發(fā)布時(shí)間：2018-06-10 04:27

  本文選題：概率圖模型 + 因子��； 參考：《青島大學(xué)》2017年碩士論文

【摘要】：概率圖模型利用圖形結(jié)構(gòu)所隱含的結(jié)構(gòu)特征,將概率分布變量間的關(guān)系給表示出來(lái),不僅變得更加直觀,同時(shí)也一定程度的簡(jiǎn)化了運(yùn)算。由于這樣的優(yōu)勢(shì),概率圖模型在不確定性推理中占據(jù)著重要的位置,并且在醫(yī)療診斷、人工智能、數(shù)據(jù)挖掘等方面有著很好的表現(xiàn)。對(duì)概率圖模型的模型表示,以及相應(yīng)的獨(dú)立性知識(shí)進(jìn)行研究,并討論了分布和圖之間的關(guān)系,給出幾個(gè)新的算法。第一部分介紹了幾個(gè)常用概率分布的表示,例如表格CPD、確定性CPD等離散節(jié)點(diǎn)變量的表示,高斯模型等連續(xù)節(jié)點(diǎn)變量的表示,以及混合模型。第二部分詳細(xì)介紹了貝葉斯網(wǎng)絡(luò)的模型表示,包括網(wǎng)絡(luò)結(jié)構(gòu)和獨(dú)立性,其中一種特殊的貝葉斯網(wǎng)絡(luò)—樸素貝葉斯網(wǎng)絡(luò),討論了貝葉斯網(wǎng)絡(luò)中分布和圖之間的關(guān)系,給出一個(gè)分布已知的情況下利用次序關(guān)系構(gòu)建網(wǎng)絡(luò)結(jié)構(gòu)圖的算法,并且提供了一種利用父節(jié)點(diǎn)尋找最優(yōu)次序關(guān)系的思路。第三部分介紹了馬爾可夫網(wǎng)絡(luò)的結(jié)構(gòu)圖以及參數(shù)化問(wèn)題,而參數(shù)化的過(guò)程一般被認(rèn)為是因子化的過(guò)程,于是給出了兩個(gè)新的搜索算法,分別關(guān)于最大團(tuán)和極大團(tuán),這為因子化做準(zhǔn)備,然后討論馬爾可夫網(wǎng)絡(luò)中的獨(dú)立性,并說(shuō)明它們之間的包含關(guān)系,同時(shí)介紹貝葉斯網(wǎng)絡(luò)向馬爾可夫網(wǎng)絡(luò)的轉(zhuǎn)化。最后對(duì)文章做出總結(jié),同時(shí)對(duì)分布和圖的轉(zhuǎn)化、算法的改進(jìn)以及兩大網(wǎng)絡(luò)間的轉(zhuǎn)化等方面所面臨的問(wèn)題做了說(shuō)明。
[Abstract]:The probabilistic graph model not only becomes more intuitive, but also simplifies the operation to a certain extent by using the implicit structural characteristics of the graph structure to express the relationship between the probability distribution variables. Because of this advantage, probabilistic graph model plays an important role in uncertain reasoning, and has a good performance in medical diagnosis, artificial intelligence, data mining and so on. The model representation of probabilistic graph model and the corresponding independence knowledge are studied. The relationship between distribution and graph is discussed and several new algorithms are given. The first part introduces the representation of several commonly used probability distributions, such as the representation of discrete node variables such as table CPD, deterministic CPDs, continuous node variables such as Gao Si model, and mixed models. In the second part, the model representation of Bayesian network is introduced in detail, including network structure and independence. A special Bayesian network-naive Bayesian network is introduced. The relationship between distribution and graph in Bayesian network is discussed. This paper presents an algorithm to construct the network structure diagram by using the order relation in the case of known distribution, and provides a way to find the optimal order relation by using the parent node. In the third part, we introduce the structure diagram and parameterization of Markov networks, and the parameterization process is generally considered as a factorization process. This is the preparation for factorization, then the independence of Markov networks is discussed, the inclusions between them are explained, and the transformation from Bayesian networks to Markov networks is also introduced. Finally, the paper summarizes the problems faced by the transformation of the distribution and graph, the improvement of the algorithm and the transformation between the two networks.
【學(xué)位授予單位】：青島大學(xué)
【學(xué)位級(jí)別】：碩士
【學(xué)位授予年份】：2017
【分類(lèi)號(hào)】：O21

【參考文獻(xiàn)】

相關(guān)期刊論文 前1條

1 劉建偉;黎海恩;周佳佳;羅雄麟;;概率圖模型的表示理論綜述[J];電子學(xué)報(bào);2016年05期

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本文編號(hào)：2001973