Tree-Structured Recurrent Switching Linear Dynamical Systems for Multi-Scale Modeling
This work addresses the problem of multi-scale modeling for researchers and practitioners in fields like control systems or time-series analysis, offering an incremental improvement by combining hierarchical linear dynamics with Bayesian inference.
The authors tackled the trade-off between interpretability and accuracy in modeling nonlinear dynamical systems by developing a tree-structured recurrent switching linear dynamical system, which outperformed existing methods in both interpretability and predictive capability on synthetic and real examples.
Many real-world systems studied are governed by complex, nonlinear dynamics. By modeling these dynamics, we can gain insight into how these systems work, make predictions about how they will behave, and develop strategies for controlling them. While there are many methods for modeling nonlinear dynamical systems, existing techniques face a trade off between offering interpretable descriptions and making accurate predictions. Here, we develop a class of models that aims to achieve both simultaneously, smoothly interpolating between simple descriptions and more complex, yet also more accurate models. Our probabilistic model achieves this multi-scale property through a hierarchy of locally linear dynamics that jointly approximate global nonlinear dynamics. We call it the tree-structured recurrent switching linear dynamical system. To fit this model, we present a fully-Bayesian sampling procedure using Polya-Gamma data augmentation to allow for fast and conjugate Gibbs sampling. Through a variety of synthetic and real examples, we show how these models outperform existing methods in both interpretability and predictive capability.