Joint estimation of multiple related biological networks

Abstract

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.

Causal Inference by using Invariant Prediction: Identification and Confidence Intervals

“…However, a softer approach that allows for variation in causal structure across data subsets might sometimes be appropriate (see for example Oates et al . ()).…”

Nonparametric Bayesian Inference in Biostatistics

“…These topics include approaches for multiple graphs (Oates et al 2014;Peterson et al 2014), approaches for matrix-variate data (Wang & West 2009;Dobra et al 2011), and hierarchical models that include biological networks as a component of a more complex model (Chekouo et al 2015), among others. The Bayesian approaches we have presented offer a coherent framework in which edge selection and parameter estimation are performed simultaneously.…”

Context-specificity in causal signaling networks revealed by phosphoprotein profiling

“…Although interested in learning context-specific networks, we expect a good proportion of agreement between contexts. Therefore, rather than learn networks for each context separately, we used a joint approach to learn all networks together (Oates et al, 2014). A prior network was used ( Figure S3); this was curated manually with input from literature (Weinberg, 2013) and online resources.…”

“…A prior network was used ( Figure S3); this was curated manually with input from literature (Weinberg, 2013) and online resources. The extent to which context-specific networks are encouraged to agree with each other and with the prior network is controlled by two parameters, and respectively, as described in detail in Oates et al (2014). These parameters were set (to = 3 and = 15) by considering a grid of possible values and selecting an option that provides a reasonable, but conservative amount of agreement, allowing for discovery of context-specific edges that are not in the canonical prior network.…”