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Learning Linear Dynamical Systems via Spectral Filtering

Author(s): Hazan, Elad; Singh, Karan; Zhang, Cyril

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Abstract: We present an efficient and practical algorithm for the online prediction of discrete-time linear dynamical systems with a symmetric transition matrix. We circumvent the non-convex optimization problem using improper learning: carefully overparameterize the class of LDSs by a polylogarithmic factor, in exchange for convexity of the loss functions. From this arises a polynomial-time algorithm with a near-optimal regret guarantee, with an analogous sample complexity bound for agnostic learning. Our algorithm is based on a novel filtering technique, which may be of independent interest: we convolve the time series with the eigenvectors of a certain Hankel matrix.
Publication Date: 2017
Citation: Hazan, Elad, Karan Singh, and Cyril Zhang. "Learning Linear Dynamical Systems via Spectral Filtering." In Advances in Neural Information Processing Systems 30 (2017).
ISSN: 1049-5258
Type of Material: Conference Article
Journal/Proceeding Title: Advances in Neural Information Processing Systems
Version: Final published version. Article is made available in OAR by the publisher's permission or policy.

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