:00 - 16:00
FSC1217, Fong Shu Chuen Library, HSH Campus, Hong Kong Baptist UniversityAbstract: Let $G$ be a nilpotent Lie groups of step 2. In this talk, we first discuss a Laguerre calculus on $G$. An excellent example of this research direction is the result that was obtained by Professor Peter Greiner. The second part of the talk will use this calculus to construct heat kernel and fundamental solution for sub-Laplacian on the group. - Wednesday, 8th June, 2016
Title: Operators on Manifolds with Higher Singularities Speaker: Prof. Bert-Wolfgang Schulze, Institut für Mathematik, Universität Potsdam, Germany Time/Place: 16:00 - 17:00
FSC1217, Fong Shu Chuen Library, HSH Campus, Hong Kong Baptist UniversityAbstract: The talk is devoted to a new approach to algebras of pseudo-differential operators on manifolds with higher singularities. The results are obtained in joint work with Der-Chen Chang. We first outline aspects on a category $mathfrak{M}_k$ of topological spaces $M$ with singularities of order $kin N,$ where $k=0$ indicates smoothness, $k=1$ conical or edge singularities. Smooth manifolds with boundary are included in the case $k=1,$ where the boundary is the edge and the model cone $overline{mathbb{R}}_+,$ the inner normal to the boundary. Elliptic operators $A$ on $M$ in the latter situation are only Fredholm when we impose elliptic boundary conditions; those may be of trace and potential type, and they are involved in Boutet de Monvel's pseudo-differential algebra as boundary symbols and connected with a corresponding symbolic contribution of the operator $A,$ namely, its boundary symbol. More generally, operators $A$ on $mathfrak{M}_k$ for arbitrary $k$ form an operator algebra and generate a hierarchy of symbols with $k+1$ components, operating on $k$ infinite - in general - singular model cones rather than $overline{mathbb{R}}_+$. We illustrate the role of these higher singular operator algebras and show the existence of parametrices of elliptic elements within the structure. In addition we give some typical examples. - Friday, 24th June, 2016
Title: Adaptive Estimation of a Planar Convex Set Speaker: Prof. Tony CAI, Department of Statistics, The Wharton School, University of Pennsylvania, USA Time/Place: 15:00 - 16:00
FSC1217, Fong Shu Chuen Library, HSH Campus, Hong Kong Baptist UniversityAbstract: In this talk, I will present some recent work on adaptive estimation of an unknown planar compact, convex set from noisy measurements of its support function. Both the problem of estimating the support function at a point and that of estimating the whole convex set are considered. For pointwise estimation, we study the problem in a general non-asymptotic framework, which evaluates the performance of a procedure at each individual set, instead of the worst case performance over a large parameter space as in the conventional minimax theory. A data-driven adaptive estimator is proposed and is shown to be optimally adaptive to every compact, convex set. For estimating the whole convex set, we propose estimators that are shown to adaptively achieve the optimal rate of convergence. - Saturday, 25th June, 2016
Title: The Latent Low Rank Model to Colocalize Genetic Risk Variants in Multiple GWAS Speaker: Dr. LIU Jin, Centre for Quantitative Medicine, Duke-NUS Medical Schoo, Singapore Time/Place: 11:00 - 12:00
FSC1217, Fong Shu Chuen Library, HSH Campus, Hong Kong Baptist UniversityAbstract: Scientists in the life science field have long been seeking genetic variants associated with complex diseases (or traits) to advance our understanding of complex genetic disorders and to provide effective disease treatment. However, many complex diseases are driven by the combined effect of many genetic variants, each of which may have only a small effect. To identify these genetic variants, large sample sizes are required but meeting such a requirement is usually beyond the capacity of a single GWAS. Exploring the pleiotropy across multiple related diseases is a promising strategy for identifying genetic variants with small effects, thereby uncovering the mystery of biological mechanisms in complex diseases. In this work we introduce a new approach, latent low rank model (LLR), to leverage pleiotropy across multiple traits to increase power for fine-mapping. LLR uses a latent variable Z to indicate the null and non-null states of loci for each trait. Meanwhile, the prior probability of the latent variable Z is modulated by a low-rank matrix X which is constrained by the nuclear norm. To estimate parameters in LLR, we first propose a standard regularized EM algorithm. To make computing sustainable in the era of big data, we further describe an EM boosting algorithm with not only high efficiency but also the same virtue of convergence. We demonstrate in extensive simulations that LLR greatly improves fine-mapping accuracy compared to existing methods. We analyze summary data from 19 traits and identify many pleiotropic risk loci. We believe that LLR can serve as a computationally and statistically useful tool for integrative data analysis. - Tuesday, 28th June, 2016
Title: Set-valued portfolios and set-valued risks Speaker: Prof. Ilya Molchanov, Institute of Mathematical Statistics and Actuarial Science, University of Bern, Switzerland Time/Place: 14:30 - 15:30
FSC1217, Fong Shu Chuen Library, HSH Campus, Hong Kong Baptist UniversityAbstract: Using the concept of set-valued portfolios, it is possible to incorporate dependencies between the distribution of the multivariate gain and the exchange rules. The set-valued portfolio is considered acceptable if it possesses a selection (i.e. a random vector which almost surely belongs to it) with all individually acceptable components. The corresponding set-valued risk measure is said to be the selection risk measure. The talk surveys its main properties, discusses the primal and dual representations, gives examples, and shows how to approximate its values from below and from above using rather elementary arguments. Applications of selection risk measures to the practical risk assessment are also presented. A special attention is paid to applications of selection risk measures to risk assessment of financial groups - Wednesday, 29th June, 2016
Title: Optimal Estimation for Quantile Regression with Functional Response Speaker: Dr. WANG Xiao, Department of Statistics, Purdue University, USA Time/Place: 10:00 - 11:00
FSC1217, Fong Shu Chuen Library, HSH Campus, Hong Kong Baptist UniversityAbstract: Quantile regression with functional response and scalar covariates has become an important statistical tool for many neuroimaging studies. In this paper, we study optimal estimation of varying coefficient functions in the framework of reproducing kernel Hilbert space. Minimax rates of convergence under both fixed and random designs are established. We have developed easily implementable estimators which are shown to be rate-optimal. Simulations and real data analysis are conducted to examine the finite-sample performance. This is a joint work with Zhengwu Zhang, Linglong Kong, and Hongtu Zhu. - Thursday, 30th June, 2016
Title: The Evolution of Data Science and Statistics Speaker: Prof. Michael R. KOSOROK, Department of Biostatistics, School of Public Health, University of North Carolina at Chapel Hill, USA Time/Place: 15:00 - 16:00
FSC1217, Fong Shu Chuen Library, HSH Campus, Hong Kong Baptist UniversityAbstract: The field of data science has been evolving in one way or another for over a hundred years and incorporates a number of disciplines including statistics, computer science, mathematics, library science, engineering, as well as many other domains. The current ascension of data science seems to have initiated around the beginning of the 21st century, with the term being attributed to a 2001 publication by statistician William Cleveland in the International Statistical Review. The field of statistics has been and continues to play an important role in this domain because of the inferential perspective it provides and the necessity of this perspective—in both designing studies which generate data and in drawing conclusions about data through analytics—to ensure suitable reproducibility and generalizability of results. Many other disciplines also bring tremendous value to the data science endeavor. For all of the disciplines involved, significant changes at the core of our various perspectives are happening. Moreover, data science is becoming a new, convergent discipline which is greater than the sum of its parts. These dramatic changes are both challenges and opportunities. As statisticians, computer scientists, mathematicians, and other contributing researchers, we will need to learn to better communicate with, learn about, work with, and respect one another. We will all need to think much more broadly and creatively than ever before. In this presentation, I will discuss several specific relevant research and educational endeavors currently underway, some potential future opportunities, and several perspectives about the path forward.