Dynamic importance sampling in Bayesian networks based on probability trees

In this paper we introduce a new dynamic importance sampling propagation algorithm for Bayesian networks. Importance sampling is based on using an auxiliary sampling distribution from which a set of configurations of the variables in the network is drawn, and the performance of the algorithm depends on the variance of the weights associated with the simulated configurations. The basic idea of dynamic importance sampling is to use the simulation of a configuration to modify the sampling distribution in order to improve its quality and so reducing the variance of the future weights. The paper shows that this can be achieved with a low computational effort. The experiments carried out show that the final results can be very good even in the case that the initial sampling distribution is far away from the optimum. 2004 Elsevier Inc. All rights reserved.Spanish Ministry of Science and Technology, project Elvira II (TIC2001-2973-C05-01 and 02

Approximate probability propagation with mixtures of truncated exponentials

AbstractMixtures of truncated exponentials (MTEs) are a powerful alternative to discretisation when working with hybrid Bayesian networks. One of the features of the MTE model is that standard propagation algorithms can be used. However, the complexity of the process is too high and therefore approximate methods, which tradeoff complexity for accuracy, become necessary. In this paper we propose an approximate propagation algorithm for MTE networks which is based on the Penniless propagation method already known for discrete variables. We also consider how to use Markov Chain Monte Carlo to carry out the probability propagation. The performance of the proposed methods is analysed in a series of experiments with random networks

Modeling Semi-Arid River-Aquifer Systems With Bayesian Networks and Artificial Neural Networks

In semiarid areas, precipitations usually appear in the form of big and brief floods, which affect the aquifer through water infiltration, causing groundwater temperature changes. These changes may have an impact on the physical, chemical and biological processes of the aquifer and, thus, modeling the groundwater temperature variations associated with stormy precipitation episodes is essential, especially since this kind of precipitation is becoming increasingly frequent in semiarid regions. In this paper, we compare the predictive performance of two popular tools in statistics and machine learning, namely Bayesian networks (BNs) and artificial neural networks (ANNs), in modeling groundwater temperature variation associated with precipitation events. More specifically, we trained a total of 2145 ANNs with different node configurations, from one to five layers. On the other hand, we trained three different BNs using different structure learning algorithms. We conclude that, while both tools are equivalent in terms of accuracy for predicting groundwater temperature drops, the computational cost associated with the estimation of Bayesian networks is significantly lower, and the resulting BN models are more versatile and allow a more detailed analysis

Chain event graphs : theory and application

This thesis is concerned with the Graphical model known as the Chain Event Graph (CEG) [1][60][61], and develops the theory that appears in the currently published papers on this work. Results derived are analogous to those produced for Bayesian Networks (BNs), and I show that for asymmetric problems the CEG is generally superior to the BN both as a representation of the problem and as an analytical tool. The CEG is designed to embody the conditional independence structure of problems whose state spaces are asymmetric and do not admit a natural Product Space structure. In this they differ from BNs and other structures with variable-based topologies. Chapter 1 details researchers' attempts to adapt BNs to model such problems, and outlines the advantages CEGs have over these adaptations. Chapter 2 describes the construction of CEGs. In chapter 3I create a semantic structure for the reading of CEGs, and derive results expressible in the form of context-specific conditional independence statements, that allow us to delve much more deeply into the independence structure of a problem than we can do with BNs. In chapter 4I develop algorithms for the updating of a CEG following observation of an event, analogous to the Local Message Passing algorithms used with BNs. These are more efficient than the BN-based algorithms when used with asymmetric problems. Chapter 5 develops the theory of Causal manipulation of CEGs, and introduces the singular manipulation, a class of interventions containing the set of interventions possible with BNs. I produce Back Door and Front Door Theorems analogous to those of Pearl [42], but more flexible as they allow asymmetric manipulations of asymmetric problems. The ideas and results of chapters 2 to 5 are summarised in chapter 6