MLDS: Multilinear Dynamical System

Unofficial Python implementation of MLDS:
"Multilinear dynamical systems for tensor time series.", Rogers, Mark, Lei Li, and Stuart J. Russell. Advances in Neural Information Processing Systems 26 (2013): 2634-2642.
The original implementation is found at the author's homepage [link].

Model

$$\mathcal{Z}_1\sim\mathcal{N}(\mathcal{U}0,\mathcal{Q}0)$$ $$\mathcal{Z}{n+1}|\mathcal{Z}{n}\sim\mathcal{N}(\mathcal{A}\otimes\mathcal{Z}_n,\mathcal{Q})$$

Then, original tensors are represented by

$$\mathcal{X}_n|\mathcal{Z}_n\sim\mathcal{N}(\mathcal{C}\otimes\mathcal{Z}_n,\mathcal{R})$$

where,

• the initial state covariance, $\mathcal{Q}_0$
• the transition covariance, $\mathcal{Q}$
• the observation covariace, $\mathcal{R}$

The shapes of these covariaces can be specified in 'full', 'diag', and 'isotropic', independently.

Reference

@article{rogers2013multilinear,
  title={Multilinear dynamical systems for tensor time series},
  author={Rogers, Mark and Li, Lei and Russell, Stuart J},
  journal={Advances in Neural Information Processing Systems},
  volume={26},
  pages={2634--2642},
  year={2013},
  publisher={Citeseer}
}