Asymptotic Model Selection for Directed Networks with Hidden Variables
نویسندگان
چکیده
We extend the Bayesian Information Criterion (BIC), an asymptotic approximation for the marginal likelihood, to Bayesian networks with hidden variables. This approximation can be used to select models given large samples of data. The standard BIC as well as our extension punishes the complexity of a model according to the dimension of its parameters. We argue that the dimension of a Bayesian network with hidden variables is the rank of the Jacobian matrix of the transformation between the parameters of the network and the parameters of the observable variables. We compute the dimensions of several networks including the naive Bayes model with a hidden root node.
منابع مشابه
Asymptotic Model Selection and Identifiability of Directed Tree Models with Hidden Variables
The standard Bayesian Information Criterion (BIC) is derived under some regularity conditions which are not always satisfied by the graphical models with hidden variables. In this paper we derive the BIC score for Bayesian networks in the case when the data is binary and the underlying graph is a rooted tree and all the inner nodes represent hidden variables. This provides a direct generalizati...
متن کاملGraphical Models and Exponential Families
We provide a classi cation of graphical models according to their representation as subfamilies of exponential families. Undirected graphical models with no hidden variables are linear exponential families (LEFs), directed acyclic graphical models and chain graphs with no hidden variables, including Bayesian networks with several families of local distributions, are curved exponential families ...
متن کاملFactorized Asymptotic Bayesian Hidden Markov Models
This paper addresses the issue of model selection for hidden Markov models (HMMs). We generalize factorized asymptotic Bayesian inference (FAB), which has been recently developed for model selection on independent hidden variables (i.e., mixture models), for time-dependent hidden variables. As with FAB in mixture models, FAB for HMMs is derived as an iterative lower bound maximization algorithm...
متن کاملVariational algorithms for approximate Bayesian inference
The Bayesian framework for machine learning allows for the incorporation of prior knowledge in a coherent way, avoids overfitting problems, and provides a principled basis for selecting between alternative models. Unfortunately the computations required are usually intractable. This thesis presents a unified variational Bayesian (VB) framework which approximates these computations in models wit...
متن کاملCredit Risk Measurement of Trusted Customers Using Logistic Regression and Neural Networks
The issue of credit risk and deferred bank claims is one of the sensitive issues of banking industry, which can be considered as the main cause of bank failures. In recent years, the economic slowdown accompanied by inflation in Iran has led to an increase in deferred bank claims that could put the country's banking system in serious trouble. Accordingly, the current paper presents a prediction...
متن کامل