Causal Learning via Manifold Regularization

This paper frames causal structure estimation as a machine learning task. The idea is to treat indicators of causal relationships between variables as `labels' and to exploit available data on the variables of interest to provide features for the labelling task. Background scientific knowledge or any available interventional data provide labels on some causal relationships and the remainder are treated as unlabelled. To illustrate the key ideas, we develop a distance-based approach (based on bivariate histograms) within a manifold regularization framework. We present empirical results on three different biological data sets (including examples where causal effects can be verified by experimental intervention), that together demonstrate the efficacy and general nature of the approach as well as its simplicity from a user's point of view.
This work was supported by the UK Medical Research Council (University Unit Programme number MC UU 00002/2). CJO was supported by the ARC Centre of Excellence for Mathematics and Statistics, Australia, and the Lloyd's Register Foundation programme on data-centric engineering at the Alan Turing Institute, UK.