Discovering causal interactions using Bayesian network scoring and information gain

Background: The problem of learning causal influences from data has recently attracted much attention. Standard statistical methods can have difficulty learning discrete causes, which interacting to affect a target, because the assumptions in these methods often do not model discrete causal relationships well. An important task then is to learn such interactions from data. Motivated by the problem of learning epistatic interactions from datasets developed in genome-wide association studies (GWAS), researchers conceived new methods for learning discrete interactions. However, many of these methods do not differentiate a model representing a true interaction from a model representing non-interacting causes with strong individual affects. The recent algorithm MBS-IGain addresses this difficulty by using Bayesian network learning and information gain to discover interactions from high-dimensional datasets. However, MBS-IGain requires marginal effects to detect interactions containing more than two causes. If the dataset is not high-dimensional, we can avoid this shortcoming by doing an exhaustive search. Results: We develop Exhaustive-IGain, which is like MBS-IGain but does an exhaustive search. We compare the performance of Exhaustive-IGain to MBS-IGain using low-dimensional simulated datasets based on interactions with marginal effects and ones based on interactions without marginal effects. Their performance is similar on the datasets based on marginal effects. However, Exhaustive-IGain compellingly outperforms MBS-IGain on the datasets based on 3 and 4-cause interactions without marginal effects. We apply Exhaustive-IGain to investigate how clinical variables interact to affect breast cancer survival, and obtain results that agree with judgements of a breast cancer oncologist. Conclusions: We conclude that the combined use of information gain and Bayesian network scoring enables us to discover higher order interactions with no marginal effects if we perform an exhaustive search. We further conclude that Exhaustive-IGain can be effective when applied to real data

Learning predictive interactions using information gain and Bayesian network scoring

Background The problems of correlation and classification are long-standing in the fields of statistics and machine learning, and techniques have been developed to address these problems. We are now in the era of high-dimensional data, which is data that can concern billions of variables. These data present new challenges. In particular, it is difficult to discover predictive variables, when each variable has little marginal effect. An example concerns Genomewide Association Studies (GWAS) datasets, which involve millions of single nucleotide polymorphism (SNPs), where some of the SNPs interact epistatically to affect disease status. Towards determining these interacting SNPs, researchers developed techniques that addressed this specific problem. However, the problem is more general, and so these techniques are applicable to other problems concerning interactions. A difficulty with many of these techniques is that they do not distinguish whether a learned interaction is actually an interaction or whether it involves several variables with strong marginal effects. Methodology/Findings We address this problem using information gain and Bayesian network scoring. First, we identify candidate interactions by determining whether together variables provide more information than they do separately. Then we use Bayesian network scoring to see if a candidate interaction really is a likely model. Our strategy is called MBS-IGain. Using 100 simulated datasets and a real GWAS Alzheimer's dataset, we investigated the performance of MBS-IGain. Conclusions/Significance When analyzing the simulated datasets, MBS-IGain substantially out-performed nine previous methods at locating interacting predictors, and at identifying interactions exactly. When analyzing the real Alzheimer's dataset, we obtained new results and results that substantiated previous findings. We conclude that MBS-IGain is highly effective at finding interactions in high-dimensional datasets. This result is significant because we have increasingly abundant high-dimensional data in many domains, and to learn causes andperform prediction/classification using these data, we often must first identify interactions

Pan-cancer analysis of TCGA data reveals notable signaling pathways

Background: A signal transduction pathway (STP) is a network of intercellular information flow initiated when extracellular signaling molecules bind to cell-surface receptors. Many aberrant STPs have been associated with various cancers. To develop optimal treatments for cancer patients, it is important to discover which STPs are implicated in a cancer or cancer-subtype. The Cancer Genome Atlas (TCGA) makes available gene expression level data on cases and controls in ten different types of cancer including breast cancer, colon adenocarcinoma, glioblastoma, kidney renal papillary cell carcinoma, low grade glioma, lung adenocarcinoma, lung squamous cell carcinoma, ovarian carcinoma, rectum adenocarcinoma, and uterine corpus endometriod carcinoma. Signaling Pathway Impact Analysis (SPIA) is a software package that analyzes gene expression data to identify whether a pathway is relevant in a given condition. Methods: We present the results of a study that uses SPIA to investigate all 157 signaling pathways in the KEGG PATHWAY database. We analyzed each of the ten cancer types mentioned above separately, and we perform a pan-cancer analysis by grouping the data for all the cancer types. Results: In each analysis several pathways were found to be markedly more significant than all the other pathways. We call them notable. Research has already established a connection between many of these pathways and the corresponding cancer type. However, some of our discovered pathways appear to be new findings. Altogether there were 37 notable findings in the separate analyses, 26 of them occurred in 7 pathways. These 7 pathways included the 4 notable pathways discovered in the pan-cancer analysis. So, our results suggest that these 7 pathways account for much of the mechanisms of cancer. Furthermore, by looking at the overlap among pathways, we identified possible regions on the pathways where the aberrant activity is occurring. Conclusions: We obtained 37 notable findings concerning 18 pathways. Some of them appear to be new discoveries. Furthermore, we identified regions on pathways where the aberrant activity might be occurring. We conclude that our results will prove to be valuable to cancer researchers because they provide many opportunities for laboratory and clinical follow-up studies

A Bayesian method for evaluating and discovering disease loci associations

Background: A genome-wide association study (GWAS) typically involves examining representative SNPs in individuals from some population. A GWAS data set can concern a million SNPs and may soon concern billions. Researchers investigate the association of each SNP individually with a disease, and it is becoming increasingly commonplace to also analyze multi-SNP associations. Techniques for handling so many hypotheses include the Bonferroni correction and recently developed Bayesian methods. These methods can encounter problems. Most importantly, they are not applicable to a complex multi-locus hypothesis which has several competing hypotheses rather than only a null hypothesis. A method that computes the posterior probability of complex hypotheses is a pressing need. Methodology/Findings: We introduce the Bayesian network posterior probability (BNPP) method which addresses the difficulties. The method represents the relationship between a disease and SNPs using a directed acyclic graph (DAG) model, and computes the likelihood of such models using a Bayesian network scoring criterion. The posterior probability of a hypothesis is computed based on the likelihoods of all competing hypotheses. The BNPP can not only be used to evaluate a hypothesis that has previously been discovered or suspected, but also to discover new disease loci associations. The results of experiments using simulated and real data sets are presented. Our results concerning simulated data sets indicate that the BNPP exhibits both better evaluation and discovery performance than does a p-value based method. For the real data sets, previous findings in the literature are confirmed and additional findings are found. Conclusions/Significance: We conclude that the BNPP resolves a pressing problem by providing a way to compute the posterior probability of complex multi-locus hypotheses. A researcher can use the BNPP to determine the expected utility of investigating a hypothesis further. Furthermore, we conclude that the BNPP is a promising method for discovering disease loci associations. © 2011 Jiang et al

Uniform random generation of large acyclic digraphs

Directed acyclic graphs are the basic representation of the structure underlying Bayesian networks, which represent multivariate probability distributions. In many practical applications, such as the reverse engineering of gene regulatory networks, not only the estimation of model parameters but the reconstruction of the structure itself is of great interest. As well as for the assessment of different structure learning algorithms in simulation studies, a uniform sample from the space of directed acyclic graphs is required to evaluate the prevalence of certain structural features. Here we analyse how to sample acyclic digraphs uniformly at random through recursive enumeration, an approach previously thought too computationally involved. Based on complexity considerations, we discuss in particular how the enumeration directly provides an exact method, which avoids the convergence issues of the alternative Markov chain methods and is actually computationally much faster. The limiting behaviour of the distribution of acyclic digraphs then allows us to sample arbitrarily large graphs. Building on the ideas of recursive enumeration based sampling we also introduce a novel hybrid Markov chain with much faster convergence than current alternatives while still being easy to adapt to various restrictions. Finally we discuss how to include such restrictions in the combinatorial enumeration and the new hybrid Markov chain method for efficient uniform sampling of the corresponding graphs.Comment: 15 pages, 2 figures. To appear in Statistics and Computin

Corrected score methods for estimating Bayesian networks with error-prone nodes

Motivated by inferring cellular signaling networks using noisy flow cytometry data, we develop procedures to draw inference for Bayesian networks based on error-prone data. Two methods for inferring causal relationships between nodes in a network are proposed based on penalized estimation methods that account for measurement error and encourage sparsity. We discuss consistency of the proposed network estimators and develop an approach for selecting the tuning parameter in the penalized estimation methods. Empirical studies are carried out to compare the proposed methods and a naive method that ignores measurement error with applications to synthetic data and to single cell flow cytometry data

An evolutionary technique to approximate multiple optimal alignments

The alignment of observed and modeled behavior is an essential aid for organizations, since it opens the door for root-cause analysis and enhancement of processes. The state-of-the-art technique for computing alignments has exponential time and space complexity, hindering its applicability for medium and large instances. Moreover, the fact that there may be multiple optimal alignments is perceived as a negative situation, while in reality it may provide a more comprehensive picture of the model’s explanation of observed behavior, from which other techniques may benefit. This paper presents a novel evolutionary technique for approximating multiple optimal alignments. Remarkably, the memory footprint of the proposed technique is bounded, representing an unprecedented guarantee with respect to the state-of-the-art methods for the same task. The technique is implemented into a tool, and experiments on several benchmarks are provided.Peer ReviewedPostprint (author's final draft

Dynamic reliability assessment of flare systems by combining fault tree analysis and Bayesian networks

YesFlaring is a combustion process commonly used in the oil and gas industry to dispose flammable waste gases. Flare flameout occurs when these gases escape unburnt from the flare tip causing the discharge of flammable and/or toxic vapor clouds. The toxic gases released during this process have the potential to initiate safety hazards and cause serious harm to the ecosystem and human health. Flare flameout could be caused by environmental conditions, equipment failure, and human error. However, to better understand the causes of flare flameout, a rigorous analysis of the behavior of flare systems under failure conditions is required. In this article, we used fault tree analysis (FTA) and the dynamic Bayesian network (DBN) to assess the reliability of flare systems. In this study, we analyzed 40 different combinations of basic events that can cause flare flameout to determine the event with the highest impact on system failure. In the quantitative analysis, we use both constant and time-dependent failure rates of system components. The results show that combining these two approaches allows for robust probabilistic reasoning on flare system reliability, which can help improving the safety and asset integrity of process facilities. The proposed DBN model constitutes a significant step to improve the safety and reliability of flare systems in the oil and gas industry

Constraint solving in uncertain and dynamic environments - a survey

International audienceThis article follows a tutorial, given by the authors on dynamic constraint solving at CP 2003 (Ninth International Conference on Principles and Practice of Constraint Programming) in Kinsale, Ireland. It aims at offering an overview of the main approaches and techniques that have been proposed in the domain of constraint satisfaction to deal with uncertain and dynamic environments