Title: | Recent developments around soliton gas theory |
Speaker: | Dr. Fudong Wang, Great Bay University, China |
Time/Place: | 16:00 - 17:00 FSC1217, Fong Shu Chuen Library, HSH Campus, Hong Kong Baptist University |
Abstract: | In this talk, I will first introduce some basic concepts in the focusing Nonlinear Schrodinger (fNLS) soliton gas theory within a framework developed by El and Tovbis in 2020. Then we will discuss some new results on the spectral theory for fNLS soliton gases. Specifically, I will show how to compute the averaged conserved quantatites for the fNLS gases. Lastly, we will also briefly touch another method within the soliton gas theory—the primitive potential method developed by Zakharov. Some related recent work will be metioned as well. |
Title: | QR and LR Algorithms |
Speaker: | Professor Tin-Yau Tam, Department Chair and Seneca C. and Mary B. Weeks Chair in Mathematics, University of Nevada, USA |
Time/Place: | 11:00 - 12:00 FSC1217, Fong Shu Chuen Library, HSH Campus, Hong Kong Baptist University |
Abstract: | We will discuss the following algorithms, their history, and their extensions in Lie group: (a) Francis-Kublanovskaya’s QR algorithm. (b) Rutishauser’s LR algorithm. These results are related to several important matrix decompositions, namely, SVD, QR decomposition, Gelfand-Naimark decomposition, LU decomposition, Jordan decomposition and their Lie counterparts: Cartan decomposition, Iwasawa decomposition, Bruhat decomposition, complete multiplicative Jordan decomposition. |
Title: | Robust mendelian randomization with a binary outcome |
Speaker: | Dr. Zhonghua LIU, Department of Biostatistics, Columbia University |
Time/Place: | 16:30 - 17:30 FSC1217, Fong Shu Chuen Library, HSH Campus, Hong Kong Baptist University |
Abstract: | Mendelian randomization uses genetic variants as instrumental variables (IV) to infer the causal effect of an exposure on the outcome of interest even in the presence of unmeasured confounding. However, the exclusion restriction and/or IV independence conditions can be violated in practice. Moreover, little work has been done for a binary outcome. In this paper, we first establish identification results for a binary outcome with a single possibly invalid IV. Second, we propose a novel model parameterization to resolve the variation dependence issue when estimating causal risk difference. Third, we propose maximum likelihood and doubly robust estimators for the causal risk difference that are guaranteed to lie in the interval (-1,1). Extensive simulation studies confirmed our theoretical results. We also apply the proposed method to estimate the causal effect of adiposity on the risk of hypertension in the UK Biobank. |
Title: | On the usage of spectral information about matrices arising from parallel-in-time integration |
Speaker: | Prof Matthias Bolten, University of Wuppertal |
Time/Place: | 11:00 - 12:00 FSC1217, Fong Shu Chuen Library, HSH Campus, Hong Kong Baptist University |
Abstract: | In the development of iterative solvers for linear systems information about the spectrum of the system matrix is of large importance. For normal matrices this information alone suffices to accurately describe the behavior of the method. As the all-at-once systems arising from time integration are non-normal, this information is much less useful. Nevertheless spectral information is used to analyze numerical methods, e.g., using local Fourier analysis. To overcome the low accuracy of the obtained bounds block techniques like semi-algebraic mode analysis have been proposed and for preconditioning results from the literature on Krylov subspace methods can be applied. Finally, we recently extended the concept of the generating symbol to provide more accurate predictions. In the talk an overview about the different approaches of using spectral information to analyze parallel-in-time methods will be provided. |
Title: | Classification with deep neural networks |
Speaker: | Prof Lei Shi, Fudan University |
Time/Place: | 14:00 - 15:00 FSC1217, Fong Shu Chuen Library, HSH Campus, Hong Kong Baptist University |
Abstract: | Classification with deep neural networks (DNNs) has made impressive advancements in various learning tasks. Due to the unboundedness of the target function, generalization analysis for DNN classifiers with logistic loss remains scarce. Recent progress in establishing a unified framework of generalization analysis for both bounded and unbounded target functions is reported. The analysis is based on a novel oracle-type inequality, which enables us to deal with the boundedness restriction of the target function. In particular, for logistic classifiers trained by deep, fully connected neural networks, the optimal convergence rates are obtained only by requiring the H"{o}lder smoothness of the conditional probability. Under certain circumstances, such as when decision boundaries are smooth and the two classes are separable, the derived convergence rates can be independent of the input dimension. |
Title: | Convergence analysis of online learning algorithms in reproducing kernel Hilbert space |
Speaker: | Prof Zhengchu Guo, Zhejiang University |
Time/Place: | 15:00 - 16:00 FSC1217, Fong Shu Chuen Library, HSH Campus, Hong Kong Baptist University |
Abstract: | Analyzing and processing large-scale data sets is becoming ubiquitous in the era of big data. Online learning has attracted increasing interest in recent years due to its low computational complexity and storage requirements, it has been applied to various learning tasks. In this talk, we will present some results of online learning algorithms in Reproducing Kernel Hilbert space. |
Title: | Quantitative stratification of the singular set of harmonic maps and extensions |
Speaker: | Prof Changyu Guo, Shandong University |
Time/Place: | 11:00 - 12:00 FSC1217, Fong Shu Chuen Library, HSH Campus, Hong Kong Baptist University |
Abstract: | In this talk, I will give an overview of the regularity theory concerning the singular set of harmonic mappings into closed manifolds. In particular, we recall the classical stratification theory for harmonic mappings based on the fundamental work of Schoen-Uhlenbeck [J. Diff. Geom.1982], L. Simon [CVPDE 1995] and F.H. Lin [Ann. Math. 1999]. Then we introduce the quantitative stratification theory developed by Cheeger-Naber [Invent. Math. 2013], and by Naber-Valtorta [Ann. Math. 2017, arXiv 2024]. Then we briefly discuss the natural extension to biharmonic mappings. |
Title: | Parsimonious Model Averaging with a Diverging Number of Parameters |
Speaker: | Professor Hua LIANG, Department of Statistics, George Washington University, Washington DC, USA |
Time/Place: | 16:00 - 17:00 FSC1217, Fong Shu Chuen Library, HSH Campus, Hong Kong Baptist University |
Abstract: | Model averaging generally provides better predictions than model selection, but the existing model averaging methods cannot lead to parsimonious models. Parsimony is an especially important property when the number of parameters is large. To achieve a parsimonious model averaging coefficient estimator, we suggest a novel criterion for choosing weights. Asymptotic properties are derived in two practical scenarios: (i) one or more correct models exist in the candidate model set; and (ii) all candidate models are misspecified. Under the former scenario, it is proved that our method can put the weight one to the smallest correct model and the resulting model averaging estimators of coefficients have many zeros and thus lead to a parsimonious model. The asymptotic distribution of the estimators is also provided. Under the latter scenario, prediction is mainly focused on and we prove that the proposed procedure is asymptotically optimal in the sense that its squared prediction loss and risk are asymptotically identical to those of the best but infeasible model averaging estimator. Numerical analysis shows the promise of the proposed procedure over existing model averaging and selection methods. This is a joint work with Xinyu Zhang, Guohua Zou, and Raymond J. Carroll. |
Title: | Quantile regression and homogeneity detection of a large dimensional panel data semiparametric model |
Speaker: | Professor Rui LI, School of Statistics and Information, Shanghai University of International Business and Economics, Shanghai, China |
Time/Place: | 17:00 - 18:00 FSC1217, Fong Shu Chuen Library, HSH Campus, Hong Kong Baptist University |
Abstract: | In this article, we study the quantile regression and homogeneity detection of a single index varying coefficient panel data model with fixed effect which shows nonlinear time trend and is subject-specific. Based on polynomial spline approximation, we get initial estimates of link function, trend functions and index parameters, and establish the nonparametric convergence rate and asymptotic normality accordingly. Noting that the trend functions within a group may share the same impact on response variable, which motivates us to further identify the possible homogeneity of individual effect by integrating regularization with binary segmentation algorithm. Subsequently, we propose more efficient estimates via grouped observations and improve large sample properties. Simulation studies and a real application of Air pollution data and Integrated surface data (APD&ISD) are conducted to illustrate the finite sample performance of the proposed method. |
We organize conferences and workshops every year. Hope we can see you in future.
Learn MoreProf. M. Cheng, Dr. Y. S. Hon, Dr. K. F. Lam, Prof. L. Ling, Dr. T. Tong and Prof. L. Zhu have been awarded research grants by Hong Kong Research Grant Council (RGC) — congratulations!
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