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SOE: Fachverband Physik sozio-ökonomischer Systeme

SOE 16: Networks (joint session SOE / DY / BP)

SOE 16.4: Vortrag

Donnerstag, 23. März 2017, 10:30–10:45, GÖR 226

Phase transition in detecting causal relationships from obervationaland interventional data — •Alexander K. Hartmann¹ and Gregory Nuel² — ¹Institut for Physics, University of Oldenburg, Germany — ²Laboratory of Probability and Stochastic Models (LPMA), Université Pierre et Marie Curie, Paris, France

Analysing data of, e.g., gene-expression experiments, and modelling it via network-based approaches is one of the main data analysis tasks in modern science. If one is interested in modelling correlations, approaches like the inverse Ising model can be used, which is already algorithmically challenging. If one wants to analyse even causal relationships, i.e., beyond correlations, it becomes even harder.

One way out is to include interventions to the system, e.g., by knocking out genes when studying gene expression. This allows, in principle, to get a grip on the causal structure of a system. Here, we model the data using Gaussian Bayesian networks defined on directed acyclic graphs (DAGs). Our approach [1] allows for multiple interventions in each single experiment and calculating joint maximum likelihoods (MLs) for the complete network. Furthermore, we have to sample different causal orderings, which induce different DAGs. The sampling is efficient because we approximate the full ML by probabilities of orderings of triplets. This allows us to study the quality of the causality detection as a function of the fraction of interventional experiments. We observe an information phase transition between phases where the causal structure cannot be detected and where it can be detected.

[1] A. Rau, F. Jaffrézic, and G. Nuel, BMC Sys. Biol. 7:111 (2013)