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Event(s) on July 2016


  • Monday, 4th July, 2016

    Title: Testing the influence of functional variables on functional responses
    Speaker: Prof. Valentin PATILEA, Head of the CREST lab, Ecole nationale de la statistique, France
    Time/Place: 15:00  -  16:00
    FSC1217, Fong Shu Chuen Library, HSH Campus, Hong Kong Baptist University
    Abstract: The problem considered is the test of the effect of Hilbert space valued covariates on Hilbert space valued responses. This general framework includes functional regression models checks against general alternatives, as well as testing conditional independence with functional data. The significance test for functional regressors in nonparametric regression with general covariates and scalar or functional responses is another example. We propose a new test based on kernel smoothing. The test statistic is asymptotically standard normal under the null hypothesis provided the smoothing parameter tends to zero at a suitable rate. The one-sided test is consistent against any fixed alternative and detects local alternatives a la Pitman approaching the null hypothesis. In particular we show that neither the dimension of the outcome nor the dimension of the functional covariates influences the theoretical power of the test against such local alternatives. Simulation experiments and a real data application illustrate the performance of the new test with finite samples. Keywords: dimension reduction,functional data analysis,hypothesis testing,kernel methods.


  • Friday, 8th July, 2016

    Title: Algorithm Development for Bilevel Mixed Integer Convex Programs
    Speaker: Dr. ZENG Bo, Department of Industrial Engineering, University of Pittsburgh, USA
    Time/Place: 16:00  -  16:45
    FSC1217, Fong Shu Chuen Library, HSH Campus, Hong Kong Baptist University
    Abstract: Although they are widely used as decision support tools in power systems, transportation systems or security applications, bilevel mixed integer programs (BMIPs) have been known as computationally unsolved for a very long time. In this talk, we first review existing research on this topic and analyze the fundamental challenges. Then, we present a reformulation and decomposition strategy, along with its theoretical properties, to handle the complicated structure of BMIP. Finally, numerical results on practical and simulated instances, including those of nonlinear BMIP models, are provided to demonstrate the computational advantages over existing methods.


  • Friday, 8th July, 2016

    Title: Distributionally Robust Optimization with Matrix Moment Constraints: Lagrange Duality and Cutting Plane Methods
    Speaker: LIU Yongchao , Department of Mathematics, Dalian Maritime University , China
    Time/Place: 16:45  -  17:30
    FSC1217, Fong Shu Chuen Library, HSH Campus, Hong Kong Baptist University
    Abstract: A key step in solving minimax distributionally robust optimization (DRO) problems is to reformulate the inner maximization w.r.t. probability measure as a semiinfinite programming problem through Lagrange dual. Slater type conditions have been widely used for zero dual gap when the ambiguity set is defined through moments. In this paper, we investigate effective ways for verifying the Slater type conditions and introduce other conditions which are based on lower semicontinuity of the optimal value function of the inner maximization problem. Moreover, we apply a well known random discretization scheme to approximate the semiinfinite constraints of the dual problem and demonstrate equivalence of the approach to random discretization of the ambiguity set. Two cutting plane schemes are consequently proposed: one for the discretized dualized DRO and the other for the minimax DRO with discretized ambiguity set. Convergence analysis is presented for the approximation schemes in terms of the optimal value, optimal solutions and stationary points. Comparative numerical results are reported for the resulting algorithms.


  • Monday, 18th July, 2016

    Title: An introduction to meta-analysis
    Speaker: Dr. ZHENG Guian, Department of Cardiology, Zhangzhou Hospital affiliated to Fujian Medical University, China
    Time/Place: 15:00  -  16:00
    FSC1217, Fong Shu Chuen Library, HSH Campus, Hong Kong Baptist University
    Abstract: Meta-analysis refers to secondary data analysis where information from individual research articles is synthesized to arrive at a summary estimate. It comprises several related steps of framing a question or a problem, formulating search strategies, collection of journal articles or primary studies, extraction of data from the studies, critical appraisal of studies, judging homogeneity of studies, and synthesis of information from them. In this lecture, Guian will give a brief overview of the key processes of conducting a meta-analysis.


  • Monday, 18th July, 2016

    Title: Meta-analysis in evidence-based medicine
    Speaker: Dr. Yichao Zheng, Department of Gastroenterology and Hepatology, Zhangzhou Hospital affiliated to Fujian Medical University, China
    Time/Place: 16:00  -  17:00
    FSC1217, Fong Shu Chuen Library, HSH Campus, Hong Kong Baptist University
    Abstract: Meta-analysis is conducted to assess the strength of evidence present on a disease and treatment, and thus plays a central role in evidence-based medicine. It can prevent the delays in introduction of effective treatments and lead to the timely identification of adverse effects. Moreover, meta-analysis can be used to evaluate the accuracy of the diagnostic and prognostic tests, as well as to identify risk factors of the diseases. In the present lecture, Yichao will give examples in which meta-analysis was used to assess the outcome of a treatment, performance of a test and risk factor of a disease successfully.


  • Saturday, 23rd July, 2016

    Title: Sharp bounds for Boltzmann and Landau collision operators
    Speaker: Dr. He LingBing, Department of Mathematical Sciences, Tsinghua University, China
    Time/Place: 14:00  -  15:00
    FSC1217, Fong Shu Chuen Library, HSH Campus, Hong Kong Baptist University
    Abstract: In this talk, we will provide a stable method to get sharp bounds for Boltzmann and Landau operators in weighted Sobolev spaces and in anisotropic spaces. The main ingredients are two types of dyadic decompositions performed in both phase and frequency spaces and also the geometric decomposition to catch the main structure of the operator. As applications, we will show that our results are related closely to the asymptotic problem of grazing collisions limit and the asymptotics of the Boltzmann equation from short-range interactions to long-range interactions.


  • Saturday, 23rd July, 2016

    Title: On the global dynamics of three dimensional incompressible magnetohydrodynamics
    Speaker: Dr. YU Pin, Department of Mathematical Sciences, Tsinghua University, China
    Time/Place: 15:00  -  16:00
    FSC1217, Fong Shu Chuen Library, HSH Campus, Hong Kong Baptist University
    Abstract: We construct and study global solutions for the 3-dimensional imcompressible MHD systems with arbitrary small viscosity. In particular, we provide a rigorous justification for the following dynamical phenomenon observed in many contexts: the solution at the beginning behave like non-dispersive waves and the shape of the solution persists for a very long time (proportional to the Reynolds number); thereafter, the solution will be damped due to the long-time accumulation of the diffusive effects; eventually, the total energy of the system becomes extremely small compared to the viscosity so that the diffusion takes over and the solution afterwards decays fast in time. We do not assume any symmetry condition. The size of data and the a priori estimates do not depend on viscosity. The proof is built upon a novel use of the basic energy identity and a geometric study of the characteristic hypersurfaces. The approach is partly inspired by Christodoulou-Klainerman's proof of the nonlinear stability of Minkowski space in general relativity. This is a joint work with Ling-Bing HE (Tsinghua University) and Li XU (Chinese Academy of Sciences).


  • Friday, 29th July, 2016

    Title: Barzilai-Borwein Step Size for Stochastic Gradient Descent
    Speaker: Prof. Shiqian Ma, Department of Systems Engineering and Engineering Management , The Chinese University of Hong Kong, Hong Kong
    Time/Place: 11:00  -  12:00
    FSC1217, Fong Shu Chuen Library, HSH Campus, Hong Kong Baptist University
    Abstract: One of the major issues in stochastic gradient descent (SGD) methods is how to choose an appropriate step size while running the algorithm. Since the traditional line search technique does not apply for stochastic optimization algorithms, the common practice in SGD is either to use a diminishing step size, or to tune a fixed step size by hand, which can be time consuming in practice. In this work, we propose to use the Barzilai-Borwein (BB) method to automatically compute step sizes for SGD and its variant: stochastic variance reduced gradient (SVRG) method, which leads to two algorithms: SGD-BB and SVRG-BB. We prove that SVRG-BB converges linearly for strongly convex objective functions. As a by-product, we prove the linear convergence result of SVRG with Option I, whose convergence result is missing in the literature. Numerical experiments on standard data sets show that the performance of SGD-BB and SVRG-BB is comparable to and sometimes even better than SGD and SVRG with best-tuned step sizes, and is superior to some advanced SGD variants.