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Probability Models of Data Generation
Published in Richard M. Golden, Statistical Machine Learning, 2020
The Markov blanket of a random variable x~ in a Bayesian network is the minimal set of all random variables which must be observable in order to completely specify the behavior of x~. A learning machine, for example, can learn the probabilistic rules governing the behavior of a random variable x~ in a Bayesian network by only observing the joint frequency distribution of x~ and the random variables in the Markov blanket of x~.
Advanced Properties of Bayesian Networks
Published in Richard E. Neapolitan, Xia Jiang, Artificial Intelligence, 2018
Richard E. Neapolitan, Xia Jiang
Let V be a set of random variables, P be theirjoint probability distribution, and X ∊ V. Then a Markov blanket M of X is any set of variables such that X is conditionally independent of all the other variables given M. That is,
Beyond Purchase Intentions: Mining Behavioral Intentions of Social-Network Users
Published in International Journal of Human–Computer Interaction, 2022
A Markov Blanket of a variable t is a minimal variable subset conditioned on which all other variables are probabilistically independent of t. The Markov Blanket of a BN node, MB(t) is the set of its parents, P(t); children, C(t); and spouses, U(t) as encoded by the structure of the BN. As shown in Koller and Sahami (1996), the Markov Blanket of a given target variable is the theoretically optimal set of variables to predict its value. However, simply considering all the features in the Markov Blanket of the behavioral intention node is unsatisfactory in our case, due to the existence of latent variables. Thus, a better strategy would be to first find an “approximated” Markov Blanket of the target node, which includes the variables in the sets P(t), C(t), and U(t) as discussed above. Then, identify the Markov Blanket of each latent variable that is also a member of the target’s approximated Markov Blanket and include the features in the union of those blankets in our feature set (in addition, of course, to features in ). That is, our feature set is:
Variable Selection for Artificial Neural Networks with Applications for Stock Price Prediction
Published in Applied Artificial Intelligence, 2019
Let be a set of the random variables involved in a model. Then, the Markov blanket of a random variable is defined as a minimal set of random variables such that when it is conditioned, is independent of the rest of random variables . The Markov blanket is identified as the union of the set of parent nodes of node , the set of child nodes , and the spouse nodes of in the Bayesian network structure.
Adoption of electric vehicles: Which factors are really important?
Published in International Journal of Sustainable Transportation, 2021
Elena Higueras-Castillo, Alberto Guillén, Luis-Javier Herrera, Francisco Liébana-Cabanillas
This algorithm is based on the Markov blanket concept. Given a set of input variables X and an output variable Y, a set of variables Mi in X is said to be a Markov blanket for a variable xi in X with respect to Y, if that is, if Mi has itself all the information that xi has about Y. A Markov blanket is thus, a group of variables subsuming the information content of a certain variable. The algorithm operates in a backwards way, starting from the complete set of variables X, and iteratively discarding those which are detected to have a Markov Blanket in the remaining set of variables (named from now on XG).