报告题目I: 高维缺失数据的EM算法
报 告 人: 李启寨（中国科学院数学与系统科学研究院研究员，国家优秀青年科学基金获得者）
报告摘要：Missing data are frequently encountered in high dimensional problems, but they are usually difficult to deal with by using standard algorithms, such as the expectation–maximization algorithm and its variants. To tackle this difficulty, some problem-specific algorithms have been developed in the literature, but there still lacks a general algorithm.This work is to fill the gap:we propose a general algorithm for high dimensional missing data problems. The algorithm works by iterating between an imputation step and a regularized optimization step. At the imputation step, the missing data are imputed conditionally on the observed data and the current estimatesof parameters and, at the regularized optimization step, a consistent estimate is found via the regularization approach for the minimizer of a Kullback–Leibler divergence defined on the pseudocomplete data. For high dimensional problems, the consistent estimate can be found under sparsity constraints. The consistency of the averaged estimate for the true parameter can be established under quite general conditions. The algorithm is illustrated by using high dimensional Gaussian graphical models, high dimensional variable selection and a random coefficient model.
报告时间: 2018年12月13日(周四)15:30-16:15
报告地点:磬苑校区数学科学学院H306
报告题目II: Simultaneous Multiple Change-point Detection in the Spatio-Temporal Linear Models
报 告 人: 金百锁（中国科学技术大学管理学院副教授）
报告摘要：We consider a general class of spatio-temporal linear models, where the number of predictors can tend to infinity at each time point. A procedure for simultaneously detecting multiple change-points is developed rigorously via the construction of adaptive group lasso penalty. Consistency of the multiple change-point estimation is established under mild conditions even when the true number of change-points diverges with the sample size, i.e., the number of time points n. The adaptive group lasso can be substituted by the group lasso, and other non-convex group selection algorithms including group SCAD, and group MCP, etc. The simulation studies show that our procedure is accurate.The housing transaction price in Baton Rouge and the commodity apartment price rises in Hong Kong are analyzed by the propose methodology.
报告时间: 2018年12月13日(周四) 16:15-17:00
报告地点:磬苑校区数学科学学院H306
报告题目III: A robust t-process regression model with independent errors
报 告 人: 王占锋（中国科学技术大学管理学院副教授）
报告摘要：Gaussian process regression (GPR) model is well-known to be susceptible to outliers. Robust process regression models based on t-process or other heavy-tailed processes have been developed to address the problem. However, due to the nature of the current definition for heavy-tailed processes, the unknown process regression function and the random errors are always defined jointly and thus dependently. This definition, mainly owing to thedependence assumption involved, is not justified in many practical problems and thus limits the application of those robust approaches. It also results in a limitation of the statistical properties and robust analysis. In this paper, we propose a new robust process regression model enabling independent random errors. An efficient estimation procedure is developed. We illustratethat the estimated random-effects are useful in detecting outlying curves. Statistical properties, such as unbiasedness and information consistency, are provided. Numerical studies show that the proposed method is robust against outliers and has a better performance in prediction compared with the existing models.
报告时间: 2018年12月13日(周四) 17:00-17:45
报告地点:磬苑校区数学科学学院H306
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科学技术处
2018年12月10日