Abductive learning of quantized stochastic processes with probabilistic finite automata

We present an unsupervised learning algorithm (GenESeSS) to infer the causal structure of quantized stochastic processes, defined as stochastic dynamical systems evolving over discrete time, and producing quantized observations. Assuming ergodicity and stationarity, GenESeSS infers probabilistic finite state automata models from a sufficiently long observed trace. Our approach is abductive; attempting to infer a simple hypothesis, consistent with observations and modelling framework that essentially fixes the hypothesis class. The probabilistic automata we infer have no initial and terminal states, have no structural restrictions and are shown to be probably approximately correct-learnable. Additionally, we establish rigorous performance guarantees and data requirements, and show that GenESeSS correctly infers long-range dependencies. Modelling and prediction examples on simulated and real data establish relevance to automated inference of causal stochastic structures underlying complex physical phenomena.