概率圖模型是圖靈獎獲得者Pearl開發出來的用圖來表示變量概率依賴關係的理論。概率圖模型理論分為概率圖模型表示理論,概率圖模型推理理論和概率圖模型學習理論。

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在人工智能、統計學、計算機係統、計算機視覺、自然語言處理和計算生物學等許多領域中,許多問題都可以被視為從局部信息中尋找一致的全局結論。概率圖模型框架為這一範圍廣泛的問題提供了一個統一的視圖,能夠在具有大量屬性和巨大數據集的問題中進行有效的推理、決策和學習。這門研究生水平的課程將為您在複雜問題中運用圖模型中解決核心研究主題提供堅實的基礎。本課程將涵蓋三個方麵: 核心表示,包括貝葉斯網絡和馬爾科夫網絡,以及動態貝葉斯網絡;概率推理算法,包括精確和近似; 以及圖模型的參數和結構的學習方法。進入這門課程的學生應該預先具備概率、統計學和算法的工作知識,盡管這門課程的設計是為了讓有較強數學背景的學生趕上並充分參與。希望通過本課程的學習,學生能夠獲得足夠的實際應用的多變量概率建模和推理的工作知識,能夠用通用模型在自己的領域內製定和解決廣泛的問題。並且可以自己進入更專業的技術文獻。

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We present an information-based uncertainty quantification method for general Markov Random Fields. Markov Random Fields (MRF) are structured, probabilistic graphical models over undirected graphs, and provide a fundamental unifying modeling tool for statistical mechanics, probabilistic machine learning, and artificial intelligence. Typically MRFs are complex and high-dimensional with nodes and edges (connections) built in a modular fashion from simpler, low-dimensional probabilistic models and their local connections; in turn, this modularity allows to incorporate available data to MRFs and efficiently simulate them by leveraging their graph-theoretic structure. Learning graphical models from data and/or constructing them from physical modeling and constraints necessarily involves uncertainties inherited from data, modeling choices, or numerical approximations. These uncertainties in the MRF can be manifested either in the graph structure or the probability distribution functions, and necessarily will propagate in predictions for quantities of interest. Here we quantify such uncertainties using tight, information based bounds on the predictions of quantities of interest; these bounds take advantage of the graphical structure of MRFs and are capable of handling the inherent high-dimensionality of such graphical models. We demonstrate our methods in MRFs for medical diagnostics and statistical mechanics models. In the latter, we develop uncertainty quantification bounds for finite size effects and phase diagrams, which constitute two of the typical predictions goals of statistical mechanics modeling.

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We present an information-based uncertainty quantification method for general Markov Random Fields. Markov Random Fields (MRF) are structured, probabilistic graphical models over undirected graphs, and provide a fundamental unifying modeling tool for statistical mechanics, probabilistic machine learning, and artificial intelligence. Typically MRFs are complex and high-dimensional with nodes and edges (connections) built in a modular fashion from simpler, low-dimensional probabilistic models and their local connections; in turn, this modularity allows to incorporate available data to MRFs and efficiently simulate them by leveraging their graph-theoretic structure. Learning graphical models from data and/or constructing them from physical modeling and constraints necessarily involves uncertainties inherited from data, modeling choices, or numerical approximations. These uncertainties in the MRF can be manifested either in the graph structure or the probability distribution functions, and necessarily will propagate in predictions for quantities of interest. Here we quantify such uncertainties using tight, information based bounds on the predictions of quantities of interest; these bounds take advantage of the graphical structure of MRFs and are capable of handling the inherent high-dimensionality of such graphical models. We demonstrate our methods in MRFs for medical diagnostics and statistical mechanics models. In the latter, we develop uncertainty quantification bounds for finite size effects and phase diagrams, which constitute two of the typical predictions goals of statistical mechanics modeling.

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