Joint Problems in Learning Multiple Dynamical Systems
Niu, Mengjia; He, Xiaoyu; Ryšavý, Petr; Zhou, Quan; Mareček, Jakub
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https://hdl.handle.net/2142/130321
Description
Title
Joint Problems in Learning Multiple Dynamical Systems
Author(s)
Niu, Mengjia
He, Xiaoyu
Ryšavý, Petr
Zhou, Quan
Mareček, Jakub
Issue Date
2025-09-17
Keyword(s)
Clustering of time series
Learning linear dynamical systems
Joint problems
Abstract
Clustering of time series is a well-studied problem [53], [29], 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.
Publisher
Allerton Conference on Communication, Control, and Computing
Series/Report Name or Number
2025 61st Allerton Conference on Communication, Control, and Computing Proceedings
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