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