Causal Models as Minimal Descriptions of Multivariate Systems

By applying the minimality principle for model selection, one should seek the model that describes the data by a code of minimal length. Learning is viewed as data compression that exploits the regularities or qualitative properties found in the data, in order to build a model containing the meaningful information. The theory of causal modeling can be interpreted by this approach. The regularities are the conditional independencies reducing a factorization and the v-structure regularities. In the absence of other regularities, a causal model is faithful and offers a minimal description of a probability distribution. The causal interpretation of a faithful Bayesian network is motivated by the canonical representation it offers and faithfulness. A causal model decomposes the distribution into independent atomic blocks and is able to explain all qualitative properties found in the data. The existence of faithful models depends on the additional regularities in the data. Local structure of the conditional probability distributions allow further compression of the model. Interfering regularities, however, generate conditional independencies that do not follow from the Markov condition. These regularities has to be incorporated into an augmented model for which the inference algorithms are adapted to take into account their influences. But for other regularities, like patterns in a string, causality does not offer a modeling framework that leads to a minimal description.