Tree-Structured Recurrent Switching Linear Dynamical Systems for Multi-Scale Modeling

TL;DR

This paper introduces a hierarchical probabilistic model called Tree-Structured Recurrent Switching Linear Dynamical System that balances interpretability and accuracy in modeling complex nonlinear dynamics.

Contribution

It proposes a novel multi-scale model with a Bayesian inference method using Polya-Gamma augmentation for efficient fitting.

Findings

Outperforms existing methods in interpretability and prediction

Successfully models complex nonlinear systems with hierarchical locally linear dynamics

Demonstrates effectiveness on synthetic and real-world data

Abstract

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.