Antonio Salmerón

Review: Bayesian networks in environmental modelling

Bayesian networks (BNs), also known as Bayesian belief networks or Bayes nets, are a kind of probabilistic graphical model that has become very popular to practitioners mainly due to the powerful probability theory involved, which makes them able to deal with a wide range of problems. The goal of this review is to show how BNs are being used in environmental modelling. We are interested in the application of BNs, from January 1990 to December 2010, in the areas of the ISI Web of Knowledge related to Environmental Sciences. It is noted that only the 4.2% of the papers have been published under this item. The different steps that configure modelling via BNs have been revised: aim of the model, data pre-processing, model learning, validation and software. Our literature review indicates that BNs have barely been used for Environmental Science and their potential is, as yet, largely unexploited.

Mixtures of Truncated Exponentials in Hybrid Bayesian Networks

In this paper we propose the use of mixtures of truncated exponential (MTE) distributions in hybrid Bayesian networks. We study the properties of the MTE distribution and show how exact probability propagation can be carried out by means of a local computation algorithm. One feature of this model is that no restriction is made about the order among the variables either discrete or continuous. Computations are performed over a representation of probabilistic potentials based on probability trees, expanded to allow discrete and continuous variables simultaneously. Finally, a Markov chain Monte Carlo algorithm is described with the aim of dealing with complex networks.

Importance sampling in Bayesian networks using probability trees

In this paper a new Monte-Carlo algorithm for the propagation of probabilities in Bayesian networks is proposed. This algorithm has two stages: in the first one an approximate propagation is carried out by means of a deletion sequence of the variables. In the second stage a sample is obtained using as sampling distribution the calculations of the first step. The different configurations of the sample are weighted according to the importance sampling technique. We show how the use of probability trees to store and to approximate probability potentials, and a careful selection of the deletion sequence, make this algorithm able to propagate over large networks with extreme probabilities.

INFERENCE IN HYBRID BAYESIAN NETWORKS

Abstract Since the 1980s, Bayesian networks (BNs) have become increasingly popular for building statistical models of complex systems. This is particularly true for boolean systems, where BNs often prove to be a more efficient modelling framework than traditional reliability techniques (like fault trees and reliability block diagrams). However, limitations in the BNs’ calculation engine have prevented BNs from becoming equally popular for domains containing mixtures of both discrete and continuous variables (the so-called hybrid domains). In this paper we focus on these difficulties, and summarize some of the last decades research on inference in hybrid Bayesian networks. The discussions are linked to an example model for estimating human reliability.

Mixtures of truncated basis functions

In this paper we propose a framework, called mixtures of truncated basis functions (MoTBFs), for representing general hybrid Bayesian networks. The proposed framework generalizes both the mixture of truncated exponentials (MTEs) framework and the Mixture of Polynomials (MoPs) framework. Similar to MTEs and MoPs, MoTBFs are defined so that the potentials are closed under combination and marginalization, which ensures that inference in MoTBF networks can be performed efficiently using the Shafer-Shenoy architecture. Based on a generalized Fourier series approximation, we devise a method for efficiently approximating an arbitrary density function using the MoTBF framework. The translation method is more flexible than existing MTE or MoP-based methods, and it supports an online/anytime tradeoff between the accuracy and the complexity of the approximation. Experimental results show that the approximations obtained are either comparable or significantly better than the approximations obtained using existing methods.

Learning hybrid Bayesian networks using mixtures of truncated exponentials

In this paper we introduce an algorithm for learning hybrid Bayesian networks from data. The result of the algorithm is a network where the conditional distribution for each variable is a mixture of truncated exponentials (MTE), so that no restrictions on the network topology are imposed. The structure of the network is obtained by searching over the space of candidate networks using optimisation methods. The conditional densities are estimated by means of Gaussian kernel densities that afterwards are approximated by MTEs, so that the resulting network is appropriate for using standard algorithms for probabilistic reasoning. The behaviour of the proposed algorithm is tested using a set of real-world and artificially generated databases.

Advances in Bayesian networks

Hypercausality, Randomisation Local and Global Independence.- Interface Verification for Multiagent Probabilistic Inference.- Optimal Time-Space Tradeoff In Probabilistic Inference.- Hierarchical Junction Trees.- Algorithms for Approximate Probability Propagation in Bayesian Networks.- Abductive Inference in Bayesian Networks: A Review.- Causal Models, Value of Intervention, and Search for Opportunities.- Advances in Decision Graphs.- Real-World Applications of Influence Diagrams.- Learning Bayesian Networks by Floating Search Methods.- A Graphical Meta-Model for Reasoning about Bayesian Network Structure.- Restricted Bayesian Network Structure Learning.- Scaled Conjugate Gradients for Maximum Likelihood: An Empirical Comparison with the EM Algorithm.- Learning Essential Graph Markov Models from Data.- Fast Propagation Algorithms for Singly Connected Networks and their Applications to Information Retrieval.- Continuous Speech Recognition Using Dynamic Bayesian Networks: A Fast Decoding Algorithm.- Applications of Bayesian Networks in Meteorology.

Lazy evaluation in penniless propagation over join trees

In this paper, we investigate the application of the ideas behind Lazy propagation to the Penniless propagation scheme. Probabilistic potentials attached to the messages and the nodes of the join tree are represented in a factorized way as a product of (approximate) probability trees, and the combination operations are postponed until they are compulsory for the deletion of a variable. We tested two variations of the basic Lazy scheme: One is based on keeping a hash table for the operations with probabilistic potentials that are carried out more than once during the propagation, to avoid repeating computations; the other uses a heuristic method to determine the order of the operations when combining a set of potentials.

Estimating mixtures of truncated exponentials in hybrid bayesian networks

The MTE (Mixture of Truncated Exponentials) model allows to deal with Bayesian networks containing discrete and continuous variables simultaneously. This model offers an alternative to discretisation, since standard algorithms to compute the posterior probabilities in the network, in principle designed for discrete variables, can be directly applied over MTE models. In this paper, we study the problem of estimating these models from data. We propose an iterative algorithm based on least squares approximation. The performance of the algorithm is tested both with artificial and actual data.

Approximating Conditional MTE Distributions by Means of Mixed Trees

Mixtures of truncated exponential (MTE) distributions have been shown to be a powerful alternative to discretisation within the framework of Bayesian networks. One of the features of the MTE model is that standard propagation algorithms as Shenoy-Shafer and Lazy propagation can be used. Estimating conditional MTE densities from data is a rather difficult problem since, as far as we know, such densities cannot be expressed in parametric form in the general case. In the univariate case, regression-based estimators have been successfully employed. In this paper, we propose a method to estimate conditional MTE densities using mixed trees, which are graphical structures similar to classification trees. Criteria for selecting the variables during the construction of the tree and for pruning the leaves are defined in terms of the mean square error and entropy-like measures.