Abstract: Bayesian networks (BNs), also known as Bayesian belief networks or Bayes nets, are a kind of probabilistic graphical model that has become very popular to practitioners mainly due to the powerful probability theory involved, which makes them able to deal with a wide range of problems. The goal of this review is to show how BNs are being used in environmental modelling. We are interested in the application of BNs, from January 1990 to December 2010, in the areas of the ISI Web of Knowledge related to Environmental Sciences. It is noted that only the 4.2% of the papers have been published under this item. The different steps that configure modelling via BNs have been revised: aim of the model, data pre-processing, model learning, validation and software. Our literature review indicates that BNs have barely been used for Environmental Science and their potential is, as yet, largely unexploited.

Abstract: Conditional independence testing is an important problem, especially in Bayesian network learning and causal discovery. Due to the curse of dimensionality, testing for conditional independence of continuous variables is particularly challenging. We propose a Kernel-based Conditional Independence test (KCI-test), by constructing an appropriate test statistic and deriving its asymptotic distribution under the null hypothesis of conditional independence. The proposed method is computationally efficient and easy to implement. Experimental results show that it outperforms other methods, especially when the conditioning set is large or the sample size is not very large, in which case other methods encounter difficulties.

Abstract: Although a large body of work is devoted to finding communities in static social networks, only a few studies examined the dynamics of communities in evolving social networks. In this paper, we propose a dynamic stochastic block model for finding communities and their evolution in a dynamic social network. The proposed model captures the evolution of communities by explicitly modeling the transition of community memberships for individual nodes in the network. Unlike many existing approaches for modeling social networks that estimate parameters by their most likely values (i.e., point estimation), in this study, we employ a Bayesian treatment for parameter estimation that computes the posterior distributions for all the unknown parameters. This Bayesian treatment allows us to capture the uncertainty in parameter values and therefore is more robust to data noise than point estimation. In addition, an efficient algorithm is developed for Bayesian inference to handle large sparse social networks. Extensive experimental studies based on both synthetic data and real-life data demonstrate that our model achieves higher accuracy and reveals more insights in the data than several state-of-the-art algorithms.

Abstract: Structural equation models and Bayesian networks have been widely used to analyze causal relations between continuous variables. In such frameworks, linear acyclic models are typically used to model the data-generating process of variables. Recently, it was shown that use of non-Gaussianity identifies the full structure of a linear acyclic model, i.e., a causal ordering of variables and their connection strengths, without using any prior knowledge on the network structure, which is not the case with conventional methods. However, existing estimation methods are based on iterative search algorithms and may not converge to a correct solution in a finite number of steps. In this paper, we propose a new direct method to estimate a causal ordering and connection strengths based on non-Gaussianity. In contrast to the previous methods, our algorithm requires no algorithmic parameters and is guaranteed to converge to the right solution within a small fixed number of steps if the data strictly follows the model.

Abstract: Bayesian networks have become a widely used method in the modelling of uncertain knowledge. Owing to the difficulty domain experts have in specifying them, techniques that learn Bayesian networks from data have become indispensable. Recently, however, there have been many important new developments in this field. This work takes a broad look at the literature on learning Bayesian networks-in particular their structure-from data. Specific topics are not focused on in detail, but it is hoped that all the major fields in the area are covered. This article is not intended to be a tutorial-for this, there are many books on the topic, which will be presented. However, an effort has been made to locate all the relevant publications, so that this paper can be used as a ready reference to find the works on particular sub-topics.

Abstract: Structural equation models and Bayesian networks have been widely used to analyze causal relations between continuous variables. In such frameworks, linear acyclic models are typically used to model the data-generating process of variables. Recently, it was shown that use of non-Gaussianity identifies the full structure of a linear acyclic model, that is, a causal ordering of variables and their connection strengths, without using any prior knowledge on the network structure, which is not the case with conventional methods. However, existing estimation methods are based on iterative search algorithms and may not converge to a correct solution in a finite number of steps. In this paper, we propose a new direct method to estimate a causal ordering and connection strengths based on non-Gaussianity. In contrast to the previous methods, our algorithm requires no algorithmic parameters and is guaranteed to converge to the right solution within a small fixed number of steps if the data strictly follows the model, that is, if all the model assumptions are met and the sample size is infinite.

Abstract: Learning Bayesian networks is known to be an NP-hard problem and that is the reason why the application of a heuristic search has proven advantageous in many domains. This learning approach is computationally efficient and, even though it does not guarantee an optimal result, many previous studies have shown that it obtains very good solutions. Hill climbing algorithms are particularly popular because of their good trade-off between computational demands and the quality of the models learned. In spite of this efficiency, when it comes to dealing with high-dimensional datasets, these algorithms can be improved upon, and this is the goal of this paper. Thus, we present an approach to improve hill climbing algorithms based on dynamically restricting the candidate solutions to be evaluated during the search process. This proposal, dynamic restriction, is new because other studies available in the literature about restricted search in the literature are based on two stages rather than only one as it is presented here. In addition to the aforementioned advantages of hill climbing algorithms, we show that under certain conditions the model they return is a minimal I-map of the joint probability distribution underlying the training data, which is a nice theoretical property with practical implications. In this paper we provided theoretical results that guarantee that, under these same conditions, the proposed algorithms also output a minimal I-map. Furthermore, we experimentally test the proposed algorithms over a set of different domains, some of them quite large (up to 800 variables), in order to study their behavior in practice.

Abstract: The problem of learning the structure of Bayesian networks from complete discrete data with a limit on parent set size is considered. Learning is cast explicitly as an optimisation problem where the goal is to find a BN structure which maximises log marginal likelihood (BDe score). Integer programming, specifically the SCIP framework, is used to solve this optimisation problem. Acyclicity constraints are added to the integer program (IP) during solving in the form of cutting planes. Finding good cutting planes is the key to the success of the approach—the search for such cutting planes is effected using a sub-IP. Results show that this is a particularly fast method for exact BN learning.

Abstract: Stochastic sampling algorithms, while an attractive alternative to exact algorithms in very large Bayesian network models, have been observed to perform poorly in evidential reasoning with extremely unlikely evidence. To address this problem, we propose an adaptive importance sampling algorithm, AIS-BN, that shows promising convergence rates even under extreme conditions and seems to outperform the existing sampling algorithms consistently. Three sources of this performance improvement are (1) two heuristics for initialization of the importance function that are based on the theoretical properties of importance sampling in finite-dimensional integrals and the structural advantages of Bayesian networks, (2) a smooth learning method for the importance function, and (3) a dynamic weighting function for combining samples from different stages of the algorithm. We tested the performance of the AIS-BN algorithm along with two state of the art general purpose sampling algorithms, likelihood weighting (Fung and Chang, 1989; Shachter and Peot, 1989) and self-importance sampling (Shachter and Peot, 1989). We used in our tests three large real Bayesian network models available to the scientific community: the CPCS network (Pradhan et al., 1994), the PathFinder network (Heckerman, Horvitz, and Nathwani, 1990), and the ANDES network (Conati, Gertner, VanLehn, and Druzdzel, 1997), with evidence as unlikely as 10^-41. While the AIS-BN algorithm always performed better than the other two algorithms, in the majority of the test cases it achieved orders of magnitude improvement in precision of the results. Improvement in speed given a desired precision is even more dramatic, although we are unable to report numerical results here, as the other algorithms almost never achieved the precision reached even by the first few iterations of the AIS-BN algorithm.

Abstract: Bayesian networks have become a widely used method in the modelling of uncertain knowledge Owing to the difficulty domain experts have in specifying them, techniques that learn Bayesian networks from data have become indispensable Recently, however, there have been many important new developments in this field This work takes a broad look at the literature on learning Bayesian networks—in particular their structure—from data Specific topics are not focused on in detail, but it is hoped that all the major fields in the area are covered This article is not intended to be a tutorial—for this, there are many books on the topic, which will be presented However, an effort has been made to locate all the relevant publications, so that this paper can be used as a ready reference to find the works on particular sub-topics

Abstract: An important open problem of computational neuroscience is the generic organization of computations in networks of neurons in the brain. We show here through rigorous theoretical analysis that inherent stochastic features of spiking neurons, in combination with simple nonlinear computational operations in specific network motifs and dendritic arbors, enable networks of spiking neurons to carry out probabilistic inference through sampling in general graphical models. In particular, it enables them to carry out probabilistic inference in Bayesian networks with converging arrows (“explaining away”) and with undirected loops, that occur in many real-world tasks. Ubiquitous stochastic features of networks of spiking neurons, such as trial-to-trial variability and spontaneous activity, are necessary ingredients of the underlying computational organization. We demonstrate through computer simulations that this approach can be scaled up to neural emulations of probabilistic inference in fairly large graphical models, yielding some of the most complex computations that have been carried out so far in networks of spiking neurons.

Abstract: In multidimensional classification the goal is to assign an instance to a set of different classes. This task is normally addressed either by defining a compound class variable with all the possible combinations of classes (label power-set methods, LPMs) or by building independent classifiers for each class (binary-relevance methods, BRMs). However, LPMs do not scale well and BRMs ignore the dependency relations between classes. We introduce a method for chaining binary Bayesian classifiers that combines the strengths of classifier chains and Bayesian networks for multidimensional classification. The method consists of two phases. In the first phase, a Bayesian network (BN) that represents the dependency relations between the class variables is learned from data. In the second phase, several chain classifiers are built, such that the order of the class variables in the chain is consistent with the class BN. At the end we combine the results of the different generated orders. Our method considers the dependencies between class variables and takes advantage of the conditional independence relations to build simplified models. We perform experiments with a chain of naive Bayes classifiers on different benchmark multidimensional datasets and show that our approach outperforms other state-of-the-art methods.

Abstract: In this paper we introduce a novel approach towards the recognition of typical driving maneuvers in structured highway scenarios and identify some of the key benefits of traffic scene modeling with object-oriented Bayesian networks (OOBNs). The approach exploits the advantages of an introduced lane-related coordinate system together with individual occupancy grids for all vehicles. This combination allows for an efficient classification of the existing vehiclelane and vehicle-vehicle relations in a traffic scene and thus substantially improves the understanding of complex traffic scenes. We systematically propagate probabilities and variances within our network which results in probabilistic sets of the modeled driving maneuvers. Using this generic approach, we are able to classify a total of 27 driving maneuvers including merging and object following.

Abstract: Modern technologies and especially next generation sequencing facilities are giving a cheaper access to genotype and genomic data measured on the same sample at once. This creates an ideal situation for multifactorial experiments designed to infer gene regulatory networks. The fifth “Dialogue for Reverse Engineering Assessments and Methods” (DREAM5) challenges are aimed at assessing methods and associated algorithms devoted to the inference of biological networks. Challenge 3 on “Systems Genetics” proposed to infer causal gene regulatory networks from different genetical genomics data sets. We investigated a wide panel of methods ranging from Bayesian networks to penalised linear regressions to analyse such data, and proposed a simple yet very powerful meta-analysis, which combines these inference methods. We present results of the Challenge as well as more in-depth analysis of predicted networks in terms of structure and reliability. The developed meta-analysis was ranked first among the teams participating in Challenge 3A. It paves the way for future extensions of our inference method and more accurate gene network estimates in the context of genetical genomics.

Abstract: Gene-gene epistatic interactions likely play an important role in the genetic basis of many common diseases. Recently, machine-learning and data mining methods have been developed for learning epistatic relationships from data. A well-known combinatorial method that has been successfully applied for detecting epistasis is Multifactor Dimensionality Reduction (MDR). Jiang et al. created a combinatorial epistasis learning method called BNMBL to learn Bayesian network (BN) epistatic models. They compared BNMBL to MDR using simulated data sets. Each of these data sets was generated from a model that associates two SNPs with a disease and includes 18 unrelated SNPs. For each data set, BNMBL and MDR were used to score all 2-SNP models, and BNMBL learned significantly more correct models. In real data sets, we ordinarily do not know the number of SNPs that influence phenotype. BNMBL may not perform as well if we also scored models containing more than two SNPs. Furthermore, a number of other BN scoring criteria have been developed. They may detect epistatic interactions even better than BNMBL. Although BNs are a promising tool for learning epistatic relationships from data, we cannot confidently use them in this domain until we determine which scoring criteria work best or even well when we try learning the correct model without knowledge of the number of SNPs in that model. We evaluated the performance of 22 BN scoring criteria using 28,000 simulated data sets and a real Alzheimer's GWAS data set. Our results were surprising in that the Bayesian scoring criterion with large values of a hyperparameter called α performed best. This score performed better than other BN scoring criteria and MDR at recall using simulated data sets, at detecting the hardest-to-detect models using simulated data sets, and at substantiating previous results using the real Alzheimer's data set. We conclude that representing epistatic interactions using BN models and scoring them using a BN scoring criterion holds promise for identifying epistatic genetic variants in data. In particular, the Bayesian scoring criterion with large values of a hyperparameter α appears more promising than a number of alternatives.

Abstract: Common wisdom has it that small distinctions in the probabilities quantifying a Bayesian network do not matter much for the resultsof probabilistic queries. However, one can easily develop realistic scenarios under which small variations in network probabilities can lead to significant changes in computed queries. A pending theoretical question is then to analytically characterize parameter changes that do or do not matter. In this paper, we study the sensitivity of probabilistic queries to changes in network parameters and prove some tight bounds on the impact that such parameters can have on queries. Our analytical results pinpoint some interesting situations under which parameter changes do or do not matter. These results are important for knowledge engineers as they help them identify influential network parameters. They are also important for approximate inference algorithms that preprocessnetwork CPTs to eliminate small distinctions in probabilities.

Abstract: Despite their fame and capability in detecting out-of-control conditions, control charts are not effective tools for fault diagnosis. There are other techniques in the literature mainly based on process information and control charts patterns to help control charts for root cause analysis. However these methods are limited in practice due to their dependency on the expertise of practitioners. In this study, we develop a network for capturing the cause and effect relationship among chart patterns, process information and possible root causes/assignable causes. This network is then trained under the framework of Bayesian networks and a suggested data structure using process information and chart patterns. The proposed method provides a real time identification of single and multiple assignable causes of failures as well as false alarms while improving itself performance by learning from mistakes. It also has an acceptable performance on missing data. This is demonstrated by comparing the performance of the proposed method with methods like neural nets and K-Nearest Neighbor under extensive simulation studies.

Abstract: In this paper, we review the role of probabilistic graphical models in artificial intelligence. We start by giving an account of the early years when there was important controversy about the suitability of probability for intelligent systems. We then discuss the main milestones for the foundations of graphical models starting with Pearl's pioneering work. Some of the main techniques for problem solving (abduction, classification, and decision-making) are briefly explained. Finally, we propose some important challenges for future research and highlight relevant applications (forensic reasoning, genomics and the use of graphical models as a general optimization tool).

Abstract: This paper presents a method for high-level decision making in traffic environments. In contrast to the usual approach of modeling decision policies by hand, a Markov Decision Process (MDP) is employed to plan the optimal policy by assessing the outcomes of actions. Using probability theory, decisions are deduced automatically from the knowledge about how road users behave over time. This approach does neither depend on an explicit situation recognition nor is it limited to only a variety of situations or types of descriptions. Hence it is versatile and powerful. The contribution of this paper is a mathematical framework to derive abstract symbolic states from complex continuous temporal models encoded as Dynamic Bayesian Networks (DBN). For this purpose discrete MDP states are interpreted by random variables. To make computation feasible this space grows adaptively during planning and according to the problem to be solved.

Abstract: The Bayesian approach to machine learning amounts to inferring posterior distributions of random variables from a probabilistic model of how the variables are related (that is, a prior distribution) and a set of observations of variables There is a trend in machine learning towards expressing Bayesian models as probabilistic programs As a foundation for this kind of programming, we propose a core functional calculus with primitives for sampling prior distributions and observing variables We define combinators for measure transformers, based on theorems in measure theory, and use these to give a rigorous semantics to our core calculus The original features of our semantics include its support for discrete, continuous, and hybrid measures, and, in particular, for observations of zero-probability events We compile our core language to a small imperative language that has a straightforward semantics via factor graphs, data structures that enable many efficient inference algorithms We use an existing inference engine for efficient approximate inference of posterior marginal distributions, treating thousands of observations per second for large instances of realistic models

Abstract: The ecological sciences have benefited greatly from recent advances in wireless sensor technologies. These technologies allow researchers to deploy networks of automated sensors, which can monitor a landscape at very fine temporal and spatial scales. However, these networks are subject to harsh conditions, which lead to malfunctions in individual sensors and failures in network communications. The resulting data streams often exhibit incorrect data measurements and missing values. Identifying and correcting these is time-consuming and error-prone. We present a method for real-time automated data quality control (QC) that exploits the spatial and temporal correlations in the data to distinguish sensor failures from valid observations. The model adapts to each deployment site by learning a Bayesian network structure that captures spatial relationships between sensors, and it extends the structure to a dynamic Bayesian network to incorporate temporal correlations. This model is able to flag faulty observations and predict the true values of the missing or corrupt readings. The performance of the model is evaluated on data collected by the SensorScope Project. The results show that the spatiotemporal model demonstrates clear advantages over models that include only temporal or only spatial correlations, and that the model is capable of accurately imputing corrupted values.

Abstract: Classical dynamic Bayesian networks (DBNs) are based on the homogeneous Markov assumption and cannot deal with non-homogeneous temporal processes. Various approaches to relax the homogeneity assumption have recently been proposed. The present paper presents a combination of a Bayesian network with conditional probabilities in the linear Gaussian family, and a Bayesian multiple changepoint process, where the number and location of the changepoints are sampled from the posterior distribution with MCMC. Our work improves four aspects of an earlier conference paper: it contains a comprehensive and self-contained exposition of the methodology; it discusses the problem of spurious feedback loops in network reconstruction; it contains a comprehensive comparative evaluation of the network reconstruction accuracy on a set of synthetic and real-world benchmark problems, based on a novel discrete changepoint process; and it suggests new and improved MCMC schemes for sampling both the network structures and the changepoint configurations from the posterior distribution. The latter study compares RJMCMC, based on changepoint birth and death moves, with two dynamic programming schemes that were originally devised for Bayesian mixture models. We demonstrate the modifications that have to be made to allow for changing network structures, and the critical impact that the prior distribution on changepoint configurations has on the overall computational complexity.

Abstract: We develop a Bayesian network (BN) model that describes estuarine chlorophyll dynamics in the upper section of the Neuse River Estuary in North Carolina, using automated constraint based structure learning algorithms. We examine the functionality and usefulness of the structure learning algorithms in building model topology with real-time data under different scenarios. Generated BN models are evaluated and a final model is selected. Model results indicate that although the effect of water temperature and river flow on chlorophyll dynamics has remained unchanged following the implementation of the nitrogen Total Maximum Daily Load (TMDL) program; the response of chlorophyll levels to nutrient concentrations has been altered. The results stress the importance of incorporating expert defined constraints and links in conjunction with the automated structure learning algorithms to generate more plausible structures and minimize the sensitivity of the learning algorithms. This hybrid approach towards structure learning allows for the incorporation of existing knowledge while limiting the scope of the learning algorithms to defining the links between environmental variables for which the expert has little or no information.

Abstract: We present a novel algorithm to estimate genome-wide gene networks consisting of more than 20,000 genes from gene expression data using nonparametric Bayesian networks. Due to the difficulty of learning Bayesian network structures, existing algorithms cannot be applied to more than a few thousand genes. Our algorithm overcomes this limitation by repeatedly estimating subnetworks in parallel for genes selected by neighbor node sampling. Through numerical simulation, we confirmed that our algorithm outperformed a heuristic algorithm in a shorter time. We applied our algorithm to microarray data from human umbilical vein endothelial cells (HUVECs) treated with siRNAs, to construct a human genome-wide gene network, which we compared to a small gene network estimated for the genes extracted using a traditional bioinformatics method. The results showed that our genome-wide gene network contains many features of the small network, as well as others that could not be captured during the small network estimation. The results also revealed master-regulator genes that are not in the small network but that control many of the genes in the small network. These analyses were impossible to realize without our proposed algorithm.