Learning Algorithms for Mixtures of Linear Dynamical Systems: A Practical Approach
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kumar-nitink-meng-eecs-2024-thesis.pdf
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Thesis PDF
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708.46 KB
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Author(s)
Kumar, Nitin A.
Advisor(s)
Moitra, Ankur
Date Issued
May 2024
Publisher
Massachusetts Institute of Technology
Abstract
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.
MIT Department
Massachusetts Institute of Technology. Department of Electrical Engineering and Computer Science
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Attribution-NonCommercial-NoDerivatives 4.0 International (CC BY-NC-ND 4.0)
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