Some advances in discrete Markov networks and Bayesian networks

报告人：李本崇
报告地点：数学与统计学院415报告厅
报告时间：2018年09月20日星期四10:00-11:00
邀请人：
报告摘要：

Markov networks and Bayesian networks are two popular models for classification. Vapnik-Chervonenkis dimension and Euclidean dimension are two measures of complexity of a class of functions. We show that these two dimensional values of the concept class induced by a discrete Markov network are identical, and the value equals dimension of the toric ideal corresponding to this Markov network as long as the toric ideal is nontrivial. Furthermore, we provide a simple formula for calculating the dimensions of discrete Markov networks. For a general Bayesian network, we show that dimension of the corresponding toric ideal offers an upper bound of Euclidean dimension. Consider VC dimensions induced by the concept classes of a class of Bayesian networks, where each underlying graph is a cycle containing exactly one V-structure. We prove that the three quantities mentioned above for this kind of Bayesian networks are equal.

主讲人简介：
2001年考入东北师范大学数学与应用数学专业，2005年在该校概率论与数理统计方向读研，2007年免试读该方向的博士研究生，2012年12月博士毕业。2013年3月至今在西安电子科技大学数学与统计学院概率统计系工作。十余年来，致力于图模型和代数统计学的学习和研究，已在国际知名统计学和数学期刊Pattern Recognition, Statistica Sinica等发表和接收SCI论文10 篇；曾主持一项国家自然科学基金青年基金项目，现主持陕西省自然科学青年基金一项。