Indirect Causes, Dependencies and Causality in Bayesian Networks

Modeling causal dependencies in complex or time-dependent domains often demands cyclic dependencies. Such cycles arise from local points of views on dependencies where no singular causality is identifiable, i.e., roles of causes and effects are not universally identifiable. Modeling causation instead of correlation is of utmost importance, which is why Bayesian networks are frequently used to reason under uncertainty. Bayesian networks are probabilistic graphical models and allow for a causal modeling approach with locally specifiable and interpretable parameters, but are not defined for cyclic graph structures. If Bayesian networks are to be used for modeling uncertainties, cycles are eliminated with dynamic Bayesian networks, eliminating cycles over time. However, we show that eliminating cycles over time eliminates an anticipation of indirect influences as well, and enforces an infinitesimal resolution of time. Without a “causal design,” i.e., without representing direct and indirect causes appropriately, such networks return spurious results. In particular, the main novel contributions of this thesis can be summarized as follows. By considering specific properties of local conditional probability distributions, we show that a novel form of probabilistic graphical models rapidly adapts itself to a specific context at every timestep and, by that, correctly anticipates indirect influences under an unrestricted time granularity, even if cyclic dependencies arise. We show that this novel form of probabilistic graphical models follows familiar Bayesian networks’ syntax and semantics, despite being based on cyclic graphs. Throughout this thesis, we show that no external reasoning frameworks are required, no novel calculus needs be introduced, no computational overhead for solving common inference-, query- and learningproblems is introduced, and that familiar algorithmic schemes remain applicable. We feel confident to say that Bayesian networks and dynamic Bayesian networks can be based on cyclic graphs. In effect, we show, for the very first time, that a novel dynamic probabilistic graphical model is an intrinsic representation of a full joint probability distribution over multiple full joint probability distributions.