Joint Problems in Learning Multiple Dynamical Systems

• URL: http://arxiv.org/abs/2311.02181v3
• Date: Mon, 05 May 2025 08:49:12 GMT
• Title: Joint Problems in Learning Multiple Dynamical Systems
• Authors: Mengjia Niu, Xiaoyu He, Petr Ryšavý, Quan Zhou, 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.<n>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.<n>We present globally convergent methods and EMs, accompanied by promising computational results.
• Score: 7.8346400637756535
• 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. The key highlight of this method is that it does not require a predefined hidden state dimension but instead provides an upper bound. Additionally, it offers guidance for determining regularization in the system identification.

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