3off2: A network reconstruction algorithm based on 2-point and 3-point information statistics

Abstract

BackgroundThe reconstruction of reliable graphical models from observational data is important in bioinformatics and other computational fields applying network reconstruction methods to large, yet finite datasets. The main network reconstruction approaches are either based on Bayesian scores, which enable the ranking of alternative Bayesian networks, or rely on the identification of structural independencies, which correspond to missing edges in the underlying network. Bayesian inference methods typically require heuristic search strategies, such as hill-climbing algorithms, to sample the super-exponential space of possible networks. By contrast, constraint-based methods, such as the PC and IC algorithms, are expected to run in polynomial time on sparse underlying graphs, provided that a correct list of conditional independencies is available. Yet, in practice, conditional independencies need to be ascertained from the available observational data, based on adjustable statistical significance levels, and are not robust to sampling noise from finite datasets.ResultsWe propose a more robust approach to reconstruct graphical models from finite datasets. It combines constraint-based and Bayesian approaches to infer structural independencies based on the ranking of their most likely contributing nodes. In a nutshell, this local optimization scheme and corresponding 3off2 algorithm iteratively “take off” the most likely conditional 3-point information from the 2-point (mutual) information between each pair of nodes. Conditional independencies are thus derived by progressively collecting the most significant indirect contributions to all pairwise mutual information. The resulting network skeleton is then partially directed by orienting and propagating edge directions, based on the sign and magnitude of the conditional 3-point information of unshielded triples. The approach is shown to outperform both constraint-based and Bayesian inference methods on a range of benchmark networks. The 3off2 approach is then applied to the reconstruction of the hematopoiesis regulation network based on recent single cell expression data and is found to retrieve more experimentally ascertained regulations between transcription factors than with other available methods.ConclusionsThe novel information-theoretic approach and corresponding 3off2 algorithm combine constraint-based and Bayesian inference methods to reliably reconstruct graphical models, despite inherent sampling noise in finite datasets. In particular, experimentally verified interactions as well as novel predicted regulations are established on the hematopoiesis regulatory networks based on single cell expression data.Electronic supplementary materialThe online version of this article (doi:10.1186/s12859-015-0856-x) contains supplementary material, which is available to authorized users.

Spectral consensus strategy for accurate reconstruction of large biological networks

“…We randomly sampled 5 datasets of sizes 150 and 200 to perform the experiments under high-dimensional conditions for ANDES, and 5 datasets of size 935 for MUNIN. The embedded reconstruction methods are ARACNE [1], a mutual information-based approach, 3off2 [4], a hybrid method that combines constraint-based and scoring approaches based on multivariate information measures, and a hill-climbing algorithm using the Bayesian Dirichlet equivalent score. We also considered a random classifier in our SCS- spectral and SCS- learn step evaluations (Additional file 1: Figures S4).…”

“…As successfully demonstrated, networks are invaluable tools to comprehensively relate biological variables [1–3] and possibly gain insights into their direct causal relationships [4]. Interestingly, recent studies have shown that the available approaches would not generally perform optimally across all dataset types and the integration of diverse inference methods can provide an improved robust performance [5–8].…”

“…More recently, several mutual information-based approaches have been proposed to infer direct relationships from noisy observational datasets containing few samples [1, 2]. Nevertheless, as demonstrated by the growing number of hybrid approaches [4, 13–15], the wide range of high-dimensional data is still challenging state-of-the-art methods, both in terms of accuracy, or time and memory consumption.…”

Integration and Visualization of Translational Medicine Data for Better Understanding of Human Diseases

“…The platform is available in both server and cloud-based versions and bridges to the other major bioinformatics workflow management systems—Taverna, 51 KNIME, and gUSE. 37 Such architecture permits transparent and replicable design of analytical workflows for data exploration and formulation of data-driven hypotheses.…”

Using Unlabeled Data to Discover Bivariate Causality with Deep Restricted Boltzmann Machines

“…These approaches provide causal directions based on the estimated conditional and marginal distributions from observed non-temporal data. The bivariate methods are quite different from another state-of-art approach called 3off2 [9] where the algorithm needs three variables to infer a direction, since it considers all possible triplets in data, and looks for colliders in a graph. Therefore, the 3off2 is not suitable for bivariate cases.…”