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

Computation of Kullback–Leibler Divergence in Bayesian Networks

Kullback–Leibler divergence KL(p, q) is the standard measure of error when we have a true probability distribution p which is approximate with probability distribution q. Its efficient computation is essential in many tasks, as in approximate computation or as a measure of error when learning a probability. In high dimensional probabilities, as the ones associated with Bayesian networks, a direct computation can be unfeasible. This paper considers the case of efficiently computing the Kullback–Leibler divergence of two probability distributions, each one of them coming from a different Bayesian network, which might have different structures. The paper is based on an auxiliary deletion algorithm to compute the necessary marginal distributions, but using a cache of operations with potentials in order to reuse past computations whenever they are necessary. The algorithms are tested with Bayesian networks from the bnlearn repository. Computer code in Python is provided taking as basis pgmpy, a library for working with probabilistic graphical models.Spanish Ministry of Education and Science under project PID2019-106758GB-C31European Regional Development Fund (FEDER

Recent advances in probabilistic graphical models

Probabilistic graphical models constitute a fundamental tool for the development of intelligent systems

An Axiomatic Framework for Propagating Uncertainty in Directed Acyclic Networks

This paper presents an axiomatic system for propagating uncertainty in Pearl's causal networks, (Probabilistic Reasoning in Intelligent Systems: Networks of Plausible Inference, 1988 [7]). The main objective is to study all aspects of knowledge representation and reasoning in causal networks from an abstract point of view, independent of the particular theory being used to represent information (probabilities, belief functions or upper and lower probabilities). This is achieved by expressing concepts and algorithms in terms of valuations, an abstract mathematical concept representing a piece of information, introduced by Shenoy and Sharer [1, 2]. Three new axioms are added to Shenoy and Shafer's axiomatic framework [1, 2], for the propagation of general valuations in hypertrees. These axioms allow us to address from an abstract point of view concepts such as conditional information (a generalization of conditional probabilities) and give rules relating the decomposition of global information with the concept of independence (a generalization of probability rules allowing the decomposition of a bidimensional distribution with independent marginals in the product of its two marginals). Finally, Pearl's propagation algorithms are also developed and expressed in terms of operations with valuations.Commission of the European Communities under ESPRIT BRA 3085: DRUM

Hill-climbing and branch-and-bound algorithms for exact and approximate inference in credal networks

This paper proposes two new algorithms for inference in credal networks. These algorithms enable probability intervals to be obtained for the states of a given query variable. The first algorithm is approximate and uses the hill-climbing technique in the Shenoy–Shafer architecture to propagate in join trees; the second is exact and is a modification of Rocha and Cozman’s branch-and-bound algorithm, but applied to general directed acyclic graphs.TIN2004-06204-C03-0

Combining gene expression data and prior knowledge for inferring gene regulatory networks via Bayesian networks using structural restrictions

Ministerio de Economía y Competitividad y Fondo Europeo de Desarrollo Regional (FEDER), proyectos TEC2015-69496-R y TIN2016-77902-C3-2-

Using Value-Based Potentials for Making Approximate Inference on Probabilistic Graphical Models

The computerization of many everyday tasks generates vast amounts of data, and this has lead to the development of machine-learning methods which are capable of extracting useful information from the data so that the data can be used in future decision-making processes. For a long time now, a number of fields, such as medicine (and all healthcare-related areas) and education, have been particularly interested in obtaining relevant information from this stored data. This interest has resulted in the need to deal with increasingly complex problems which involve many different variables with a high degree of interdependency. This produces models (and in our case probabilistic graphical models) that are difficult to handle and that require very efficient techniques to store and use the information that quantifies the relationships between the problem variables. It has therefore been necessary to develop efficient structures, such as probability trees or value-based potentials, to represent the information. Even so, there are problems that must be treated using approximation since this is the only way that results can be obtained, despite the corresponding loss of information. The aim of this article is to show how the approximation can be performed with value-based potentials. Our experimental work is based on checking the behavior of this approximation technique on several Bayesian networks related to medical problems, and our experiments show that in some cases there are notable savings in memory space with limited information loss.Spanish Government PID2019-106758GB-C31European CommissionUniversidad de Granada/CBU

Discretization of expression quantitative trait loci in association analysis between genotypes and expression data

Expression quantitative trait loci are used as a tool to identify genetic causes of natural variation in gene expression. Only in a few cases the expression of a gene is controlled by a variant on a single genetic marker. There is a plethora of different complexity levels of interaction effects within markers, within genes and between marker and genes. This complexity challenges biostatisticians and bioinformatitians every day and makes findings difficult to appear. As a way to simplify analysis and better control confounders, we tried a new approach for association analysis between genotypes and expression data. We pursued to understand whether discretization of expression data can be useful in genome-transcriptome association analyses. By discretizing the dependent variable, algorithms for learning classifiers from data as well as performing block selection were used to help understanding the relationship between the expression of a gene and genetic markers. We present the results of using this approach to detect new possible causes of expression variation of DRB5, a gene playing an important role within the immune system. Together with expression of gene DRB5 obtained from the classical microarray technology, we have also measured DRB5 expression by using the more recent next-generation sequencing technology. A supplementary website including a link to the software with the method implemented can be found at http: //bios.ugr.es/DRB5

Información difusa, relaciones entre probabilidad y posibilidad

Universidad de Granada, Facultad de Ciencias. Leída el 23-03-198

Using probability trees to compute marginals with imprecise probabilities

This paper presents an approximate algorithm to obtain a posteriori intervals of probability, when available information is also given with intervals. The algorithm uses probability trees as a means of representing and computing with the convex sets of probabilities associated to the intervals