Mixed LICORS: A Nonparametric Algorithm for Predictive State Reconstruction.

Area of Science:

• Computational Science
• Machine Learning
• Data Science

Background:

• Learning nonlinear, high-dimensional dynamics from spatio-temporal data is crucial for prediction and simulation.
• Existing methods like LICORS (Goerg and Shalizi, 2012) use hard clustering, which can limit performance with limited data.

Purpose of the Study:

• To introduce mixed LICORS, an extension of the LICORS algorithm.
• To enhance the learning of nonlinear dynamics by incorporating non-parametric, expectation-maximization (EM)-like soft clustering.
• To improve out-of-sample forecasting performance, particularly in data-limited scenarios.

Main Methods:

• Developed mixed LICORS, transitioning from hard to soft clustering of predictive distributions.
• Employed a non-parametric, EM-like soft clustering approach within the algorithm.
• Validated the method through simulations to assess its predictive capabilities.

Main Results:

• Mixed LICORS retains the asymptotic predictive optimality of the original LICORS algorithm.
• Simulations demonstrate significantly improved out-of-sample forecasts compared to previous methods when using limited data.
• The algorithm is implemented in the publicly available R package LICORS.

Conclusions:

• Mixed LICORS offers a robust advancement for learning complex dynamics from spatio-temporal data.
• The soft clustering approach enhances predictive accuracy and forecasting reliability, especially in data-scarce situations.
• The availability of the R package facilitates broader application and research in this area.