报告题目： Composite likelihoods of discrete graphical models with application on U.S. Senators voting records data

报告人： 王南伟

报告时间地点：2017年6月30日11：00-11:45，理科楼407

摘要：

Discrete graphical models are an essential tool in the identification of the relationship between variables in complex high-dimensional problems. When the number of variables p is large, computing  the maximum likelihood estimate (henceforth abbreviated MLE) of the parameter is difficult. In our work, we estimate the composite MLE rather than the MLE, that is, the value of the parameter that maximizes the product of local conditional or marginal likelihoods centered around each vertex v of the graph underlying the model.

The existence of the MLE in  discrete graphical models has important consequences for inference. Determining whether this estimate exists is equivalent to finding whether the data belongs to the boundary of the marginal polytope of the model. Fienberg and Rinaldo (2012) gave a linear programming method that determines the smallest such face for relatively low-dimensional problems. In our work, we consider higher-dimensional problems. We develop the methology to obtain an outer and inner approximation to the smallest face of the marginal polytope containing the data vector. Outer approximations are obtained by looking at submodels of the original hierarchical model, and inner approximations are obtained by working with larger models.

We put our work in practice by applying it to the U.S. Senators voting records dataset.

报告人简介：

王南伟博士, 于2017年4月毕业于加拿大York University，并获统计学博士学位。他在应用统计，graphical models， exponential family distributions 等领域开展了一系列研究工作，在Annals of Statistics 和  Journal of Multivariate Analysis 国际权威期刊上发表2篇论文。