Joint Problems in Learning Multiple Dynamical Systems

• URL: http://arxiv.org/abs/2311.02181v2
• Date: Fri, 23 Feb 2024 09:12:44 GMT
• Title: Joint Problems in Learning Multiple Dynamical Systems
• Authors: Mengjia Niu and Xiaoyu He and Petr Ry\v{s}av\'y and Quan Zhou and Jakub Marecek
• Abstract summary: Clustering of time series is a well-studied problem, with applications ranging from quantitative, personalized models of metabolism obtained from metabolite concentrations to state discrimination in quantum information theory. We consider a variant, where given a set of trajectories and a number of parts, we jointly partition the set of trajectories and learn linear dynamical system (LDS) models for each part, so as to minimize the maximum error across all the models. We present globally convergent methods and EMs, accompanied by promising computational results.
• Score: 8.405361894357359
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: Clustering of time series is a well-studied problem, with applications ranging from quantitative, personalized models of metabolism obtained from metabolite concentrations to state discrimination in quantum information theory. We consider a variant, where given a set of trajectories and a number of parts, we jointly partition the set of trajectories and learn linear dynamical system (LDS) models for each part, so as to minimize the maximum error across all the models. We present globally convergent methods and EM heuristics, accompanied by promising computational results.

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