Event(s) on March 2019

• Thursday, 21st March, 2019

  Title:	Large-Scale Mediation Effect Signal Detection in Genome-wide Epigenetic Studies
  Speaker:	Dr Zhonghua LIU , Department of Statistics and Actuarial Science, University of Hong Kong, Hong Kong
  Time/Place:	14:30  -  15:15 FSC1217, Fong Shu Chuen Library, HSH Campus, Hong Kong Baptist University
  Abstract:	In genome-wide epigenetic studies, it is often of scientific interest assessing the mediator role of DNA methylation in the causal pathway from an exposure to a clinical outcome. Mediation analysis is commonly used to answer this question. This is often done via fitting two regression models: the mediator model and the outcome model, and then the product of coefficient method to integrate information from these two models and performing hypothesis testing using Sobel's test (Sobel, 1982). Another popular test is the joint significance test which declares the presence of a mediation effect if the effect of the exposure on mediator and the effect of mediator on outcome are both statistically significant. In this paper, we show that both the Sobel's test and the joint significance test are overly conservative for the detection of mediation effect in genome-wide epigenetic studies. The null hypothesis of no mediation effect is composite, and it is therefore challenging to perform large-scale hypothesis testing to detect mediation effects. We propose a novel divide-aggregate test (DAT) for the composite null hypothesis for the detection of mediation effects in genome-wide epigenetic studies. We first divide the composite null parameter space into three disjoint parts, each with a separate testing procedure. The DAT is then obtained by aggregating the statistical evidence via a weighted average of the three parts with the weights estimated as the proportion of true nulls based on the $p$-values from the mediator and outcome regression models. We further show that the DAT can outperform the Sobel's test and the joint significance test for the detection of mediation effects in genome-wide epigenetic studies. A fast Monte Carlo correction method is also proposed for computing the $p$-value of the DAT method. We show via simulation studies that the DAT method controls type I error rates and outperforms the Sobel's and the joint significance test. We applied the DAT method to the Normative Aging Study to identify putative DNA methylation sites that mediate the effect of smoking on lung function.

  
  

• Thursday, 21st March, 2019

  Title:	Penalized Interaction Estimation for Ultrahigh Dimensional Quadratic Regression
  Speaker:	Dr Binyan JIANG, Department of Applied Mathematics, Hong Kong Polytechnic University, Hong Kong
  Time/Place:	15:15  -  15:45 FSC1217, Fong Shu Chuen Library, HSH Campus, Hong Kong Baptist University
  Abstract:	Quadratic regression goes beyond the linear model by simultaneously including main effects and interactions between the covariates. The problem of interaction estimation in high dimensional quadratic regression has received extensive attention in the past decade. In this article we introduce a novel method which allows us to estimate the main effects and interactions separately. Unlike existing methods for ultrahigh dimensional quadratic regressions, our proposal does not require the widely used heredity assumption. In addition, our proposed estimates have explicit formulas and obey the invariance principle at the population level. We estimate the interactions of matrix form under penalized convex loss function. The resulting estimates are shown to be consistent even when the covariate dimension is an exponential order of the sample size. We develop an efficient ADMM algorithm to implement the penalized estimation. This ADMM algorithm fully explores the cheap computational cost of matrix multiplication and is much more efficient than existing penalized methods such as all pairs LASSO. We demonstrate the promising performance of our proposal through extensive numerical studies.

  
  

• Thursday, 21st March, 2019

  Title:	On Parsimonious and Flexible Modeling of Multivariate Failure Time Data
  Speaker:	Dr Jinfeng XU, Department of Statistics and Actuarial Science, University of Hong Kong, Hong Kong
  Time/Place:	15:45  -  16:30 FSC1217, Fong Shu Chuen Library, HSH Campus, Hong Kong Baptist University
  Abstract:	The frailty or random effects approach has been commonly used to model correlated failure time data. With the unobserved heterogeneity characterized by the random effects, it directly models the dependency and yields easy interpretation for the estimated model. In practice, however, it is often subjective and difficult to specify the distribution of the random effects. Furthermore, the (nonparametric) maximum likelihood estimation may involve numerical computation for intractable multiple integrals. To avoid these difficulties, we propose a new approach, using the idea of homogeneity pursuit, which is computationally convenient and theoretically justified by its asymptotic properties. Simulation studies and a real data application are also provided to illustrate the utility of our proposal.

  
  

• Monday, 25th March, 2019

  Title:	Sparse Grid Meets Random Hashing: Learning High Dimensional Functions of Few Variables
  Speaker:	Prof Ming YUAN, Statistics Department, Columbia University, New York, USA
  Time/Place:	15:00  -  16:00 FSC1217, Fong Shu Chuen Library, HSH Campus, Hong Kong Baptist University
  Abstract:	We investigate the optimal sample complexity of recovering a general high dimensional smooth and sparse function based on point queries. Our result provides a precise characterization of the potential loss in information when restricting to point queries as opposed to the more general linear queries, as well as the benefit of adaption. In addition, we also developed a general framework for function approximation to mitigate the curse of dimensionality that can also be easily adapted to incorporate further structure such as mixed smoothness.

  
  

• Thursday, 28th March, 2019

  Title:	A stochastic semismooth Newton method for nonconvex nonsmooth optimization
  Speaker:	Dr Andre Milzarek, Beijing International Center for Mathematical Research, Peking University, Beijing, China
  Time/Place:	10:30  -  11:30 FSC1217, Fong Shu Chuen Library, HSH Campus, Hong Kong Baptist University
  Abstract:	We present a globalized stochastic semismooth Newton method for solving optimization problems involving smooth nonconvex and nonsmooth convex terms in the objective function. The class of problems that can be solved within our algorithmic framework comprises a large variety of important applications such as expected and empirical risk minimization, structured dictionary learning, and other problems arising in machine learning, statistics, or image processing. We assume that only noisy gradient and Hessian information of the smooth part of the objective function is available via calling stochastic first- and second-order oracles. Our approach utilizes approximate second order information and stochastic semismooth Newton steps for a prox-type fixed-point equation to accelerate the basic stochastic proximal gradient method for convex composite programming. Inexact growth conditions are incorporated to monitor the quality and acceptance of the Newton steps. We prove that the proposed algorithm converges globally to stationary points in expectation and almost surely. Moreover, under standard assumptions, the method can be shown to locally turn into a pure semismooth Newton method and fast local convergence can be established with high probability. Finally, we provide numerical experiments demonstrating the efficiency of the stochastic semismooth Newton method.

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