scholarly journals Imprecise Bayesian Networks as Causal Models

Information ◽  
2018 ◽  
Vol 9 (9) ◽  
pp. 211
Author(s):  
David Kinney
Keyword(s):  
Probability Distribution ◽  
Bayesian Networks ◽  
Causal Structure ◽  
Joint Probability ◽  
Joint Probability Distribution ◽  
Imprecise Probabilities ◽  
Causal Interpretation ◽  
Markov Condition ◽  
Bayes Nets ◽  
Causal Representation

This article considers the extent to which Bayesian networks with imprecise probabilities, which are used in statistics and computer science for predictive purposes, can be used to represent causal structure. It is argued that the adequacy conditions for causal representation in the precise context—the Causal Markov Condition and Minimality—do not readily translate into the imprecise context. Crucial to this argument is the fact that the independence relation between random variables can be understood in several different ways when the joint probability distribution over those variables is imprecise, none of which provides a compelling basis for the causal interpretation of imprecise Bayes nets. I conclude that there are serious limits to the use of imprecise Bayesian networks to represent causal structure.

Bayesian Networks Model for Estimation of Distribution Algorithms

2014 ◽  
Vol 926-930 ◽  
pp. 3594-3597
Author(s):  
Cai Chang Ding ◽  
Wen Xiu Peng ◽  
Wei Ming Wang
Keyword(s):  
Probability Distribution ◽  
Bayesian Networks ◽  
Evolutionary Computation ◽  
Joint Probability ◽  
Joint Probability Distribution ◽  
Estimation Of Distribution Algorithms ◽  
Previous Generation ◽  
Mutation Operators ◽  
Estimation Of Distribution ◽  
Distribution Algorithms

Estimation of Distribution Algorithms (EDAs) are a set of algorithms that belong to the field of Evolutionary Computation. In EDAs there are neither crossover nor mutation operators. Instead, the new population of individuals is sampled from a probability distribution, which is estimated from a database that contains the selected individuals from the previous generation. Thus, the interrelations between the different variables that represent the individuals may be explicitly expressed through the joint probability distribution associated with the individuals selected at each generation.

Learning Bayesian Networks

2011 ◽  
pp. 315-321
Author(s):  
Marco F. Ramoni ◽  
Paola Sebastiani
Keyword(s):  
Probability Distribution ◽  
Bayesian Networks ◽  
Bayesian Network ◽  
Graphical Models ◽  
Graphical Model ◽  
Joint Probability ◽  
Joint Probability Distribution ◽  
Probabilistic Graphical Model ◽  
Conditional Probability Distribution ◽  
Statistics And Probability

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.

Learning Bayesian Networks

2011 ◽  
pp. 674-677
Author(s):  
Marco F. Ramoni ◽  
Paola Sebastiani
Keyword(s):  
Probability Distribution ◽  
Bayesian Networks ◽  
Bayesian Network ◽  
Graphical Models ◽  
Graphical Model ◽  
Joint Probability ◽  
Joint Probability Distribution ◽  
Probabilistic Graphical Model ◽  
Conditional Probability Distribution ◽  
Statistics And Probability

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.

Learning Bayesian Networks

2011 ◽  
pp. 1124-1128
Author(s):  
Marco F. Ramoni ◽  
Paola Sebastiani
Keyword(s):  
Probability Distribution ◽  
Bayesian Networks ◽  
Bayesian Network ◽  
Graphical Models ◽  
Graphical Model ◽  
Joint Probability ◽  
Joint Probability Distribution ◽  
Probabilistic Graphical Model ◽  
Conditional Probability Distribution ◽  
Statistics And Probability

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.

scholarly journals The Degree Analysis of an Inhomogeneous Growing Network with Two Types of Vertices

2014 ◽  
Vol 2014 ◽  
pp. 1-13
Author(s):  
Huilin Huang
Keyword(s):  
Probability Distribution ◽  
Law Of Large Numbers ◽  
Joint Probability ◽  
Joint Probability Distribution ◽  
Degree Sequences ◽  
Strong Law ◽  
Large Numbers ◽  
Different Types ◽  
Azuma's Inequality ◽  
Growing Network

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.

Sign in / Sign up

Export Citation Format

Share Document