Abductive learning of quantized stochastic processes with probabilistic finite automata

Area of Science:

• Complex Systems
• Machine Learning
• Statistical Inference

Background:

• Stochastic dynamical systems generate complex data.
• Inferring causal structures in these systems is challenging.
• Quantized observations require specialized modeling approaches.

Purpose of the Study:

• To present GenESeSS, an unsupervised algorithm for causal structure inference.
• To model quantized stochastic processes using probabilistic finite state automata.
• To establish theoretical guarantees and demonstrate practical applicability.

Main Methods:

• Unsupervised learning algorithm (GenESeSS).
• Abductive inference for hypothesis generation.
• Probabilistic finite state automata modeling.
• Analysis of ergodicity and stationarity assumptions.

Main Results:

• GenESeSS infers causal structures of quantized stochastic processes.
• Probabilistic automata models are probably approximately correct-learnable.
• Rigorous performance guarantees and data requirements established.
• Successful inference of long-range dependencies demonstrated.

Conclusions:

• GenESeSS provides a robust method for automated causal inference.
• The algorithm is applicable to complex physical phenomena.
• Validated through modeling and prediction on simulated and real data.