Proper Learning of LDS

This is the source code for the paper Proper Learning of Linear Dynamical Systems as a Non-Commutative Polynomial Optimisation Problem:

@misc{https://doi.org/10.48550/arxiv.2002.01444,
  doi = {10.48550/ARXIV.2002.01444},
  url = {https://arxiv.org/abs/2002.01444},
  author = {Zhou, Quan and Marecek, Jakub},
  title = {Proper Learning of Linear Dynamical Systems as a Non-Commutative Polynomial Optimisation Problem},
  publisher = {arXiv},  
  year = {2020}, 
}

It inculdes the scripts, workspace and data files for each figure in the paper. In particular, it includes scripts in Python ("py"), Julia ("jl"), and MATLAB ("m").

Dependencies

1. Mosek/9.2 https://www.mosek.com/downloads/list/9/

2. Python scripts:

• Python/3.9.6

• inputlds https://raw.githubusercontent.com/jmarecek/OnlineLDS/master/inputlds.py

• ncpol2sdpa 1.12.2 https://ncpol2sdpa.readthedocs.io/en/stable/index.html

3. Julia scripts:

• Julia/1.5.2

• NCTSSOS https://github.com/wangjie212/NCTSSOS

• TSSOS https://github.com/wangjie212/TSSOS

4. Matlab scripts:

• Matlab/R2021a

• Statistics and Machine Learning Toolbox https://www.mathworks.com/help/stats/

• System Identification Toolbox https://www.mathworks.com/help/ident/

• Optimization Toolbox https://www.mathworks.com/help/optim/

• Some old codes use PRETTYPLOT https://uk.mathworks.com/matlabcentral/fileexchange/27237-prettyplot to make plots in MATLAB. The plots in our draft are all made in Python.