
Automated Analytic Asymptotic Evaluation of the Marginal Likelihood for Latent Models
We present and implement two algorithms for analytic asymptotic evaluati...
read it

Asymptotic Model Selection for Naive Bayesian Networks
We develop a closed form asymptotic formula to compute the marginal like...
read it

Efficient Approximations for the Marginal Likelihood of Incomplete Data Given a Bayesian Network
We discuss Bayesian methods for learning Bayesian networks when data set...
read it

Algebraic Statistics in Model Selection
We develop the necessary theory in computational algebraic geometry to p...
read it

Effective Dimensions of Hierarchical Latent Class Models
Hierarchical latent class (HLC) models are treestructured Bayesian netw...
read it

Dimension of Marginals of Kronecker Product Models
A Kronecker product model is the set of visible marginal probability dis...
read it

On Testing Whether an Embedded Bayesian Network Represents a Probability Model
Testing the validity of probabilistic models containing unmeasured (hidd...
read it
Asymptotic Model Selection for Directed Networks with Hidden Variables
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.
READ FULL TEXT
Comments
There are no comments yet.