Department of Mathematics and Statistics

Department of Mathematics and Statistics
Department of Mathematics and Statistics
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Joint Seminars in Statistics & Biostatistics

Statistics & Biostatistics - Xiang Li (Queen's University)

Wednesday, February 26th, 2020

Time: 11:30-12:20 Place: Jeffery Hall 225

Speaker: Prof. Xiang Li (Queen's University, Dept. of Chemical Engineering)

Title: Decomposition Based Global Optimization

Abstract: Large-scale nonconvex optimization arises from a variety of scientific and engineering problems. Often such optimization problem is simplified into an easier convex or mixed-integer convex optimization problem, but the solution of the simplified problem is unlikely to be optimal or feasible for the original problem. Recent advances in decomposition based global optimization provides a promising way to solve large-scale nonconvex optimization problems within reason time. In this presentation, we will first discuss the principle of generalized Benders decomposition (GBD), including the reformulation into a master problem using strong Lagrangian duality, the construction of upper and lower bounding problems, and the finite convergence property. We also show how GBD can be applied to decompose multi-scenario problems. Then we introduce two variants of GBD. The first variant, called nonconvex generalized Benders decomposition (NGBD), is able to solve a class of nonconvex problems that GBD cannot solve. The second variant, called joint decomposition (JD), enhances GBD/NGBD via the integration of Lagrangian decomposition. Finally, we demonstrate the computational advantages of GBD, NGBD and JD via some engineering problems.

Statistics & Biostatistics - Qingling Duan (Queen's University)

Wednesday, November 20th, 2019

Time: 11:30-12:30 Place: Jeffery Hall 225

Speaker: Qingling Duan (Queen's National Scholar in Bioinformatics, School of Computing and Dept. of Biomedical & Molecular Sciences, Queen's University)

Title: Statistical methods for the study of genomic risk factors of complex traits

Abstract: The overarching goal of my research program is to identify and characterize genomic factors that modulate multifactorial traits such as drug response, allergies and asthma. My team leads the collection and analysis of multiple types of ‘omics (i.e. genomics, transcriptomics, epigenomics and metagenomics) datasets from human cohorts. Specifically, we hypothesize that gene-gene and gene-environment interactions account in part for the missing heritability of complex traits. We test this using additive and multiplicative models in addition to network analysis and data integration to characterize novel biological pathways and underlying disease mechanisms. For example, we have identified main and interaction effects of genetic variants and environmental exposures (e.g., smoking, dog ownership, breastfeeding) on risk of early childhood asthma. In addition, we report novel gene networks associated with risk of asthma and response to chemotherapy among cancer patients. I am a lead investigator of the Canadian Healthy Infant Longitudinal Development (CHILD) cohort study and the Canadian Respiratory Research Network which supports the Canadian Chronic Obstructive Lung Disease (CanCOLD). My laboratory is currently funded by the Canadian Institute of Health Research, Queen’s University and the Canadian Foundation for Innovation.

Statistics & Biostatistics - Yanglei Song (Queen's University)

Wednesday, November 6th, 2019

Time: 11:30-12:30 Place: Jeffery Hall 225

Speaker: Yanglei Song (Queen's University)

Abstract: I will start with a discussion on the recent development in the normal approximation (a.k.a. central limit theorem) and bootstrap for the sum of high dimensional random vectors, empirical processes and U-processes. Statistical applications will also be provided. Then I will talk about a piece of ongoing work in this line, with Xiaohui Chen and Kengo Kato. Its abstract is as follows: This paper studies the non-asymptotic inference for the supremum of an incomplete, non-degenerate U-process. The process is indexed by a function class of order r, whose complexity possibly increases with the sample size n. For each function, its corresponding U-statistic involves the average of O(n^r) numbers, which is prohibitively demanding even for moderate r. Thus we study its incomplete version, where each subsample of size r is included in the average with a very small probability. We first approximate the supremum of such incomplete U-process by that of an appropriate Gaussian process in the Kolmogorov distance and then propose valid bootstrap methods to address the practical issue of unknown covariance function. Finally, we discuss its application in testing the qualitative features, such as convexity, of nonparametric functions.