Learning Algorithms for Mixtures of Linear Dynamical Systems: A Practical Approach

In this work, we give the first implementation of an algorithm to learn a mixture of linear dynamical systems (LDS’s), and an analysis of algorithms to learn a single linear dynamical system. Following the work of Bakshi et al. ([1]), we implement a recent polynomial-time algorithm based on a tensor decomposition with learning guarantees in a general setting, with some simplifications and minor optimizations. Our largest contribution is giving the first expectation-maximization (E-M) algorithm for learning a mixture of LDS’s, and an experimental evaluation against the Tensor Decomposition algorithm. We find that the E-M algorithm performs extremely well, and much better than the Tensor Decomposition algorithm. We analyze performance of these and other algorithms to learn both a single LDS and a mixture of LDS’s under various conditions (such as how much noise is present) and algorithm settings.

Name thesis:degree_name

Master

Department dc:contributor.department

Massachusetts Institute of Technology. Department of Electrical Engineering and Computer Science

Grantor dc:publisher

Massachusetts Institute of Technology

Year dc:date.issued

2024

Author dc:creator

• Kumar, Nitin A.

Advisor dc:contributor.advisor

• Moitra, Ankur

Statement dc:rights

• Attribution-NonCommercial-NoDerivatives 4.0 International (CC BY-NC-ND 4.0)
• Copyright retained by author(s)

Licence dc:rights.uri

• https://creativecommons.org/licenses/by-nc-nd/4.0/

Handle dc:identifier.uri

https://hdl.handle.net/1721.1/156785

OAI identifier oai:identifier

oai:dspace.mit.edu:1721.1/156785