  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.
