Approximate Probability Propagation with Mixtures of Truncated Exponentials*

Mixtures 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

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

Fast factorisation of probabilistic potentials and its application to approximate inference in Bayesian networks

We present an efficient procedure for factorising probabilistic potentials represented as probability trees. This new procedure is able to detect some regularities that cannot be captured by existing methods. In cases where an exact decomposition is not achievable, we propose a heuristic way to carry out approximate factorisations guided by a parameter called factorisation degree, which is fast to compute. We show how this parameter can be used to control the tradeoff between complexity and accuracy in approximate inference algorithms for Bayesian networks

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 con gurations 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 con gurations. The basic idea of dynamic importance sampling is to use the simulation of a con guration 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 nal results can be very good even in the case that the initial sampling distribution is far away from the optimum

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

A Review of Inference Algorithms for Hybrid Bayesian Networks

Hybrid Bayesian networks have received an increasing attention during the last years. The difference with respect to standard Bayesian networks is that they can host discrete and continuous variables simultaneously, which extends the applicability of the Bayesian network framework in general. However, this extra feature also comes at a cost: inference in these types of models is computationally more challenging and the underlying models and updating procedures may not even support closed-form solutions. In this paper we provide an overview of the main trends and principled approaches for performing inference in hybrid Bayesian networks. The methods covered in the paper are organized and discussed according to their methodological basis. We consider how the methods have been extended and adapted to also include (hybrid) dynamic Bayesian networks, and we end with an overview of established software systems supporting inference in these types of models