Evaluating the Uncertainty of a Bayesian Network Query Response by Using Joint Probability Distribution

Author(s):  
Yang Shao ◽  
Toshinori Miyoshi ◽  
Yasutaka Hasegawa ◽  
Hideyuki Ban
Author(s):  
Marco F. Ramoni ◽  
Paola Sebastiani

Born at the intersection of artificial intelligence, statistics, and probability, Bayesian networks (Pearl, 1988) are a representation formalism at the cutting edge of knowledge discovery and data mining (Heckerman, 1997). Bayesian networks belong to a more general class of models called probabilistic graphical models (Whittaker, 1990; Lauritzen, 1996) that arise from the combination of graph theory and probability theory, and their success rests on their ability to handle complex probabilistic models by decomposing them into smaller, amenable components. A probabilistic graphical model is defined by a graph, where nodes represent stochastic variables and arcs represent dependencies among such variables. These arcs are annotated by probability distribution shaping the interaction between the linked variables. A probabilistic graphical model is called a Bayesian network, when the graph connecting its variables is a directed acyclic graph (DAG). This graph represents conditional independence assumptions that are used to factorize the joint probability distribution of the network variables, thus making the process of learning from a large database amenable to computations. A Bayesian network induced from data can be used to investigate distant relationships between variables, as well as making prediction and explanation, by computing the conditional probability distribution of one variable, given the values of some others.


2018 ◽  
Vol 2 (1) ◽  
pp. 62
Author(s):  
Hasniati Hasniati ◽  
Arianti Arianti ◽  
William Philip

Bayesian Network dapat digunakan untuk menghitung probabilitas dari kehadiran berbagai gejala penyakit. Dalam tulisan ini, penulis menerapkan bayesian network model untuk menghitung probabilitas penyakit sesak nafas pada bayi. Bayesian network diterapkan berdasar pada data yang diperoleh melalui wawancara kepada dokter spesialis anak yaitu data nama penyakit, penyebab, dan gejala penyakit sesak nafas pada bayi. Struktur Bayesian Network penyakit sesak nafas bayi dibuat berdasarkan ada tidaknya keterkaitan antara gejala terhadap penyakit sesak nafas. Untuk setiap gejala yang direpresentasikan pada struktur bayesian network mempunyai estimasi parameter yang didapat dari data yang telah ada atau pengetahuan dari dokter spesialis. Data estimasi ini disebut nilai prior probaility atau nilai kepercayaan dari gejala penyakit sesak nafas bayi. Setelah diketahui prior probability, langkah berikutnya adalah menentukan Conditional probability (peluang bersyarat) antara jenis penyakit sesak nafas dengan masing-masing gejalanya. Pada langkah akhir, nilai posterior probability dihitung dengan mengambil nilai hasil joint probability distribution (JPD) yang telah diperoleh, kemudian nilai inilah yang digunakan untuk menghitung probabilitas kemunculan suatu gejala. Dengan mengambil satu contoh kasus bahwa bayi memiliki gejala sesak, lemah, gelisah dan demam, disimpulkan bahwa bayi menderita penyakit sesak nafas Pneumoni Neonatal sebesar 0,1688812743.


Author(s):  
Marco F. Ramoni ◽  
Paola Sebastiani

Born at the intersection of artificial intelligence, statistics, and probability, Bayesian networks (Pearl, 1988) are a representation formalism at the cutting edge of knowledge discovery and data mining (Heckerman, 1997). Bayesian networks belong to a more general class of models called probabilistic graphical models (Whittaker, 1990; Lauritzen, 1996) that arise from the combination of graph theory and probability theory, and their success rests on their ability to handle complex probabilistic models by decomposing them into smaller, amenable components. A probabilistic graphical model is defined by a graph, where nodes represent stochastic variables and arcs represent dependencies among such variables. These arcs are annotated by probability distribution shaping the interaction between the linked variables. A probabilistic graphical model is called a Bayesian network, when the graph connecting its variables is a directed acyclic graph (DAG). This graph represents conditional independence assumptions that are used to factorize the joint probability distribution of the network variables, thus making the process of learning from a large database amenable to computations. A Bayesian network induced from data can be used to investigate distant relationships between variables, as well as making prediction and explanation, by computing the conditional probability distribution of one variable, given the values of some others.


Author(s):  
Marco F. Ramoni ◽  
Paola Sebastiani

Born at the intersection of artificial intelligence, statistics, and probability, Bayesian networks (Pearl, 1988) are a representation formalism at the cutting edge of knowledge discovery and data mining (Heckerman, 1997). Bayesian networks belong to a more general class of models called probabilistic graphical models (Whittaker, 1990; Lauritzen, 1996) that arise from the combination of graph theory and probability theory, and their success rests on their ability to handle complex probabilistic models by decomposing them into smaller, amenable components. A probabilistic graphical model is defined by a graph, where nodes represent stochastic variables and arcs represent dependencies among such variables. These arcs are annotated by probability distribution shaping the interaction between the linked variables. A probabilistic graphical model is called a Bayesian network, when the graph connecting its variables is a directed acyclic graph (DAG). This graph represents conditional independence assumptions that are used to factorize the joint probability distribution of the network variables, thus making the process of learning from a large database amenable to computations. A Bayesian network induced from data can be used to investigate distant relationships between variables, as well as making prediction and explanation, by computing the conditional probability distribution of one variable, given the values of some others.


2014 ◽  
Vol 2014 ◽  
pp. 1-13
Author(s):  
Huilin Huang

We consider an inhomogeneous growing network with two types of vertices. The degree sequences of two different types of vertices are investigated, respectively. We not only prove that the asymptotical degree distribution of typesfor this process is power law with exponent2+1+δqs+β1-qs/αqs, but also give the strong law of large numbers for degree sequences of two different types of vertices by using a different method instead of Azuma’s inequality. Then we determine asymptotically the joint probability distribution of degree for pairs of adjacent vertices with the same type and with different types, respectively.


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