Related papers: Consistent Model Selection of Discrete Bayesian Ne…
This paper describes a Bayesian method for learning causal networks using samples that were selected in a non-random manner from a population of interest. Examples of data obtained by non-random sampling include convenience samples and…
When a hybrid Bayesian network has conditionally deterministic variables with continuous parents, the joint density function for the continuous variables does not exist. Conditional linear Gaussian distributions can handle such cases when…
Good large sample performance is typically a minimum requirement of any model selection criterion. This article focuses on the consistency property of the Bayes factor, a commonly used model comparison tool, which has experienced a recent…
This paper describes a decision theoretic formulation of learning the graphical structure of a Bayesian Belief Network from data. This framework subsumes the standard Bayesian approach of choosing the model with the largest posterior…
Standard evaluations of Bayesian deep learning methods assume that metric estimates are reliable, but we show this assumption fails under data scarcity. Method rankings are not only unreliable at small $n$, but also dataset-dependent in…
Bayesian network (BN) structure discovery algorithms typically either make assumptions about the sparsity of the true underlying network, or are limited by computational constraints to networks with a small number of variables. While these…
We study active structure learning of Bayesian networks in an observational setting, in which there are external limitations on the number of variable values that can be observed from the same sample. Random samples are drawn from the joint…
When are inferences (whether Direct-Likelihood, Bayesian, or Frequentist) obtained from partial data valid? This paper answers this question by offering a new asymptotic theory about inference with missing data that is more general than…
In Stochastic blockmodels, which are among the most prominent statistical models for cluster analysis of complex networks, clusters are defined as groups of nodes with statistically similar link probabilities within and between groups. A…
Bayesian approaches to learn the graphical structure of Bayesian Belief Networks (BBNs) from databases share the assumption that the database is complete, that is, no entry is reported as unknown. Attempts to relax this assumption involve…
This article introduces a regularization and selection methods for directed networks with nodal homophily and nodal effects. The proposed approach not only preserves the statistical efficiency of the resulting estimator, but also ensures…
It has long been known that for the comparison of pairwise nested models, a decision based on the Bayes factor produces a consistent model selector (in the frequentist sense). Here we go beyond the usual consistency for nested pairwise…
This work initiates a systematic investigation of testing high-dimensional structured distributions by focusing on testing Bayesian networks -- the prototypical family of directed graphical models. A Bayesian network is defined by a…
Stable random variables are motivated by the central limit theorem for densities with (potentially) unbounded variance and can be thought of as natural generalizations of the Gaussian distribution to skewed and heavy-tailed phenomenon. In…
Dynamic Bayesian networks have been well explored in the literature as discrete-time models: however, their continuous-time extensions have seen comparatively little attention. In this paper, we propose the first constraint-based algorithm…
We empirically show that Bayesian inference can be inconsistent under misspecification in simple linear regression problems, both in a model averaging/selection and in a Bayesian ridge regression setting. We use the standard linear model,…
Networks are a commonly used mathematical model to describe the rich set of interactions between objects of interest. Many clustering methods have been developed in order to partition such structures, among which several rely on underlying…
The Bayesian brain hypothesis postulates that the brain accurately operates on statistical distributions according to Bayes' theorem. The random failure of presynaptic vesicles to release neurotransmitters may allow the brain to sample from…
Bayesian networks are convenient graphical expressions for high dimensional probability distributions representing complex relationships between a large number of random variables. They have been employed extensively in areas such as…
For nearly any challenging scientific problem evaluation of the likelihood is problematic if not impossible. Approximate Bayesian computation (ABC) allows us to employ the whole Bayesian formalism to problems where we can use simulations…