Causal graph inference in multidimensional data sets via information theoretic methods
Florin Popescu – Fraunhofer FIRST
Despite recent advances on causal inference, for time-series the state of the art remains analysis of pairs of time-vectors (Granger causality, PSI). In context of information theoretic interpretations of causality, the type of data considered is irrelevant (Boolean, continuous, time-series) since source and conditional information can be quantified in a unified manner, be it computed using Shannon, Bayesian or Kolmogorov/Chaitin approaches. Although the presumption of non-bijective and irreversible transformations implies a time-ordering which is sometimes inferred, time information can help eliminate common-cause effects. To allow for common underlying cause, independence, and mutual interaction, causal dependencies should be valued according to both direction and significance. Multi-dimensional data requires inference of ?best causal ordering? among M variables, a combinatorial, TSP-like problem requiring non-convex algorithms which must operate within polynomial memory and time constraints (Silverstein, 1998). Iterated target-to-(M-1) cause comparison (such as MB) does not automatically lead to directed causal graph inference. Further heuristics for pruning the candidate solution set are needed: e.g. if neither of 2 possible causes seems to relate to the target, any conjunctive relation between them is unlikely to causally influence it. Causal graph inference results on sample data sets (such as LUCAS) and time series are presented.