## Learning Mixtures of Linear Dynamical Systems

### Yanxi Chen · H. Vincent Poor

##### Hall E #1003

Keywords: [ T: Miscellaneous Aspects of Machine Learning ] [ OPT: Control and Optimization ] [ MISC: Unsupervised and Semi-supervised Learning ] [ MISC: Supervised Learning ] [ MISC: Sequential, Network, and Time Series Modeling ] [ MISC: Transfer, Multitask and Meta-learning ] [ PM: Spectral Methods ] [ T: Learning Theory ] [ Theory ]

 Outstanding Paper
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Tue 19 Jul 3:30 p.m. PDT — 5:30 p.m. PDT

Oral presentation: Theory
Tue 19 Jul 10:30 a.m. PDT — noon PDT

Abstract: We study the problem of learning a mixture of multiple linear dynamical systems (LDSs) from unlabeled short sample trajectories, each generated by one of the LDS models. Despite the wide applicability of mixture models for time-series data, learning algorithms that come with end-to-end performance guarantees are largely absent from existing literature. There are multiple sources of technical challenges, including but not limited to (1) the presence of latent variables (i.e. the unknown labels of trajectories); (2) the possibility that the sample trajectories might have lengths much smaller than the dimension $d$ of the LDS models; and (3) the complicated temporal dependence inherent to time-series data. To tackle these challenges, we develop a two-stage meta-algorithm, which is guaranteed to efficiently recover each ground-truth LDS model up to error $\tilde{O}(\sqrt{d/T})$, where $T$ is the total sample size. We validate our theoretical studies with numerical experiments, confirming the efficacy of the proposed algorithm.

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