Related papers: Asymptotic Model Selection for Naive Bayesian Netw…
We develop a Bayesian approach for selecting the model which is the most supported by the data within a class of marginal models for categorical variables formulated through equality and/or inequality constraints on generalised logits…
Bayesian methods - either based on Bayes Factors or BIC - are now widely used for model selection. One property that might reasonably be demanded of any model selection method is that if a model ${M}_{1}$ is preferred to a model ${M}_{0}$,…
Bayesian hierarchical clustering (BHC) is an agglomerative clustering method, where a probabilistic model is defined and its marginal likelihoods are evaluated to decide which clusters to merge. While BHC provides a few advantages over…
Standard variational lower bounds used to train latent variable models produce biased estimates of most quantities of interest. We introduce an unbiased estimator of the log marginal likelihood and its gradients for latent variable models…
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…
An inductive probabilistic classification rule must generally obey the principles of Bayesian predictive inference, such that all observed and unobserved stochastic quantities are jointly modeled and the parameter uncertainty is fully…
In a thought-provoking paper, Efron (2011) investigated the merit and limitation of an empirical Bayes method to correct selection bias based on Tweedie's formula first reported by \cite{Robbins:1956}. The exceptional virtue of Tweedie's…
Undirected graphical models known as Markov networks are popular for a wide variety of applications ranging from statistical physics to computational biology. Traditionally, learning of the network structure has been done under the…
The Bayesian information criterion (BIC), defined as the observed data log likelihood minus a penalty term based on the sample size $N$, is a popular model selection criterion for factor analysis with complete data. This definition has also…
For marginal structural models, which recently play an important role in causal inference, we consider a model selection problem in the framework of a semiparametric approach using inverse-probability-weighted estimation or doubly robust…
In this work, we attempt to refine the classic asymptotic formulae to describe the probability distribution of likelihood-ratio statistical tests. The idea is to split the probability distribution function into two parts. One part is…
Computation of the marginal likelihood from a simulated posterior distribution is central to Bayesian model selection but is computationally difficult. I argue that the marginal likelihood can be reliably computed from a posterior sample by…
In the problem of selecting variables in a multivariate linear regression model, we derive new Bayesian information criteria based on a prior mixing a smooth distribution and a delta distribution. Each of them can be interpreted as a fusion…
This paper introduces a new version of the smoothly trimmed mean with a more general version of weights, which can be used as an alternative to the classical trimmed mean. We derive its asymptotic variance and to further investigate its…
A serious problem in learning probabilistic models is the presence of hidden variables. These variables are not observed, yet interact with several of the observed variables. Detecting hidden variables poses two problems: determining the…
The use of Bayesian information criterion (BIC) in the model selection procedure is under the assumption that the observations are independent and identically distributed (i.i.d.). However, in practice, we do not always have i.i.d. samples.…
Bayesian networks (BNs) are a widely used class of probabilistic graphical models employed in numerous application domains. However, inferring the network's graphical structure from data remains challenging. Bayesian structure learners…
We introduce a probabilistic model with implicit norm regularization for learning nonnegative matrix factorization (NMF) that is commonly used for predicting missing values and finding hidden patterns in the data, in which the matrix…
In modern data analysis, it is common to select a model before performing statistical inference. Selective inference tools make adjustments for the model selection process in order to ensure reliable inference post selection. In this paper,…
If the probability distribution model aims to approximate the hidden mother distribution, it is imperative to establish a useful criterion for the resemblance between the mother and the model distributions. This study proposes a criterion…