題目： BOLT-SSI: Fully Screening Interaction Effects for Ultra-High Dimensional Data

報告人：彭衡 博士 （香港浸會大學）

主持人：晏豔陽教授

時間：2018年11月01日（星期四）上午10：00—11：00

地點：2003网站太阳集团财院校區行政樓315

Detecting interaction effects among predictor variables and response variables is often a crucial step in regression modelling of real data for various applications. In this paper, we firstly introduce a simple sure screening procedure (SSI) for marginal likelihood to fully detect significant pure interactions between predictor variables and the response variable in the high or ultra-high dimensional generalized linear regression models. The major challenge of SSI to detect interactions comes from computational efficiency. To make SSI applicable to detect interactions in ultra-high dimensional setting, we boost the conventional SSI by discretizing continuous predictor variables, where the Boolean operation is applied in the presence of the marginal likelihood estimates, and call it BOLT-SSI. Next, we show statistical properties of SSI and BOLT-SSI, i.e., they have the sure screening property for even exponentially growing dimensionality and can control the false discovery rate at a reasonable size. To demonstrate the advantages of BOLT-SSI over existing methods, we conducted extensive simulation studies and applied BOLT-SSI to three real data sets such as Residential Building data, Supermarket data and Northern Finland Birth Cohort data. The results support our theoretical perspectives, and show that BOLT-SSI can boost the computational efficiency of sure screening for interaction effects in the presence of high-dimensional predictor variables and simultaneously improve the prediction performance in real data analysis.

報告人簡介：

彭衡博士，先後畢業于中國科技大學，香港中文大學，師從世界著名統計學家範劍青教授，現任香港浸會大學數學系副教授（終身職位），香港浸會大學深圳研究院研究員，國際統計研究院當選會員，數理統計研究所終生會員。主要從事非參數與半參數模型、模型選擇、高維數據建模、混合模型，金融計量經濟學等領域的研究，在Annals of Statistics、JASA、Biometrika等國際著名統計學雜志發表40餘篇高質量論文，google學術引用1500餘次。擔任國際期刊Statistica Sinica、Computational Statistics & Data Analysis的副主編，主持完成多項美國自然科學基金、香港研資局、國家自然科學基金。