Related papers: Asymptotic Model Selection for Naive Bayesian Netw…
We consider approximate Bayesian model choice for model selection problems that involve models whose Fisher-information matrices may fail to be invertible along other competing submodels. Such singular models do not obey the regularity…
Bayesian network structure learning is often performed in a Bayesian setting, by evaluating candidate structures using their posterior probabilities for a given data set. Score-based algorithms then use those posterior probabilities as an…
A method of calculating probability values from a system of marginal constraints is presented. Previous systems for finding the probability of a single attribute have either made an independence assumption concerning the evidence or have…
Low-dimensional probability models for local distribution functions in a Bayesian network include decision trees, decision graphs, and causal independence models. We describe a new probability model for discrete Bayesian networks, which we…
We propose and analyze nonparametric tests of the null hypothesis that a function belongs to a specified parametric family. The tests are based on BIC approximations, \pi_{BIC}, to the posterior probability of the null model, and may be…
Popular statistical software provides Bayesian information criterion (BIC) for multilevel models or linear mixed models. However, it has been observed that the combination of statistical literature and software documentation has led to…
In Bayesian statistics, the marginal likelihood, also known as the evidence, is used to evaluate model fit as it quantifies the joint probability of the data under the prior. In contrast, non-Bayesian models are typically compared using…
Double-descent refers to the unexpected drop in test loss of a learning algorithm beyond an interpolating threshold with over-parameterization, which is not predicted by information criteria in their classical forms due to the limitations…
In model selection literature, two classes of criteria perform well asymptotically in different situations: Bayesian information criterion (BIC) (as a representative) is consistent in selection when the true model is finite dimensional…
The paper presents a novel asymptotic distribution for a mle when the log--likelihood is strictly concave in the parameter for all data points; for example, the exponential family. The new asymptotic distribution can be seen as a refinement…
Data augmentation is often used to incorporate inductive biases into models. Traditionally, these are hand-crafted and tuned with cross validation. The Bayesian paradigm for model selection provides a path towards end-to-end learning of…
We study the properties of variational Bayes approximations for exponential family models with missing values. It is shown that the iterative algorithm for obtaining the variational Bayesian estimator converges locally to the true value…
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…
Given a set of possible models (e.g., Bayesian network structures) and a data sample, in the unsupervised model selection problem the task is to choose the most accurate model with respect to the domain joint probability distribution. In…
Given a set of possible models (e.g., Bayesian network structures) and a data sample, in the unsupervised model selection problem the task is to choose the most accurate model with respect to the domain joint probability distribution. In…
Approximate Bayesian computation allows for statistical analysis in models with intractable likelihoods. In this paper we consider the asymptotic behaviour of the posterior distribution obtained by this method. We give general results on…
While the Bayesian Information Criterion (BIC) and Akaike Information Criterion (AIC) are powerful tools for model selection in linear regression, they are built on different prior assumptions and thereby apply to different data generation…
How do we compare between hypotheses that are entirely consistent with observations? The marginal likelihood (aka Bayesian evidence), which represents the probability of generating our observations from a prior, provides a distinctive…
This paper is concerned with asymptotic theory for penalized spline estimator in bivariate additive model. The focus of this paper is put upon the penalized spline estimator obtained by the backfitting algorithm. The convergence of the…
Models with intractable likelihood functions arise in areas including network analysis and spatial statistics, especially those involving Gibbs random fields. Posterior parameter es timation in these settings is termed a doubly-intractable…