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Some advances in discrete Markov networks and Bayesian networks
澳门新葡8455最新网站:2018年09月16日 22:01 点击数:

报告人:李本崇

报告地点:澳门新葡8455最新网站415报告厅

报告澳门新葡8455最新网站:2018年09月20日星期四10:00-11:00

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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.

主讲人概况:

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澳门新葡8455最新网站概率统计系工作。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。

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