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

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.

Cited by in corpus (12)

• Metastable dynamics of neural circuits and networks
• Neural Latents Benchmark '21: Evaluating latent variable models of neural population activity
• GP-Tree: A Gaussian Process Classifier for Few-Shot Incremental Learning
• Reverse engineering recurrent neural networks with Jacobian switching linear dynamical systems
• Variational online learning of neural dynamics
• Unifying and generalizing models of neural dynamics during decision-making
• Variational Dynamic Mixtures
• Deep Switching State Space Model (DS${}^3$M) for Nonlinear Time Series Forecasting with Regime Switching
• Equivariant Deep Dynamical Model for Motion Prediction
• Graph Gamma Process Generalized Linear Dynamical Systems
• PRRS Outbreak Prediction via Deep Switching Auto-Regressive Factorization Modeling
• Investigating naturalistic hand movements by behavior mining in long-term video and neural recordings