Causal Consistency of Structural Equation Models

Complex systems can be modelled at various levels of detail. Ideally, causal models of the same system should be consistent with one another in the sense that they agree in their predictions of the effects of interventions. We formalise this notion of consistency in the case of Structural Equation Models (SEMs) by introducing exact transformations between SEMs. This provides a general language to consider, for instance, the different levels of description in the following three scenarios: (a) models with large numbers of variables versus models in which the `irrelevant' or unobservable variables have been marginalised out; (b) micro-level models versus macro-level models in which the macro-variables are aggregate features of the micro-variables; (c) dynamical time series models versus models of their stationary behaviour. Our analysis stresses the importance of well specified interventions in the causal modelling process and sheds light on the interpretation of cyclic SEMs.Comment: equal contribution between Rubenstein and Weichwald; accepted manuscrip

The color of smiling: computational synaesthesia of facial expressions

This note gives a preliminary account of the transcoding or rechanneling problem between different stimuli as it is of interest for the natural interaction or affective computing fields. By the consideration of a simple example, namely the color response of an affective lamp to a sensed facial expression, we frame the problem within an information- theoretic perspective. A full justification in terms of the Information Bottleneck principle promotes a latent affective space, hitherto surmised as an appealing and intuitive solution, as a suitable mediator between the different stimuli.Comment: Submitted to: 18th International Conference on Image Analysis and Processing (ICIAP 2015), 7-11 September 2015, Genova, Ital

Gene Regulatory Network Reconstruction Using Bayesian Networks, the Dantzig Selector, the Lasso and Their Meta-Analysis

Modern technologies and especially next generation sequencing facilities are giving a cheaper access to genotype and genomic data measured on the same sample at once. This creates an ideal situation for multifactorial experiments designed to infer gene regulatory networks. The fifth “Dialogue for Reverse Engineering Assessments and Methods” (DREAM5) challenges are aimed at assessing methods and associated algorithms devoted to the inference of biological networks. Challenge 3 on “Systems Genetics” proposed to infer causal gene regulatory networks from different genetical genomics data sets. We investigated a wide panel of methods ranging from Bayesian networks to penalised linear regressions to analyse such data, and proposed a simple yet very powerful meta-analysis, which combines these inference methods. We present results of the Challenge as well as more in-depth analysis of predicted networks in terms of structure and reliability. The developed meta-analysis was ranked first among the teams participating in Challenge 3A. It paves the way for future extensions of our inference method and more accurate gene network estimates in the context of genetical genomics

Learning Bounded Tree-Width Bayesian Networks via Sampling

Abstract. Learning Bayesian networks with bounded tree-width has at-tracted much attention recently, because low tree-width allows exact in-ference to be performed efficiently. Some existing methods [12, 14] tackle the problem by using k-trees to learn the optimal Bayesian network with tree-width up to k. In this paper, we propose a sampling method to ef-ficiently find representative k-trees by introducing an Informative score function to characterize the quality of a k-tree. The proposed algorithm can efficiently learn a Bayesian network with tree-width at most k. Ex-periment results indicate that our approach is comparable with exact methods, but is much more computationally efficient

Algebraic Equivalence of Linear Structural Equation Models

Despite their popularity, many questions about the algebraic constraints imposed by linear structural equation models remain open problems. For causal discovery, two of these problems are especially important: the enumeration of the constraints imposed by a model, and deciding whether two graphs define the same statistical model. We show how the half-trek criterion can be used to make progress in both of these problems. We apply our theoretical results to a small-scale model selection problem, and find that taking the additional algebraic constraints into account may lead to significant improvements in model selection accuracy