TREE-STRUCTURED RECURRENT SWITCHING LINEAR DYNAMICAL SYSTEMS FOR MULTI-SCALE MODELING
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 1 . 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 Pólya-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.
PAPER SUMMARY:
This paper introduces a probabilistic generative framework to model linear dynamical systems at multiple levels of resolution, where the entire complex, nonlinear dynamics is approximated via a hierarchy of local regimes of linear dynamics -- the global dynamic is then characterized as a switching process that switches between linear regimes in the hierarchy.
NOVELTY & SIGNIFICANCE:
The key contributions of this paper are (a) the use of tree-structured stick breaking to partition the entire dynamic space into a hierarchy of linear regimes; (b) the design of a hierarchical prior that is compatible to the tree structure; and (c) the developed Bayesian inference framework for it in Section 4.
By exploiting the tree-structured stick breaking process (Adams et al., 2010), the proposed framework is able to partition the entire dynamic space into a hierarchy of switching linear regimes.
This allows the dynamic to be queried at multiple levels of resolution. This appears to be the key difference between the proposed framework and the previous work of (Linderman et al., 2017) on recurrent switching dynamical systems that partition the dynamic space sequentially at the same level of resolution.
This seems like a non-trivial extension to the previous work of (Linderman et al., 2017) & I tend to consider this a novel contribution. That said, the paper was also not positioned against existing literature on hierarchical switching linear dynamic systems (see below) & I find it hard to evaluate the significance of the proposed framework (which explains the borderline rating)
"A Hierarchical Switching Linear Dynamical System applied to the detection of sepsis in neonatal condition monitoring", Ioan Stanculescu, Christopher K. I. Williams and Yvonne Freer. In Proceeding of the 30th Conference on Uncertainty in AI (UAI-14), pages 752-761
Could the authors please discuss the differences between the proposed work & (at least) the above? 
TECHNICAL SOUNDNESS:
The technical exposition makes sense to me. Please also discuss the processing complexity of the resulting TrSLDS framework. In exchange for the improved performance, how much slower TrSLDS is as compared
to rSLDS? I am interested to see this demonstrated in the empirical studies.
CLARITY:
The paper is clearly written.
EMPIRICAL RESULTS:
The experiments look interesting and are very extensive on both test domains. However, I do not understand why the authors decided not to compare with rSLDS using its benchmark? 
I find this somewhat sloppy and hope the authors would clarify this too. 
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Post-rebuttal update: The authors have made significant revision to their work, which sufficiently addressed all my concerns. I have upgraded my score accordingly and I am willing to support the acceptance of this paper.