概率图模型是图灵奖获得者Pearl开发出来的用图来表示变量概率依赖关系的理论。概率图模型理论分为概率图模型表示理论,概率图模型推理理论和概率图模型学习理论。

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在人工智能、统计学、计算机系统、计算机视觉、自然语言处理和计算生物学等许多领域中,许多问题都可以被视为从局部信息中寻找一致的全局结论。概率图模型框架为这一范围广泛的问题提供了一个统一的视图,能够在具有大量属性和巨大数据集的问题中进行有效的推理、决策和学习。这门研究生水平的课程将为您在复杂问题中运用图模型中解决核心研究主题提供坚实的基础。本课程将涵盖三个方面: 核心表示,包括贝叶斯网络和马尔科夫网络,以及动态贝叶斯网络;概率推理算法,包括精确和近似; 以及图模型的参数和结构的学习方法。进入这门课程的学生应该预先具备概率、统计学和算法的工作知识,尽管这门课程的设计是为了让有较强数学背景的学生赶上并充分参与。希望通过本课程的学习,学生能够获得足够的实际应用的多变量概率建模和推理的工作知识,能够用通用模型在自己的领域内制定和解决广泛的问题。并且可以自己进入更专业的技术文献。

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Bayesian networks are probabilistic graphical models with a wide range of application areas including gene regulatory networks inference, risk analysis and image processing. Learning the structure of a Bayesian network (BNSL) from discrete data is known to be an NP-hard task with a superexponential search space of directed acyclic graphs. In this work, we propose a new polynomial time algorithm for discovering a subset of all possible cluster cuts, a greedy algorithm for approximately solving the resulting linear program, and a generalised arc consistency algorithm for the acyclicity constraint. We embed these in the constraint programmingbased branch-and-bound solver CPBayes and show that, despite being suboptimal, they improve performance by orders of magnitude. The resulting solver also compares favourably with GOBNILP, a state-of-the-art solver for the BNSL problem which solves an NP-hard problem to discover each cut and solves the linear program exactly.

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Bayesian networks are probabilistic graphical models with a wide range of application areas including gene regulatory networks inference, risk analysis and image processing. Learning the structure of a Bayesian network (BNSL) from discrete data is known to be an NP-hard task with a superexponential search space of directed acyclic graphs. In this work, we propose a new polynomial time algorithm for discovering a subset of all possible cluster cuts, a greedy algorithm for approximately solving the resulting linear program, and a generalised arc consistency algorithm for the acyclicity constraint. We embed these in the constraint programmingbased branch-and-bound solver CPBayes and show that, despite being suboptimal, they improve performance by orders of magnitude. The resulting solver also compares favourably with GOBNILP, a state-of-the-art solver for the BNSL problem which solves an NP-hard problem to discover each cut and solves the linear program exactly.

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