Event(s) on August 2023

• Thursday, 3rd August, 2023

  Title:	Convergence theory of outcome weighted learning in precision medicine
  Speaker:	Prof. Daohong Xiang, School of Mathematical Sciences, Zhejiang Normal University, China
  Time/Place:	14:30  -  15:00 FSC1217, Fong Shu Chuen Library, HSH Campus, Hong Kong Baptist University
  Abstract:	Outcome-weighted learning (OWL) is one of the most popular algorithms for estimating the optimal individualized treatment rules in precision medicine. In this talk, the convergence theory of OWL for the cases of bounded and unbounded clinical outcomes is mainly studied. Fast learning rates of OWL associated with least square loss, exponential-hinge loss and r-norm SVM loss are derived explicitly.

  
  

• Thursday, 3rd August, 2023

  Title:	On recovering signal from partial frame coefficients
  Speaker:	Dr. Fusheng Lyu, School of Mathematical Sciences, Nankai University, China
  Time/Place:	15:00  -  15:30 FSC1217, Fong Shu Chuen Library, HSH Campus, Hong Kong Baptist University
  Abstract:	Frame theory is widely used in data analysis and signal processing fields. The frame coefficients are usually redundant, which makes it possible to recover the original signal after some frame coefficients are lost. In this talk, we will discuss the feasibility and smoothness of recovering finite-dimensional signals from partially disordered and phaseless disordered frame coefficients. We propose self-located robust frames and real phase retrievable frames. Among them, the self-located robust frames ensure that the signal can be recovered smoothly from partial noisy disordered frame coefficients, and the real phase retrievable frames ensure that all real finite-dimensional signals can be recovered from partial phaseless disordered frame coefficients up to a sign. We will also give several characterizations and constructions of these two types of frames.

  
  

• Thursday, 3rd August, 2023

  Title:	Tractability of approximation by general shallow networks
  Speaker:	Dr. Tong Mao, Institute of Mathematical Sciences, Claremont Graduate University, USA
  Time/Place:	15:30  -  16:00 FSC1217, Fong Shu Chuen Library, HSH Campus, Hong Kong Baptist University
  Abstract:	In this talk, we consider the approximation of functions given by an integral form. Such function spaces are called variation spaces. Although these spaces have been studied in various literature, we study them under some general assumptions. We concentrated on the constant terms and showed these terms are tractable (depending polynomially on the dimension) under some dimension-independent assumptions. Applications include approximation by power rectified linear unit networks, zonal function networks, certain radial basis function networks as well as the important problem of function extension to higher dimensional spaces.

  
  

• Monday, 14th August, 2023

  Title:	A decoupled, linear, and unconditionally energy stable finite element method for a two-phase ferrohydrodynamics model
  Speaker:	Prof. Xiaoming He, Department of Mathematics and Statistics, Missouri University of Science & Technology, USA
  Time/Place:	14:30  -  15:30 FSC 1217
  Abstract:	In this talk, we present numerical approximations of a phase-field model for two-phase ferrofluids, which consists of the Navier-Stokes equations, the Cahn-Hilliard equation, the magnetostatic equations, as well as the magnetic field equation. By combining the projection method for the Navier-Stokes equations and some subtle implicit-explicit treatments for coupled nonlinear terms, we construct a decoupled, linear, fully discrete finite element scheme to solve the highly nonlinear and coupled multi-physics system efficiently. The scheme is provably unconditionally energy stable and leads to a series of decoupled linear equations to solve at each time step. Through numerous numerical examples in simulating benchmark problems such as the Rosensweig instability and droplet deformation, we demonstrate the stability and accuracy of the numerical scheme.

  
  

• Tuesday, 15th August, 2023

  Title:	Confirmation of Candidature Seminar: A General Framework for Selecting All Sufficient Adjustment Sets in Causal Inference
  Speaker:	Mr QIN Fei, Department of Mathematics, Hong Kong Baptist University, Hong Kong
  Time/Place:	15:00  -  16:30 FSC1110, or Zoom (Meeting ID: 980 2939 7383 Passcode: 224196)
  Abstract:	The ignorability assumption is crucial for identifying treatment effects in causal inference. A set of covariates is considered a sufficient adjustment set if the ignorability assumption holds when conditioning on it. However, existing methods cannot select all sufficient adjustment sets simultaneously. To address this issue, this paper proposes a general framework involving two components. For the first component we need a quantitative measure of the ignorability assumption and we use the newly developed criterion parallel to the dual inverse regression method as an example. For the second component we need to find the cut point of the scree plot and we use the ridge ratio method as an example. The proposed methods are model-free. Unlike conditional independence testing methods, our estimation is consistent regardless of whether the number of covariates is fixed or divergent. The methods require no prior knowledge of the causal graph’s underlying structure, are easy to implement and are applicable when the covariates are normal, mixture normal or Gaussian copula distributed. Extensive simulations suggest that the proposed methods have good finite-sample performance and outperform existing methods. Finally, we apply our methods to identify all sufficient adjustment sets while analyzing a real dataset on the causal effect of maternal smoking during pregnancy on low birth weight for infants.

  
  

• Wednesday, 16th August, 2023

  Title:	Stochastic Optimization, Stochastic Variational Inequality, and the Progressive Decoupling Algorithm
  Speaker:	Professor Jie Sun, National University of Singapore and Curtin University
  Time/Place:	11:00  -  12:00 FSC1217, Fong Shu Chuen Library, HSH Campus, Hong Kong Baptist University
  Abstract:	This talk introduces basic concepts of multistage stochastic optimization and its abstract form --- the stochastic variational inequality (SVI). A scheme of solving SVI problems called the progressive decoupling algorithm (PDA) is discussed and preliminary computational results are reported.

  
  

• Tuesday, 29th August, 2023

  Title:	A Gromov--Wasserstein Geometric View of Spectrum-Preserving Graph Coarsening
  Speaker:	Dr. Yifan Chen, Department of Computer Science, Hong Kong Baptist University, Hong Kong
  Time/Place:	15:00  -  16:00 FSC1217, Fong Shu Chuen Library, HSH Campus, Hong Kong Baptist University
  Abstract:	In this talk, I will delve into a geometric perspective of graph coarsening, which is a technique for solving large-scale graph problems by working on a smaller version of the original graph. It has a long history in scientific computing and has recently gained popularity in machine learning, particularly in methods that preserve the graph spectrum. Compared to the previous spectral perspective, the proposed geometric perspective is especially useful when working with a collection of graphs, such as in graph classification and regression. Specifically, we consider a graph as an element on a metric space equipped with the Gromov--Wasserstein (GW) distance, and bound the difference between the distance of two graphs and their coarsened versions. Minimizing this difference can be done using the popular weighted kernel K-means method, which strengthens existing spectrum-preserving methods.

  
  

• Wednesday, 30th August, 2023

  Title:	How Can We Learn from Possibly Unrelated Sources? A Source-Function Weighted-Transfer Learning
  Speaker:	Professor Lu LIN, Zhongtai Securities Institute for Financial Studies, Shandong University, China
  Time/Place:	15:00  -  16:00 FSC1217, Fong Shu Chuen Library, HSH Campus, Hong Kong Baptist University
  Abstract:	The homogeneity, or more generally, the similarity between source domains and a target domain seems to be essential to a positive transfer learning. In practice, however, the similarity condition is difficult to check and is often violated. In this paper, instead of the popularly used similarity condition, a seeming similarity is introduced, which is defined by a non-orthogonality together with a smoothness. Such a condition is naturally satisfied under common situations and even contains the dissimilarity as its special case. Based on the seeming similarity together with an L_2-adjustment, a source-function weighted-transfer learning estimation (sw-TLE) is constructed. By source-function weighting, an adaptive transfer learning is achieved in the sense that the transfer learning is always positive in both similar and dissimilar scenarios. Particularly, under the case with homogenous sources, the sw-TLE even obtains the parametric or semiparametric convergence rate, though the model under study is nonparametric. The hidden relationship between the source-function weighting estimator and the James-Stein estimator is established as well, which reveals the structural reasonability of our methodology. Moreover, the strategy does apply to nonparametric and semiparametric models. The comprehensive simulation studies and real data analysis can illustrate that the new strategy is significantly better than the competitors, and is comparable with the oracle estimator.

  
  

• Wednesday, 30th August, 2023

  Title:	Subgroup analysis for high-dimensional functional regression
  Speaker:	Dr. Xiaochen ZHANG, Zhongtai Securities Institute for Financial Studies, Shandong University, China
  Time/Place:	16:00  -  17:00 FSC1217, Fong Shu Chuen Library, HSH Campus, Hong Kong Baptist University
  Abstract:	Subgroup analysis for scalar data has been well studied in the literature. However, less has been done on functional data, especially on high-dimensional functional regression. In this study, we develop a high-dimensional functional regression model for simultaneous estimation and subgroup identification for a heterogeneous population. Under mild conditions, we establish the estimation and selection consistency of the proposed method. The proposed analysis allows the number of functional predictors and number of subgroups to increase as the sample size increases. Simulation studies demonstrate satisfactory performance of the proposed method, and it is also illustrated through a real application.

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