Related papers: Consistent Model Selection of Discrete Bayesian Ne…
The main goal of this paper is to describe a method for exact inference in general hybrid Bayesian networks (BNs) (with a mixture of discrete and continuous chance variables). Our method consists of approximating general hybrid Bayesian…
In this paper, we provide new complexity results for algorithms that learn discrete-variable Bayesian networks from data. Our results apply whenever the learning algorithm uses a scoring criterion that favors the simplest model able to…
We propose a general method for distributed Bayesian model choice, using the marginal likelihood, where a data set is split in non-overlapping subsets. These subsets are only accessed locally by individual workers and no data is shared…
Recently, there has been much interest in finding globally optimal Bayesian network structures. These techniques were developed for generative scores and can not be directly extended to discriminative scores, as desired for classification.…
The choice of free parameters in network models is subjective, since it depends on what topological properties are being monitored. However, we show that the Maximum Likelihood (ML) principle indicates a unique, statistically rigorous…
The problem of learning the structure of Bayesian networks from complete discrete data with a limit on parent set size is considered. Learning is cast explicitly as an optimisation problem where the goal is to find a BN structure which…
Computing the exact likelihood of data in large Bayesian networks consisting of thousands of vertices is often a difficult task. When these models contain many deterministic conditional probability tables and when the observed values are…
A Bayesian net (BN) is more than a succinct way to encode a probabilistic distribution; it also corresponds to a function used to answer queries. A BN can therefore be evaluated by the accuracy of the answers it returns. Many algorithms for…
Maximum likelihood estimates (MLEs) are asymptotically normally distributed, and this property is used in meta-analyses to test the heterogeneity of estimates, either for a single cluster or for several sub-groups. More recently, MLEs for…
We consider a sparse linear regression model, when the number of available predictors, $p$, is much larger than the sample size, $n$, and the number of non-zero coefficients, $p_0$, is small. To choose the regression model in this…
Bayesian networks are a versatile and powerful tool to model complex phenomena and the interplay of their components in a probabilistically principled way. Moving beyond the comparatively simple case of completely observed, static data,…
In a typical supervised machine learning setting, the predictions on all test instances are based on a common subset of features discovered during model training. However, using a different subset of features that is most informative for…
This article focuses on Bayesian estimation of a hierarchical linear model (HLM) from incomplete data assumed missing at random where continuous covariates C and discrete categorical covariates $D$ have interaction effects on a continuous…
We consider the use of Bayesian information criteria for selection of the graph underlying an Ising model. In an Ising model, the full conditional distributions of each variable form logistic regression models, and variable selection…
We explore the theoretical and numerical property of a fully Bayesian model selection method in sparse ultrahigh-dimensional settings, i.e., $p\gg n$, where $p$ is the number of covariates and $n$ is the sample size. Our method consists of…
Variable clustering is important for explanatory analysis. However, only few dedicated methods for variable clustering with the Gaussian graphical model have been proposed. Even more severe, small insignificant partial correlations due to…
We give a new consistent scoring function for structure learning of Bayesian networks. In contrast to traditional approaches to scorebased structure learning, such as BDeu or MDL, the complexity penalty that we propose is data-dependent and…
We propose a novel nonparametric online predictor for discrete labels conditioned on multivariate continuous features. The predictor is based on a feature space discretization induced by a full-fledged k-d tree with randomly picked…
A structural equation model (SEM) is an effective framework to reason over causal relationships represented via a directed acyclic graph (DAG). Recent advances have enabled effective maximum-likelihood point estimation of DAGs from…
Feedforward neural networks (FNNs) can be viewed as non-linear regression models, where covariates enter the model through a combination of weighted summations and non-linear functions. Although these models have some similarities to the…