Colloquium/Seminar

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Event(s) on December 2018


  • Tuesday, 18th December, 2018

    Title: Models and algorithms of total variation-based methods in images restoration
    Speaker: Ms FANG Yingying, Department of Mathematics, Hong Kong Baptist University, HKSAR, China
    Time/Place: 10:30  -  12:00
    FSC1217, Fong Shu Chuen Library, HSH Campus, Hong Kong Baptist University
    Abstract: The variational method is one of the best-known methods for ill-posed imaging problems. It turns various tasks in image restoration into minimizing a suitable objective function combined with a data fidelity term and a regularization term. Particularly, variational method with the total variation(TV) regularizer is preferred for its superiority in preserving the sharp edges. However, the total variation regularized models are difficult to minimize due to the non-smoothness of the total variation term. Meanwhile, the nonconvex TV models can bring about the non-uniqueness problem of the solution. Therefore, We explored an efficient semismooth Newton augmented Lagrangian method for the general TV-based convex model in image problems and also did some modificatons on the non-convex models in specific problems.


  • Thursday, 27th December, 2018

    Title: Variable Selection for Highly Correlated Predictors
    Speaker: Prof Annie Qu, Department of Statistics, University of Illinois at Urbana-Champaign, USA
    Time/Place: 09:00  -  10:00
    FSC1217, Fong Shu Chuen Library, HSH Campus, Hong Kong Baptist University
    Abstract: When predictors are highly correlated, standard variable selection methods could fail to be consistent. This is especially critical in high-dimensional settings when the number of predictors exceeds the sample size. In this paper, we propose a new Semi-standard PArtial Covariance (SPAC) approach which is able to reduce correlation effects from other predictors while incorporating the magnitude of coefficients. The proposed SPAC variable selection is effective in choosing covariates which have direct association with the response variable, while removing the predictors which are not directly associated with the response but are highly correlated with the relevant predictors. We show that the proposed method with the Lasso penalty and the SCAD penalty enjoys strong sign consistency in both finite-dimensional and high-dimensional settings under regularity conditions. Numerical studies and the ‘HapMap’ gene data application also confirm that the proposed method outperforms the traditional Lasso, adaptive Lasso, SCAD, and Peter–Clark-simple methods for highly correlated predictors. This is joint work with Fei Xue.


  • Monday, 31st December, 2018

    Title: A General Framework for Quantile Estimation with Incomplete Data
    Speaker: Dr. Linglong Kong, Department of Mathematical and Statistical Sciences, University of Alberta, Canada
    Time/Place: 11:00  -  12:00
    Abstract: Quantile estimation has attracted significant research interests in recent years. However, there has been only a limited literature on quantile estimation in the presence of incomplete data. In this paper, we propose a general framework to address this problem. Our framework combines the two widely adopted approaches for missing data analysis, the imputation approach and the inverse probability weighting approach, via the empirical likelihood method. The proposed method is capable of dealing with many different missingness settings. We mainly study three of them: (i) estimating the marginal quantile of a response that is subject to missingness while there are fully observed covariates; (ii) estimating the conditional quantile of a fully observed response while the covariates are partially available; and (iii) estimating the conditional quantile of a response that is subject to missingness with fully observed covariates and extra auxiliary variables. The proposed method allows multiple models for both the missingness probability and the data distribution. The resulting estimators are multiply robust in the sense that they are consistent if any one of these models is correctly specified. The asymptotic distributions are established using the empirical process theory.