Event(s) on February 2023

• Thursday, 2nd February, 2023

  Title:	Network functional varying coefficient model
  Speaker:	Professor Yanyuan Ma, Department of Statistics, Penn State University, USA
  Time/Place:	15:00  -  16:00 FSC1217
  Abstract:	We consider functional responses with network dependence observed for each individual at irregular time points. To model both the inter-individual dependence as well as within-individual dynamic correlation, we propose a network functional varying coefficient (NFVC) model. The response of each individual is characterized by a linear combination of responses from its connected nodes and its own exogenous covariates. All the model coefficients are allowed to be time dependent. The NFVC model adds to the richness of both the classical network autoregression model and the functional regression models. To overcome the complexity caused by the network inter-dependence, we devise a special nonparametric least squares type estimator, which is feasible when the responses are observed at irregular time points for different individuals. The estimator takes advantage of the sparsity of the network structure to reduce the computational burden. To further conduct the functional principal component analysis, a novel within-individual covariance function estimation method is proposed and studied. Theoretical properties of our estimators are analyzed, which involve techniques related to empirical processes, nonparametrics, functional data analysis and various concentration inequalities. We analyze a social network data to illustrate the powerfulness of the proposed procedure.

  
  

• Thursday, 2nd February, 2023

  Title:	Sample size determination for interval estimation of the prevalence of a sensitive attribute under randomized response models
  Speaker:	Professor Shifang Qiu, Department of Statistics, Chongqing University of Technology, China
  Time/Place:	16:00  -  17:00 FSC1217
  Abstract:	Studies with sensitive questions should include a sufficient number of respondents to adequately address the research interest. While studies with an inadequate number of respondents may not yield significant conclusions, studies with an excess of respondents become wasteful of investigators’ budget. Therefore, it is an important step in survey sampling to determine the required number of participants. In this article, we derive sample size formulas based on confidence interval estimation of prevalence for four randomized response models, namely, the Warner’s randomized response model, unrelated question model, item count technique model and cheater detection model. Specifically, our sample size formulas control, with a given assurance probability, the width of a confidence interval within the planned range. Simulation results demonstrate that all formulas are accurate in terms of empirical coverage probabilities and empirical assurance probabilities. All formulas are illustrated using a real-life application about the use of unethical tactics in negotiation.

  
  

• Friday, 3rd February, 2023

  Title:	Some studies on distributed multi-agent optimization
  Speaker:	Dr. Zhan Yu, The University of Hong Kong
  Time/Place:	11:00  -  12:00 FSC1217, or Zoom (Meeting ID: 979 5764 2212)
  Abstract:	In this talk, we introduce a distributed optimization problem over a multi-agent network. For solving the problem, a distributed gradient-free (zeroth-order) mirror descent method is provided by introducing a randomized gradient-free oracle in the mirror descent scheme associated with each local agent. We introduce two types of approximating sequences related to local agents. After describing the main ideas on estimating the error bounds, we introduce the ergodic convergence results of the two approximating sequences. The method is applicable to some tough environments where the first-order gradient information is inaccessible or costly to evaluate and the objective function is nonsmooth. We will also briefly discuss some other methods related to distributed optimization.

  
  

• Friday, 10th February, 2023

  Title:	High Dimensional Data Recovery
  Speaker:	Prof Michael Ng, Department of Mathematics, The University of Hong Kong, Hong Kong
  Time/Place:	11:30 FSC1217, Fong Shu Chuen Library, HSH Campus, Hong Kong Baptist University
  Abstract:	In recent years, high dimensional data recovery has been extensively studied and analyzed, which can be applied to many data science applications such as recommendation, image recovery and statistical estimation. In this talk, we present several variants of data recovery models and their applications. We provide theoretical insight to create a rigorous scientific basis for solving such data recovery problems. Numerical examples are also given to demonstrate the usefulness of these models.

  
  

• Tuesday, 14th February, 2023

  Title:	Confirmation of Candidature Seminar: Image Segmentation with Shape Compactness Regularization
  Speaker:	Ms ZHANG Kehui, Department of Mathematics, Hong Kong Baptist University, Hong Kong
  Time/Place:	14:30  -  15:10 FSC1217, Fong Shu Chuen Library, HSH Campus, Hong Kong Baptist University
  Abstract:	We propose a PD-STD block in CNN to solve a high-order segmentation model due to a compactness term involving a squared sum of pairwise potentials. Existing algorithms suffer from the drawback of being computationally costly. And they are hard to reach a local minimum because numerous parameters need to be fine-tuned. To address the problems, we use the Fenchel-Legendre transformation to rewrite the model as a min-max problem and first develop a simple primal-dual optimization algorithm PD-TD. Moreover, we relax the constraint on the solution and propose another algorithm PD-STD which achieves better performance. Based on the variational explanation of the softmax layer, the PD-STD algorithm can be combined with DCNNs to integrate the spatial prior into the DCNNs and guarantee the outputs of DCNNs are compact. Our methods are faster and more powerful, as evidenced by several image segmentation experiments. In particular, we applied our method to the popular DeepLabV3 and the state-of-art IrisParseNet image segmentation networks, the results show that our method can yield competing performance.

  
  

• Tuesday, 14th February, 2023

  Title:	Confirmation of Candidature Seminar: Statistical Methods for Meta-Analysis of Binary Data
  Speaker:	Mr WEI Jiajin, Department of Mathematics, Hong Kong Baptist University, Hong Kong
  Time/Place:	15:10  -  15:50 FSC1217, Fong Shu Chuen Library, HSH Campus, Hong Kong Baptist University
  Abstract:	Meta-analysis is a statistical method to synthesize evidence from multiple independent studies that address the same scientific questions. In clinical studies, experimental data are commonly composed of binary outcomes, and consequently, meta-analyses of binary data have attracted increasing attention in evidence-based medicine. In particular, the reciprocal of a binomial proportion, or equivalently the inverse binomial proportion, has been recognized as an important parameter in statistics and related areas. To the best of our knowledge, however, there is little work on the interval estimation for the inverse binomial proportion and so is yet to be further developed. To fill the gap, we apply four different methods to construct the confidence intervals (CIs) for the inverse binomial proportion, namely the Wald, score, arctangent and beta prime CIs, and further study their respective statistical properties. Simulation studies are also conducted to evaluate the finite sample performance of the proposed CIs, followed by a recent meta-analysis on the prevalence of heart failure among COVID-19 patients with mortality to demonstrate their usefulness in practice. Moreover, some future work on meta-analysis of binary data will also be briefly introduced, including interval estimation for the number needed to treat and semiparametric methods for meta-analysis and meta-regression.

  
  

• Tuesday, 14th February, 2023

  Title:	Confirmation of Candidature Seminar: Variability Test for Varying Coefficient Models
  Speaker:	Ms WANG Yuyuan, Department of Mathematics, Hong Kong Baptist University, Hong Kong
  Time/Place:	15:50  -  16:30 FSC1217, Fong Shu Chuen Library, HSH Campus, Hong Kong Baptist University
  Abstract:	In this proposal, we consider the variability test problem for varying coefficient models. In order to test this hypothesis, we plan to apply empirical likelihood ratio test, K-L divergence estimator and comparison of error density. The proposed methods can be extended to a number of useful models, such as nonparametric regression models, generalized nonparametric models or generalized varying coefficient models, et al. It is proven that the empirical log-likelihood ratio statistic, under the null hypothesis, is asymptotically Chi-squared distribution with 1 degree of freedom.

  
  

• Tuesday, 14th February, 2023

  Title:	Confirmation of Candidature Seminar: Learning Rates of Convolutional Neural Networks with Correntropy Induced Loss
  Speaker:	Mr ZHANG Yingqiao, Department of Mathematics, Hong Kong Baptist University, Hong Kong
  Time/Place:	16:30  -  17:10 FSC1217, Fong Shu Chuen Library, HSH Campus, Hong Kong Baptist University
  Abstract:	Deep convolutional neural networks are widely used in practice including image recognition, natural language processing, bioinformatics and many other fields. But most recent studies on convolutional neural network theory are based on least square loss function. This paper investigates deep convolutional neural networks with correntropy induced loss function under the assumption that noise has a finite pth-moment. We show that, with target function in additive ridge functions format, convolutional neural networks followed by one fully connected layer with ReLU activation functions can reach optimal learning rates up to a logarithmic factor. In addition, we present a more general error bound and learning rate when the target function lies in a Sobolev space on the sphere.

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