Learning Bayesian networks for discrete data

Time-varying dynamic Bayesian network learning for an fMRI study of emotion processing

This article presents a novel method for learning time-varying dynamic Bayesian networks. The proposed method breaks down the dynamic Bayesian network learning problem into a sequence of regression inference problems and tackles each problem using the Markov neighborhood regression technique. Notably, the method demonstrates scalability concerning data dimensionality, accommodates time-varying network structure, and naturally handles multi-subject data. The proposed method exhibits consistency and offers superior performance compared to existing methods in terms of estimation accuracy and computational efficiency, as supported by extensive numerical experiments. To showcase its effectiveness, we apply the proposed method to an fMRI study investigating the effective connectivity among various regions of interest (ROIs) during an emotion-processing task. Our findings reveal the pivotal role of the subcortical-cerebellum in emotion processing.

Enhanced construction of gene regulatory networks using hub gene information

BACKGROUND

Gene regulatory networks reveal how genes work together to carry out their biological functions. Reconstructions of gene networks from gene expression data greatly facilitate our understanding of underlying biological mechanisms and provide new opportunities for biomarker and drug discoveries. In gene networks, a gene that has many interactions with other genes is called a hub gene, which usually plays an essential role in gene regulation and biological processes. In this study, we developed a method for reconstructing gene networks using a partial correlation-based approach that incorporates prior information about hub genes. Through simulation studies and two real-data examples, we compare the performance in estimating the network structures between the existing methods and the proposed method.

RESULTS

In simulation studies, we show that the proposed strategy reduces errors in estimating network structures compared to the existing methods. When applied to Escherichia coli, the regulation network constructed by our proposed ESPACE method is more consistent with current biological knowledge than the SPACE method. Furthermore, application of the proposed method in lung cancer has identified hub genes whose mRNA expression predicts cancer progress and patient response to treatment.

CONCLUSIONS

We have demonstrated that incorporating hub gene information in estimating network structures can improve the performance of the existing methods.

Bayesian networks to identify statistical dependencies. A case study of Spanish university students' habits

OBJECTIVE

The present study sought to discover the relationships among different features characterizing Spanish university students' habits through a Bayesian network (BN). The set of features with the strongest influence in specific features can be determined.

METHODS

A BN was built from a dataset composed of 13 relevant features, determining the dependencies and conditional independencies from empirical data in a multivariate context. The structure was learned with the bnlearn package in R language introducing prior knowledge, and the parameters were obtained with Netica software. Three reasoning patterns were considered to make inferences: intercausal, evidential, and causal reasoning.

RESULTS

BN determined the different relationships. Through inference several conclusions were achieved, for instance a high probability value of physical activity in low state was obtained when active peers were instantiated to none state, self-rated fitness to fair state, bmi to normal weight, sitting time to moderate, age to 22-25, and gender to woman state.

CONCLUSIONS

Bayesian networks may help to characterize Spanish University students' habits.

Bayesian network modeling: A case study of an epidemiologic system analysis of cardiovascular risk

An extensive, in-depth study of cardiovascular risk factors (CVRF) seems to be of crucial importance in the research of cardiovascular disease (CVD) in order to prevent (or reduce) the chance of developing or dying from CVD. The main focus of data analysis is on the use of models able to discover and understand the relationships between different CVRF. In this paper a report on applying Bayesian network (BN) modeling to discover the relationships among thirteen relevant epidemiological features of heart age domain in order to analyze cardiovascular lost years (CVLY), cardiovascular risk score (CVRS), and metabolic syndrome (MetS) is presented. Furthermore, the induced BN was used to make inference taking into account three reasoning patterns: causal reasoning, evidential reasoning, and intercausal reasoning. Application of BN tools has led to discovery of several direct and indirect relationships between different CVRF. The BN analysis showed several interesting results, among them: CVLY was highly influenced by smoking being the group of men the one with highest risk in CVLY; MetS was highly influence by physical activity (PA) being again the group of men the one with highest risk in MetS, and smoking did not show any influence. BNs produce an intuitive, transparent, graphical representation of the relationships between different CVRF. The ability of BNs to predict new scenarios when hypothetical information is introduced makes BN modeling an Artificial Intelligence (AI) tool of special interest in epidemiological studies. As CVD is multifactorial the use of BNs seems to be an adequate modeling tool.

Weak Convergence Rates of Population Versus Single-Chain Stochastic Approximation MCMC Algorithms

In this paper we establish the theory of weak convergence (toward a normal distribution) for both single-chain and population stochastic approximation Markov chain Monte Carlo (MCMC) algorithms (SAMCMC algorithms). Based on the theory, we give an explicit ratio of convergence rates for the population SAMCMC algorithm and the single-chain SAMCMC algorithm. Our results provide a theoretic guarantee that the population SAMCMC algorithms are asymptotically more efficient than the single-chain SAMCMC algorithms when the gain factor sequence decreases slower than O(1 / t), where t indexes the number of iterations. This is of interest for practical applications.

Weak Convergence Rates of Population Versus Single-Chain Stochastic Approximation MCMC Algorithms

In this paper we establish the theory of weak convergence (toward a normal distribution) for both single-chain and population stochastic approximation Markov chain Monte Carlo (MCMC) algorithms (SAMCMC algorithms). Based on the theory, we give an explicit ratio of convergence rates for the population SAMCMC algorithm and the single-chain SAMCMC algorithm. Our results provide a theoretic guarantee that the population SAMCMC algorithms are asymptotically more efficient than the single-chain SAMCMC algorithms when the gain factor sequence decreases slower than O(1 / t), where t indexes the number of iterations. This is of interest for practical applications.

Bayesian Method for Causal Discovery of Latent-Variable Models from a Mixture of Experimental and Observational Data

This paper describes a Bayesian method for learning causal Bayesian networks through networks that contain latent variables from an arbitrary mixture of observational and experimental data. The paper presents Bayesian methods (including a new method) for learning the causal structure and parameters of the underlying causal process that is generating the data, given that the data contain a mixture of observational and experimental cases. These learning methods were applied using as input various mixtures of experimental and observational data that were generated from the ALARM causal Bayesian network. The paper reports how these structure predictions and parameter estimates compare with the true causal structures and parameters as given by the ALARM network. The paper shows that (1) the new method for learning Bayesian network structure from a mixture of data that this paper introduce, Gibbs Volume method, best estimates the probability of the data given the latent variable model and (2) using large data (>10,000 cases), another model, the implicit latent variable method, is asymptotically correct and efficient.

Comparing statistical methods for constructing large scale gene networks

The gene regulatory network (GRN) reveals the regulatory relationships among genes and can provide a systematic understanding of molecular mechanisms underlying biological processes. The importance of computer simulations in understanding cellular processes is now widely accepted; a variety of algorithms have been developed to study these biological networks. The goal of this study is to provide a comprehensive evaluation and a practical guide to aid in choosing statistical methods for constructing large scale GRNs. Using both simulation studies and a real application in E. coli data, we compare different methods in terms of sensitivity and specificity in identifying the true connections and the hub genes, the ease of use, and computational speed. Our results show that these algorithms performed reasonably well, and each method has its own advantages: (1) GeneNet, WGCNA (Weighted Correlation Network Analysis), and ARACNE (Algorithm for the Reconstruction of Accurate Cellular Networks) performed well in constructing the global network structure; (2) GeneNet and SPACE (Sparse PArtial Correlation Estimation) performed well in identifying a few connections with high specificity.

Learning Bayesian networks: approaches and issues

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.