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【ML】Probabilistic Graphical Mode

【ML】Probabilistic Graphical Mode

作者: 盐果儿 | 来源:发表于2022-08-29 02:30 被阅读0次

    Probabilistic Graphical Model (PGM, or Graphical Model) is a probabilistic model for which a graph expresses the conditional dependence structure between random variables. Two branches of graphical representations of distributions are commonly used, namely, Bayesian networks and Markov random fields.

    Bayesian network is a probabilistic graphical model that represents a set of variables and their conditional dependencies via a directed acyclic graph.


    Bayesian Network Syntax

    The graph: G = {V, E}    X_{1}, X_{2}, ..., X{n} \in V

    A set of local conditional distributions: P = {p(X_{i} | pa(X_{i})),  X_{i} \in V}

    Bayesian Network Semantics

    A Bayesian Network N with nodes X_{1}, X_{2}, ... , X_{n}defined a joint distribution

    p_{N}(X_{1}, X_{2}, ..., X_{n}) = \prod ^n _{i=1} p(X_{i} | pa(X_{i}))

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