Joint estimation of multiple related biological networks

Graphical models are widely used to make inferences concerning interplay in multivariate systems. In many applications, data are collected from multiple related but nonidentical units whose underlying networks may differ but are likely to share features. Here we present a hierarchical Bayesian formulation for joint estimation of multiple networks in this nonidentically distributed setting. The approach is general: given a suitable class of graphical models, it uses an exchangeability assumption on networks to provide a corresponding joint formulation. Motivated by emerging experimental designs in molecular biology, we focus on time-course data with interventions, using dynamic Bayesian networks as the graphical models. We introduce a computationally efficient, deterministic algorithm for exact joint inference in this setting. We provide an upper bound on the gains that joint estimation offers relative to separate estimation for each network and empirical results that support and extend the theory, including an extensive simulation study and an application to proteomic data from human cancer cell lines. Finally, we describe approximations that are still more computationally efficient than the exact algorithm and that also demonstrate good empirical performance.Comment: Published in at http://dx.doi.org/10.1214/14-AOAS761 the Annals of Applied Statistics (http://www.imstat.org/aoas/) by the Institute of Mathematical Statistics (http://www.imstat.org

Scalable Exact Parent Sets Identification in Bayesian Networks Learning with Apache Spark

In Machine Learning, the parent set identification problem is to find a set of random variables that best explain selected variable given the data and some predefined scoring function. This problem is a critical component to structure learning of Bayesian networks and Markov blankets discovery, and thus has many practical applications, ranging from fraud detection to clinical decision support. In this paper, we introduce a new distributed memory approach to the exact parent sets assignment problem. To achieve scalability, we derive theoretical bounds to constraint the search space when MDL scoring function is used, and we reorganize the underlying dynamic programming such that the computational density is increased and fine-grain synchronization is eliminated. We then design efficient realization of our approach in the Apache Spark platform. Through experimental results, we demonstrate that the method maintains strong scalability on a 500-core standalone Spark cluster, and it can be used to efficiently process data sets with 70 variables, far beyond the reach of the currently available solutions

Parallel Implementation of Efficient Search Schemes for the Inference of Cancer Progression Models

The emergence and development of cancer is a consequence of the accumulation over time of genomic mutations involving a specific set of genes, which provides the cancer clones with a functional selective advantage. In this work, we model the order of accumulation of such mutations during the progression, which eventually leads to the disease, by means of probabilistic graphic models, i.e., Bayesian Networks (BNs). We investigate how to perform the task of learning the structure of such BNs, according to experimental evidence, adopting a global optimization meta-heuristics. In particular, in this work we rely on Genetic Algorithms, and to strongly reduce the execution time of the inference -- which can also involve multiple repetitions to collect statistically significant assessments of the data -- we distribute the calculations using both multi-threading and a multi-node architecture. The results show that our approach is characterized by good accuracy and specificity; we also demonstrate its feasibility, thanks to a 84x reduction of the overall execution time with respect to a traditional sequential implementation

A Parallel Algorithm for Exact Bayesian Structure Discovery in Bayesian Networks

Exact Bayesian structure discovery in Bayesian networks requires exponential time and space. Using dynamic programming (DP), the fastest known sequential algorithm computes the exact posterior probabilities of structural features in $O(2(d+1)n2^n)$ time and space, if the number of nodes (variables) in the Bayesian network is $n$ and the in-degree (the number of parents) per node is bounded by a constant $d$. Here we present a parallel algorithm capable of computing the exact posterior probabilities for all $n(n-1)$ edges with optimal parallel space efficiency and nearly optimal parallel time efficiency. That is, if $p=2^k$ processors are used, the run-time reduces to $O(5(d+1)n2^{n-k}+k(n-k)^d)$ and the space usage becomes $O(n2^{n-k})$ per processor. Our algorithm is based the observation that the subproblems in the sequential DP algorithm constitute a $n$-$D$ hypercube. We take a delicate way to coordinate the computation of correlated DP procedures such that large amount of data exchange is suppressed. Further, we develop parallel techniques for two variants of the well-known \emph{zeta transform}, which have applications outside the context of Bayesian networks. We demonstrate the capability of our algorithm on datasets with up to 33 variables and its scalability on up to 2048 processors. We apply our algorithm to a biological data set for discovering the yeast pheromone response pathways.Comment: 32 pages, 12 figure

How to understand the cell by breaking it: network analysis of gene perturbation screens

Modern high-throughput gene perturbation screens are key technologies at the forefront of genetic research. Combined with rich phenotypic descriptors they enable researchers to observe detailed cellular reactions to experimental perturbations on a genome-wide scale. This review surveys the current state-of-the-art in analyzing perturbation screens from a network point of view. We describe approaches to make the step from the parts list to the wiring diagram by using phenotypes for network inference and integrating them with complementary data sources. The first part of the review describes methods to analyze one- or low-dimensional phenotypes like viability or reporter activity; the second part concentrates on high-dimensional phenotypes showing global changes in cell morphology, transcriptome or proteome.Comment: Review based on ISMB 2009 tutorial; after two rounds of revisio