时间：2019年10月30日10：00-11：00
地点：理科大楼A楼1514室
题目：BOLT-SSI: Fully Screening Interaction Effects for Ultra-High Dimensional Data
报告人：彭衡 香港浸会大学数学系副教授
摘要：
Detecting interaction effects among predict variables to response variables is often an crucial step in regression modeling of real data for various applications. In this paper by marginal likelihood functions, we firstly introduce a simple sure screening procedure (SSI) to fully detect significant pure interaction between predict variables and the response variable in the high or ultra-high dimensional generalized linear regression models. Furthermore, we suggest to discretize continuous predict variables, and utilize the Boolean operation for the marginal likelihood estimates. The so called BOLT-SSI procedure is proposed to accelerate the sure screening speed of the procedure. We investigate the sure screening properties of SSI and BOLT-SSI. Our studies have several important features. First, to most ultra-high dimensional data in practice, the proposed sure screening methods can fully detect any pure interaction effects among ultra-high dimensional data. It is an impossible finished task from theoretical insight. Second, the proposed method efficiently takes the advantages of computer architecture to speedup the proposed algorithm and make trade-off between the computation burden and statistical modeling efficiency. Specially, regarding the interaction effect detecting study as a special example, by this study we show the limitation of theoretical investigation from the practical insight, and illustrate that how to make trade-off between engineering techniques and theoretical investigations.
报告人简介：
彭衡，香港浸会大学数学系副教授，香港浸会大学深圳研究院研究员，国际统计研究院当选会员，数理统计研究所终生会员。主要从事非参数与半参数模型、模型选择、高维数据建模、混合模型等领域的研究，在 Annals of Statistics、JASA、Biometrika 等国际著名统计学杂志发表 40 余篇高质量论文。担任国际期刊 StatisticaSinica、Computational Statistics & Data Analysis 的副主编，主持完成多项美国自然科学基金、香港研资局、国家自然科学基金。