Related papers: Automated Analytic Asymptotic Evaluation of the Ma…

We develop a closed form asymptotic formula to compute the marginal likelihood of data given a naive Bayesian network model with two hidden states and binary features. This formula deviates from the standard BIC score. Our work provides a…

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…

The standard Bayesian Information Criterion (BIC) is derived under 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…

Hierarchical learning models, such as mixture models and Bayesian networks, are widely employed for unsupervised learning tasks, such as clustering analysis. They consist of observable and hidden variables, which represent the given data…

Hierarchical statistical models are widely employed in information science and data engineering. The models consist of two types of variables: observable variables that represent the given data and latent variables for the unobservable…

We study mixed models with a single grouping factor, where inference about unknown parameters requires optimizing a marginal likelihood defined by an intractable integral. Low-dimensional numerical integration techniques are regularly used…

Implementing Bayesian inference is often computationally challenging in applications involving complex models, and sometimes calculating the likelihood itself is difficult. Synthetic likelihood is one approach for carrying out inference…

We discuss Bayesian methods for learning Bayesian networks when data sets are incomplete. In particular, we examine asymptotic approximations for the marginal likelihood of incomplete data given a Bayesian network. We consider the Laplace…

The Ising model has become a popular psychometric model for analyzing item response data. The statistical inference of the Ising model is typically carried out via a pseudo-likelihood, as the standard likelihood approach suffers from a high…

Approximate Bayesian computation (ABC) is a popular technique for approximating likelihoods and is often used in parameter estimation when the likelihood functions are analytically intractable. Although the use of ABC is widespread in many…

Although approximate Bayesian computation (ABC) has become a popular technique for performing parameter estimation when the likelihood functions are analytically intractable there has not as yet been a complete investigation of the…

The accurate asymptotic evaluation of marginal likelihood integrals is a fundamental problem in Bayesian statistics. Following the approach introduced by Watanabe, we translate this into a problem of computational algebraic geometry,…

Machine learning provides algorithms that can learn from data and make inferences or predictions on data. Bayesian networks are a class of graphical models that allow to represent a collection of random variables and their condititional…

We propose using recognition networks for approximate inference inBayesian networks (BNs). A recognition network is a multilayerperception (MLP) trained to predict posterior marginals given observedevidence in a particular BN. The input to…

The marginal likelihood is a well established model selection criterion in Bayesian statistics. It also allows to efficiently calculate the marginal posterior model probabilities that can be used for Bayesian model averaging of quantities…

In computational mechanics, multiple models are often present to describe a physical system. While Bayesian model selection is a helpful tool to compare these models using measurement data, it requires the computationally expensive…

This article presents a Bayesian inferential method where the likelihood for a model is unknown but where data can easily be simulated from the model. We discretize simulated (continuous) data to estimate the implicit likelihood in a…

This paper develops asymptotic theory for estimation of parameters in regression models for binomial response time series where serial dependence is present through a latent process. Use of generalized linear model (GLM) estimating…

We propose a general approach to construct weighted likelihood estimating equations with the aim of obtaining robust parameter estimates. We modify the standard likelihood equations by incorporating a weight that reflects the statistical…

This paper develops a Bayesian computational platform at the interface between posterior sampling and optimization in models whose marginal likelihoods are difficult to evaluate. Inspired by adversarial optimization, namely Generative…