152 research outputs found
Approximating probability density functions in hybrid Bayesian networks with mixtures of truncated exponentials
Mixtures of truncated exponentials (MTE) potentials are an alternative to discretization and Monte Carlo methods for solving hybrid Bayesian networks. Any probability density function (PDF) can be approximated by an MTE potential, which can always be marginalized in closed form. This allows propagation to be done exactly using the Shenoy-Shafer architecture for computing marginals, with no restrictions on the construction of a join tree. This paper presents MTE potentials that approximate standard PDF’s and applications of these potentials for solving inference problems in hybrid Bayesian networks. These approximations will extend the types of inference problems that can be modeled with Bayesian networks, as demonstrated using three examples
Answering queries in hybrid Bayesian networks using importance sampling
In this paper we propose an algorithm for answering queries in hybrid Bayesian networks where the underlying probability distribution is of class MTE (mixture of truncated exponentials). The algorithm is based on importance sampling simulation. We show how, like existing importance sampling algorithms for discrete networks, it is able to provide answers to multiple queries simultaneously using a single sample. The behaviour of the new algorithm is experimentally tested and compared with previous methods existing in the literature
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
Practical Aspects of Solving Hybrid Bayesian Networks Containing Deterministic Conditionals
This is the author's final draft. Copyright 2015 WileyIn this paper we discuss some practical issues that arise in solv-
ing hybrid Bayesian networks that include deterministic conditionals
for continuous variables. We show how exact inference can become
intractable even for small networks, due to the di culty in handling
deterministic conditionals (for continuous variables). We propose some
strategies for carrying out the inference task using mixtures of polyno-
mials and mixtures of truncated exponentials. Mixtures of polynomials
can be de ned on hypercubes or hyper-rhombuses. We compare these
two methods. A key strategy is to re-approximate large potentials
with potentials consisting of fewer pieces and lower degrees/number
of terms. We discuss several methods for re-approximating potentials.
We illustrate our methods in a practical application consisting of solv-
ing a stochastic PERT network
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 arti cially generated databases
Conditional density approximations with mixtures of polynomials
Mixtures of polynomials (MoPs) are a non-parametric density estimation technique especially designed for hybrid Bayesian networks with continuous and discrete variables. Algorithms to learn one- and multi-dimensional (marginal) MoPs from data have recently been proposed. In this paper we introduce two methods for learning MoP approximations of conditional densities from data. Both approaches are based on learning MoP approximations of the joint density and the marginal density of the conditioning variables, but they differ as to how the MoP approximation of the quotient of the two densities is found. We illustrate and study the methods using data sampled from known parametric distributions, and we demonstrate their applicability by learning models based on real neuroscience data. Finally, we compare the performance of the proposed methods with an approach for learning mixtures of truncated basis functions (MoTBFs). The empirical results show that the proposed methods generally yield models that are comparable to or significantly better than those found using the MoTBF-based method
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