Related papers: Asymptotic Model Selection for Directed Networks w…

Undirected graphical models are widely used in statistics, physics and machine vision. However Bayesian parameter estimation for undirected models is extremely challenging, since evaluation of the posterior typically involves the…

We introduce a class of neural networks derived from probabilistic models in the form of Bayesian networks. By imposing additional assumptions about the nature of the probabilistic models represented in the networks, we derive neural…

Identifying the number of communities is a fundamental problem in community detection, which has received increasing attention recently. However, rapid advances in technology have led to the emergence of large-scale networks in various…

Independence-based (IB) assignments to Bayesian belief networks were originally proposed as abductive explanations. IB assignments assign fewer variables in abductive explanations than do schemes assigning values to all evidentially…

Neural networks are one of the most popularly used methods in machine learning and artificial intelligence nowadays. Due to the universal approximation theorem (Hornik et al. (1989)), a neural network with one hidden layer can approximate…

Testing the validity of probabilistic models containing unmeasured (hidden) variables is shown to be a hard task. We show that the task of testing whether models are structurally incompatible with the data at hand, requires an exponential…

Factorial hidden Markov models (FHMMs) are powerful tools of modeling sequential data. Learning FHMMs yields a challenging simultaneous model selection issue, i.e., selecting the number of multiple Markov chains and the dimensionality of…

In networks of dynamic systems, one challenge is to identify the interconnection structure on the basis of measured signals. Inspired by a Bayesian approach in [1], in this paper, we explore a Bayesian model selection method for identifying…

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 this paper we investigate the geometry of a discrete Bayesian network whose graph is a tree all of whose variables are binary and the only observed variables are those labeling its leaves. We provide the full geometric description of…

Many statistical applications involve models for which it is difficult to evaluate the likelihood, but from which it is relatively easy to sample. Approximate Bayesian computation is a likelihood-free method for implementing Bayesian…

We propose a new method for parameter learning in Bayesian networks with qualitative influences. This method extends our previous work from networks of binary variables to networks of discrete variables with ordered values. The specified…

The estimation of Bayesian networks given high-dimensional data, in particular gene expression data, has been the focus of much recent research. Whilst there are several methods available for the estimation of such networks, these typically…

Bayesian variable selection is a powerful tool for data analysis, as it offers a principled method for variable selection that accounts for prior information and uncertainty. However, wider adoption of Bayesian variable selection has been…

Mixture models are becoming a popular tool for the clustering and classification of high-dimensional data. In such high dimensional applications, model selection is problematic. The Bayesian information criterion, which is popular in lower…

We consider the problem of choosing between parametric models for a discrete observable, taking a Bayesian approach in which the within-model prior distributions are allowed to be improper. In order to avoid the ambiguity in the marginal…

The key distinguishing property of a Bayesian approach is marginalization, rather than using a single setting of weights. Bayesian marginalization can particularly improve the accuracy and calibration of modern deep neural networks, which…

Bayesian variable selection has gained much empirical success recently in a variety of applications when the number $K$ of explanatory variables $(x_1,...,x_K)$ is possibly much larger than the sample size $n$. For generalized linear…

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…

Bayesian networks are widely utilised in various fields, offering elegant representations of factorisations and causal relationships. We use surjective functions to reduce the dimensionality of the Bayesian networks by combining states and…