scholarly journals Cutset Sampling for Bayesian Networks

2007 ◽  
Vol 28 ◽  
pp. 1-48 ◽  
Author(s):  
B. Bidyuk ◽  
R. Dechter
Keyword(s):  
Bayesian Networks ◽  
Bayesian Network ◽  
Network Structure ◽  
Sampling Methodology ◽  
Exact Inference ◽  
Inference Algorithms

The paper presents a new sampling methodology for Bayesian networks that samples only a subset of variables and applies exact inference to the rest. Cutset sampling is a network structure-exploiting application of the Rao-Blackwellisation principle to sampling in Bayesian networks. It improves convergence by exploiting memory-based inference algorithms. It can also be viewed as an anytime approximation of the exact cutset-conditioning algorithm developed by Pearl. Cutset sampling can be implemented efficiently when the sampled variables constitute a loop-cutset of the Bayesian network and, more generally, when the induced width of the network's graph conditioned on the observed sampled variables is bounded by a constant w. We demonstrate empirically the benefit of this scheme on a range of benchmarks.

scholarly journals Learning Diverse Bayesian Networks

2019 ◽  
Vol 33 ◽  
pp. 7793-7800
Author(s):  
Cong Chen ◽  
Changhe Yuan
Keyword(s):  
Bayesian Networks ◽  
Bayesian Network ◽  
Network Structure ◽  
Search Algorithm ◽  
Noisy Data ◽  
Local Neighborhood ◽  
Causal Ordering ◽  
True Model ◽  
Underlying Network ◽  
Novel Method

Much effort has been directed at developing algorithms for learning optimal Bayesian network structures from data. When given limited or noisy data, however, the optimal Bayesian network often fails to capture the true underlying network structure. One can potentially address the problem by finding multiple most likely Bayesian networks (K-Best) in the hope that one of them recovers the true model. However, it is often the case that some of the best models come from the same peak(s) and are very similar to each other; so they tend to fail together. Moreover, many of these models are not even optimal respective to any causal ordering, thus unlikely to be useful. This paper proposes a novel method for finding a set of diverse top Bayesian networks, called modes, such that each network is guaranteed to be optimal in a local neighborhood. Such mode networks are expected to provide a much better coverage of the true model. Based on a globallocal theorem showing that a mode Bayesian network must be optimal in all local scopes, we introduce an A* search algorithm to efficiently find top M Bayesian networks which are highly probable and naturally diverse. Empirical evaluations show that our top mode models have much better diversity as well as accuracy in discovering true underlying models than those found by K-Best.

A Petri Net-Based Tool for the Analysis of Generalized Continuous Time Bayesian Networks

2013 ◽  
pp. 118-143 ◽  
Author(s):  
Daniele Codetta-Raiteri ◽  
Luigi Portinale
Keyword(s):  
Bayesian Networks ◽  
Bayesian Network ◽  
Petri Net ◽  
Continuous Time ◽  
Dynamic Bayesian Network ◽  
Software Tool ◽  
Inference Algorithms ◽  
Continuous Time Bayesian Networks ◽  
Generalized Stochastic Petri Net

A software tool for the analysis of Generalized Continuous Time Bayesian Networks (GCTBN) is presented. GCTGBN extend CTBN introducing in addition to continuous time-delayed variables, non-delayed or “immediate” variables. The tool is based on the conversion of a GCTBN model into a Generalized Stochastic Petri Net (GSPN), which is an actual mean to perform the inference (analysis) of the GCTBN. Both the inference tasks (prediction and smoothing) can be performed in this way. The architecture and the methodologies of the tool are presented. In particular, the conversion rules from GCTBN to GSPN are described, and the inference algorithms exploiting GSPN transient analysis are presented. A running example supports their description: a case study is modelled as a GCTBN and analyzed by means of the tool. The results are verified by modelling and analyzing the system as a Dynamic Bayesian Network, another form of Bayesian Network, assuming discrete time.

AN INTRODUCTION TO HIDDEN MARKOV MODELS AND BAYESIAN NETWORKS

2001 ◽  
Vol 15 (01) ◽  
pp. 9-42 ◽  
Author(s):  
ZOUBIN GHAHRAMANI
Keyword(s):  
Bayesian Networks ◽  
Hidden Markov Models ◽  
Markov Models ◽  
Recent Literature ◽  
Hidden Markov ◽  
Continuous Variables ◽  
State Variables ◽  
Exact Inference ◽  
Markov Chain Sampling ◽  
Inference Algorithms

We provide a tutorial on learning and inference in hidden Markov models in the context of the recent literature on Bayesian networks. This perspective makes it possible to consider novel generalizations of hidden Markov models with multiple hidden state variables, multiscale representations, and mixed discrete and continuous variables. Although exact inference in these generalizations is usually intractable, one can use approximate inference algorithms such as Markov chain sampling and variational methods. We describe how such methods are applied to these generalized hidden Markov models. We conclude this review with a discussion of Bayesian methods for model selection in generalized HMMs.

System Reliability Evaluation Using Bayesian Networks

2013 ◽  
Vol 756-759 ◽  
pp. 2457-2461
Author(s):  
Lin Ying Liu ◽  
Qin Sun ◽  
Yao Wang
Keyword(s):  
Bayesian Networks ◽  
Bayesian Network ◽  
System Reliability ◽  
Network Inference ◽  
Fault Tree ◽  
Reliability Evaluation ◽  
Flow Chart ◽  
Inference Algorithms ◽  
Network Method ◽  
Bayesian Network Inference

Bayesian network method for system reliability evaluation which is based on a Bayesian network that transformed from a fault tree has gotten much attention these years. After a brief introduction to the method how to transform a fault tree into a Bayesian network, the paper elaborates the Bayesian network inference algorithms. The paper focuses on the way how the inference algorithms can be applied to the practice of system reliability evaluation and designs a systematic flow chart used to evaluate system reliability in a Bayesian network way. The experiment demonstrates the feasibility of the systematic flow chart.

scholarly journals Hybrid Optimization Algorithm for Bayesian Network Structure Learning

Information ◽  
2019 ◽  
Vol 10 (10) ◽  
pp. 294 ◽  
Author(s):  
Xingping Sun ◽  
Chang Chen ◽  
Lu Wang ◽  
Hongwei Kang ◽  
Yong Shen ◽  
...  
Keyword(s):  
Artificial Intelligence ◽  
Bayesian Networks ◽  
Bayesian Network ◽  
Network Structure ◽  
Structure Learning ◽  
Expert Knowledge ◽  
Hybrid Optimization ◽  
Experimental Simulation ◽  
Bayesian Network Structure ◽  
Bayesian Network Structure Learning

Since the beginning of the 21st century, research on artificial intelligence has made great progress. Bayesian networks have gradually become one of the hotspots and important achievements in artificial intelligence research. Establishing an effective Bayesian network structure is the foundation and core of the learning and application of Bayesian networks. In Bayesian network structure learning, the traditional method of utilizing expert knowledge to construct the network structure is gradually replaced by the data learning structure method. However, as a result of the large amount of possible network structures, the search space is too large. The method of Bayesian network learning through training data usually has the problems of low precision or high complexity, which make the structure of learning differ greatly from that of reality, which has a great influence on the reasoning and practical application of Bayesian networks. In order to solve this problem, a hybrid optimization artificial bee colony algorithm is discretized and applied to structure learning. A hybrid optimization technique for the Bayesian network structure learning method is proposed. Experimental simulation results show that the proposed hybrid optimization structure learning algorithm has better structure and better convergence.

scholarly journals A Mixture Copula Bayesian Network Model for Multimodal Genomic Data

2017 ◽  
Author(s):  
Qingyang Zhang ◽  
Xuan Shi
Keyword(s):  
Bayesian Networks ◽  
Bayesian Network ◽  
Network Model ◽  
Network Structure ◽  
Genomic Data ◽  
The Cancer Genome Atlas ◽  
Bayesian Network Model ◽  
Atlas Data ◽  
Cancer Genome Atlas ◽  
Genome Atlas

AbstractGaussian Bayesian networks have become a widely used framework to estimate directed associations between joint Gaussian variables, where the network structure encodes decomposition of multivariate normal density into local terms. However, the resulting estimates can be inaccurate when normality assumption is moderately or severely violated, making it unsuitable to deal with recent genomic data such as the Cancer Genome Atlas data. In the present paper, we propose a mixture copula Bayesian network model which provides great flexibility in modeling non-Gaussian and multimodal data for causal inference. The parameters in mixture copula functions can be efficiently estimated by a routine Expectation-Maximization algorithm. A heuristic search algorithm based on Bayesian information criterion is developed to estimate the network structure, and prediction can be further improved by the best-scoring network out of multiple predictions from random initial values. Our method outperforms Gaussian Bayesian networks and regular copula Bayesian networks in terms of modeling flexibility and prediction accuracy, as demonstrated using a cell signaling dataset. We apply the proposed methods to the Cancer Genome Atlas data to study the genetic and epigenetic pathways that underlie serous ovarian cancer.

scholarly journals A mixture copula Bayesian network model for multimodal genomic data

2017 ◽  
Vol 16 ◽  
pp. 117693511770238 ◽  
Author(s):  
Qingyang Zhang ◽  
Xuan Shi
Keyword(s):  
Bayesian Networks ◽  
Bayesian Network ◽  
Network Model ◽  
Network Structure ◽  
Genomic Data ◽  
The Cancer Genome Atlas ◽  
Bayesian Network Model ◽  
Atlas Data ◽  
Cancer Genome Atlas ◽  
Genome Atlas

Gaussian Bayesian networks have become a widely used framework to estimate directed associations between joint Gaussian variables, where the network structure encodes the decomposition of multivariate normal density into local terms. However, the resulting estimates can be inaccurate when the normality assumption is moderately or severely violated, making it unsuitable for dealing with recent genomic data such as the Cancer Genome Atlas data. In the present paper, we propose a mixture copula Bayesian network model which provides great flexibility in modeling non-Gaussian and multimodal data for causal inference. The parameters in mixture copula functions can be efficiently estimated by a routine expectation–maximization algorithm. A heuristic search algorithm based on Bayesian information criterion is developed to estimate the network structure, and prediction can be further improved by the best-scoring network out of multiple predictions from random initial values. Our method outperforms Gaussian Bayesian networks and regular copula Bayesian networks in terms of modeling flexibility and prediction accuracy, as demonstrated using a cell signaling data set. We apply the proposed methods to the Cancer Genome Atlas data to study the genetic and epigenetic pathways that underlie serous ovarian cancer.

scholarly journals A Review of Inference Algorithms for Hybrid Bayesian Networks

2018 ◽  
Vol 62 ◽  
pp. 799-828 ◽  
Author(s):  
Antonio Salmerón ◽  
Rafael Rumí ◽  
Helge Langseth ◽  
Thomas D. Nielsen ◽  
Anders L. Madsen
Keyword(s):  
Bayesian Networks ◽  
Bayesian Network ◽  
Closed Form ◽  
Dynamic Bayesian Networks ◽  
Software Systems ◽  
Continuous Variables ◽  
Hybrid Bayesian Networks ◽  
Closed Form Solutions ◽  
Inference Algorithms ◽  
The Difference

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.

scholarly journals Exploiting Structure in Weighted Model Counting Approaches to Probabilistic Inference

2011 ◽  
Vol 40 ◽  
pp. 729-765 ◽  
Author(s):  
W. Li ◽  
P. Poupart ◽  
P. Van Beek
Keyword(s):  
Bayesian Networks ◽  
Bayesian Network ◽  
Large Scale ◽  
Search Algorithm ◽  
Exact Inference ◽  
Backtracking Search ◽  
Space Efficiency ◽  
Counting Approach ◽  
Model Counting ◽  
Weighted Model

Previous studies have demonstrated that encoding a Bayesian network into a SAT formula and then performing weighted model counting using a backtracking search algorithm can be an effective method for exact inference. In this paper, we present techniques for improving this approach for Bayesian networks with noisy-OR and noisy-MAX relations---two relations that are widely used in practice as they can dramatically reduce the number of probabilities one needs to specify. In particular, we present two SAT encodings for noisy-OR and two encodings for noisy-MAX that exploit the structure or semantics of the relations to improve both time and space efficiency, and we prove the correctness of the encodings. We experimentally evaluated our techniques on large-scale real and randomly generated Bayesian networks. On these benchmarks, our techniques gave speedups of up to two orders of magnitude over the best previous approaches for networks with noisy-OR/MAX relations and scaled up to larger networks. As well, our techniques extend the weighted model counting approach for exact inference to networks that were previously intractable for the approach.

BAYESIAN NETWORK WITH INTERVAL PROBABILITY PARAMETERS

2011 ◽  
Vol 20 (05) ◽  
pp. 911-939 ◽  
Author(s):  
WEI-YI LIU ◽  
KUN YUE
Keyword(s):  
Bayesian Networks ◽  
Bayesian Network ◽  
Network Structure ◽  
Representation Learning ◽  
Interval Data ◽  
Causal Relationships ◽  
Interval Probability ◽  
Bayesian Network Structure ◽  
Probabilistic Description ◽  
Interval Valued

Interval data are widely used in real applications to represent the values of quantities in uncertain situations. However, the implied probabilistic causal relationships among interval-valued variables with interval data cannot be represented and inferred by general Bayesian networks with point-based probability parameters. Thus, it is desired to extend the general Bayesian network with effective mechanisms of representation, learning and inference of probabilistic causal relationships implied in interval data. In this paper, we define the interval probabilities, the bound-limited weak conditional interval probabilities and the probabilistic description, as well as the multiplication rules. Furthermore, we propose the method for learning the Bayesian network structure from interval data and the algorithm for corresponding approximate inferences. Experimental results show that our methods are feasible, and we conclude that the Bayesian network with interval probability parameters is the expansion of the general Bayesian network.

Sign in / Sign up

Export Citation Format

Share Document