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Probabilistic causality and detecting collections of interdependence patterns



Interdependent effects are usually distinguished from statistical interaction by using the sufficient causes framework. This almost always involves expressing probability distributions as deterministic logic functions, where certain conditions invariably produce or prevent an outcome. Using an idea from the philosophy literature, that a cause is defined as an event which increases the probability of an outcome, a probabilistic sufficient causes framework is developed here. It expresses distributions with probabilistic logic functions and is used to define interdependence without determinism. The connections, between probabilistic logic and the inequalities which define convex polytopes in the space of the distribution parameters, are given. Interdependence is defined for the response behaviour of individuals, defined by latent variables, and is not directly observable. It is shown that the formulation of the models as geometric objects enables the use of algebraic tools to compute observable constraints for detecting interdependence. Novel constraints are derived for detecting causal interdependence patterns and the corresponding statistical tests are described.