Tree-structured recurrent switching linear dynamical systems (TrSLDS) are an extension of recurrent switching linear dynamical systems (rSLDS) from Linderman et al., 2017.
Similar to rSLDS, TrSLDS introduces a dependency between the continuous and discrete latent states which allows the probability distribtuion of the discrete states to depend on the continuous states; this depdency paritiions the space, where each partition has it's own linear dynamics. While rSLDS partitions the space using (sequential) stick-breaking, TrSLDS utilizes tree-structured stick-breaking to partition the space:
A priori, it is natural to expect that locally linear dynamics of nearby regions in the latent space are similar. Thus, in the context of tree-structured stick breaking, we impose that partitions that share a common parent should have similar dynamics. We explicitly model this by enforcing a hierarchical prior on the dynamics that respects the tree structure which allows for a multi-scale view of the system.
The model is efficenitly learned through Gibbs sampling. Complete details of the algorithm are given in the following paper:
@InProceedings{Nassar2018b,
author = {Josue Nassar and Scott W. Linderman and Monica Bugallo and Il Memming Park},
title = {Tree-Structured Recurrent Switching Linear Dynamical Systems for Multi-Scale Modeling},
booktitle = {International Conference on Learning Representations (ICLR)},
year = {2019},
url = {https://openreview.net/pdf?id=HkzRQhR9YX},
}
Here is a link to the ICLR paper.
This package is built upon the following two packages:
github.com/slinderman/pypolyagamma
github.com/pytorch/pytorch
To get started, check out the lorenz example which will fit a tree-structured recurrent switching linear dynamical system to a Lorenz attractor, similar to Figure 3 of the ICLR paper.