Information-theoretic model selection for optimal prediction of stochastic dynamical systems from data.

Area of Science:

• Complex Systems Science
• Dynamical Systems Theory
• Information Theory

Background:

• Data-driven models are crucial for real-world systems lacking mechanistic or phenomenological descriptions.
• Traditional delay-coordinate embedding methods are effective for deterministic systems but inadequate for stochastic ones.
• Stochastic models are necessary when operational determinism is not met.

Purpose of the Study:

• To develop a new toolkit for analyzing stochastic dynamical systems.
• To introduce an information-theoretic criterion for selecting embedding dimensions in data-driven models.
• To enhance the predictive optimality of models for stochastic systems.

Main Methods:

• An information-theoretic criterion, the negative log-predictive likelihood, is proposed for embedding dimension selection.
• A nonparametric estimator for the negative log-predictive likelihood is developed.
• The performance of the new criterion is compared against active information storage.

Main Results:

• The negative log-predictive likelihood provides a method for selecting embedding dimensions for stochastic systems.
• The developed estimator demonstrates effectiveness in model selection.
• Candidate predictors for stochastic systems can be compared to an information-theoretic lower bound.

Conclusions:

• The negative log-predictive likelihood is a valuable tool for modeling stochastic dynamical systems.
• This approach advances the analysis of complex systems where determinism is absent.
• The findings offer a framework for comparing predictive models of stochastic processes.