Bayesian network learning and applications in Bioinformatics

Abstract A Bayesian network (BN) is a compact graphic representation of the probabilistic re- lationships among a set of random variables. The advantages of the BN formalism include its rigorous mathematical basis, the characteristics of locality both in knowl- edge representation and during inference, and the innate way to deal with uncertainty. Over the past decades, BNs have gained increasing interests in many areas, including bioinformatics which studies the mathematical and computing approaches to under- stand biological processes. In this thesis, I develop new methods for BN structure learning with applications to bi- ological network reconstruction and assessment. The first application is to reconstruct the genetic regulatory network (GRN), where each gene is modeled as a node and an edge indicates a regulatory relationship between two genes. In this task, we are given time-series microarray gene expression measurements for tens of thousands of genes, which can be modeled as true gene expressions mixed with noise in data generation, variability of the underlying biological systems etc. We develop a novel BN structure learning algorithm for reconstructing GRNs. The second application is to develop a BN method for protein-protein interaction (PPI) assessment. PPIs are the foundation of most biological mechanisms, and the knowl- edge on PPI provides one of the most valuable resources from which annotations of genes and proteins can be discovered. Experimentally, recently-developed high- throughput technologies have been carried out to reveal protein interactions in many organisms. However, high-throughput interaction data often contain a large number of iv spurious interactions. In this thesis, I develop a novel in silico model for PPI assess- ment. Our model is based on a BN that integrates heterogeneous data sources from different organisms. The main contributions are: 1. A new concept to depict the dynamic dependence relationships among random variables, which widely exist in biological processes, such as the relationships among genes and genes' products in regulatory networks and signaling pathways. This con- cept leads to a novel algorithm for dynamic Bayesian network learning. We apply it to time-series microarray gene expression data, and discover some missing links in a well-known regulatory pathway. Those new causal relationships between genes have been found supportive evidences in literature. 2. Discovery and theoretical proof of an asymptotic property of K2 algorithm ( a well-known efficient BN structure learning approach). This property has been used to identify Markov blankets (MB) in a Bayesian network, and further recover the BN structure. This hybrid algorithm is evaluated on a benchmark regulatory pathway, and obtains better results than some state-of-art Bayesian learning approaches. 3. A Bayesian network based integrative method which incorporates heterogeneous data sources from different organisms to predict protein-protein interactions (PPI) in a target organism. The framework is employed in human PPI prediction and in as- sessment of high-throughput PPI data. Furthermore, our experiments reveal some interesting biological results. 4. We introduce the learning of a TAN (Tree Augmented Naïve Bayes) based net- work, which has the computational simplicity and robustness to high-throughput PPI assessment. The empirical results show that our method outperforms naïve Bayes and a manual constructed Bayesian Network, additionally demonstrate sufficient informa- tion from model organisms can achieve high accuracy in PPI prediction

Causal graphical models in systems genetics: A unified framework for joint inference of causal network and genetic architecture for correlated phenotypes

Causal inference approaches in systems genetics exploit quantitative trait loci (QTL) genotypes to infer causal relationships among phenotypes. The genetic architecture of each phenotype may be complex, and poorly estimated genetic architectures may compromise the inference of causal relationships among phenotypes. Existing methods assume QTLs are known or inferred without regard to the phenotype network structure. In this paper we develop a QTL-driven phenotype network method (QTLnet) to jointly infer a causal phenotype network and associated genetic architecture for sets of correlated phenotypes. Randomization of alleles during meiosis and the unidirectional influence of genotype on phenotype allow the inference of QTLs causal to phenotypes. Causal relationships among phenotypes can be inferred using these QTL nodes, enabling us to distinguish among phenotype networks that would otherwise be distribution equivalent. We jointly model phenotypes and QTLs using homogeneous conditional Gaussian regression models, and we derive a graphical criterion for distribution equivalence. We validate the QTLnet approach in a simulation study. Finally, we illustrate with simulated data and a real example how QTLnet can be used to infer both direct and indirect effects of QTLs and phenotypes that co-map to a genomic region.Comment: Published in at http://dx.doi.org/10.1214/09-AOAS288 the Annals of Applied Statistics (http://www.imstat.org/aoas/) by the Institute of Mathematical Statistics (http://www.imstat.org

Benchpress: a scalable and platform-independent workflow for benchmarking structure learning algorithms for graphical models

Describing the relationship between the variables in a study domain and modelling the data generating mechanism is a fundamental problem in many empirical sciences. Probabilistic graphical models are one common approach to tackle the problem. Learning the graphical structure is computationally challenging and a fervent area of current research with a plethora of algorithms being developed. To facilitate the benchmarking of different methods, we present a novel automated workflow, called benchpress for producing scalable, reproducible, and platform-independent benchmarks of structure learning algorithms for probabilistic graphical models. Benchpress is interfaced via a simple JSON-file, which makes it accessible for all users, while the code is designed in a fully modular fashion to enable researchers to contribute additional methodologies. Benchpress currently provides an interface to a large number of state-of-the-art algorithms from libraries such as BiDAG, bnlearn, GOBNILP, pcalg, r.blip, scikit-learn, TETRAD, and trilearn as well as a variety of methods for data generating models and performance evaluation. Alongside user-defined models and randomly generated datasets, the software tool also includes a number of standard datasets and graphical models from the literature, which may be included in a benchmarking workflow. We demonstrate the applicability of this workflow for learning Bayesian networks in four typical data scenarios. The source code and documentation is publicly available from http://github.com/felixleopoldo/benchpress.Comment: 30 pages, 1 figur

How long, O Bayesian network, will I sample thee? A program analysis perspective on expected sampling times

Bayesian networks (BNs) are probabilistic graphical models for describing complex joint probability distributions. The main problem for BNs is inference: Determine the probability of an event given observed evidence. Since exact inference is often infeasible for large BNs, popular approximate inference methods rely on sampling. We study the problem of determining the expected time to obtain a single valid sample from a BN. To this end, we translate the BN together with observations into a probabilistic program. We provide proof rules that yield the exact expected runtime of this program in a fully automated fashion. We implemented our approach and successfully analyzed various real-world BNs taken from the Bayesian network repository