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...
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| Format: | Thesis |
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Massachusetts Institute of Technology
2024
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| Online Access: | https://hdl.handle.net/1721.1/156785 |
| _version_ | 1811078513377148928 |
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| author | Kumar, Nitin A. |
| author2 | Moitra, Ankur |
| author_facet | Moitra, Ankur Kumar, Nitin A. |
| author_sort | Kumar, Nitin A. |
| collection | MIT |
| description | 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. |
| first_indexed | 2024-09-23T11:01:23Z |
| format | Thesis |
| id | mit-1721.1/156785 |
| institution | Massachusetts Institute of Technology |
| last_indexed | 2024-09-23T11:01:23Z |
| publishDate | 2024 |
| publisher | Massachusetts Institute of Technology |
| record_format | dspace |
| spelling | mit-1721.1/1567852024-09-17T03:44:45Z Learning Algorithms for Mixtures of Linear Dynamical Systems: A Practical Approach Kumar, Nitin A. Moitra, Ankur Massachusetts Institute of Technology. Department of Electrical Engineering and Computer Science 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. M.Eng. 2024-09-16T13:48:59Z 2024-09-16T13:48:59Z 2024-05 2024-07-11T14:36:37.121Z Thesis https://hdl.handle.net/1721.1/156785 Attribution-NonCommercial-NoDerivatives 4.0 International (CC BY-NC-ND 4.0) Copyright retained by author(s) https://creativecommons.org/licenses/by-nc-nd/4.0/ application/pdf Massachusetts Institute of Technology |
| spellingShingle | Kumar, Nitin A. Learning Algorithms for Mixtures of Linear Dynamical Systems: A Practical Approach |
| title | Learning Algorithms for Mixtures of Linear Dynamical Systems: A Practical Approach |
| title_full | Learning Algorithms for Mixtures of Linear Dynamical Systems: A Practical Approach |
| title_fullStr | Learning Algorithms for Mixtures of Linear Dynamical Systems: A Practical Approach |
| title_full_unstemmed | Learning Algorithms for Mixtures of Linear Dynamical Systems: A Practical Approach |
| title_short | Learning Algorithms for Mixtures of Linear Dynamical Systems: A Practical Approach |
| title_sort | learning algorithms for mixtures of linear dynamical systems a practical approach |
| url | https://hdl.handle.net/1721.1/156785 |
| work_keys_str_mv | AT kumarnitina learningalgorithmsformixturesoflineardynamicalsystemsapracticalapproach |