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We give a polynomial-time algorithm for learning latent-state linear dynamical systems without system identification, and without assumptions on the spectral radius of the system's transition matrix.
A new approach to linear filtering and prediction problems
Rudolph Emil Kalman · 1960
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Tricks or treats with the hilbert matrix
Man-Duen Choi · 1983
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Time Series Analysis: Forecasting and Control
G. Box, G. Jenkins, and G. Reinsel · 1994
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Time Series Analysis
J. Hamilton · 1994
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Kemin Zhou, John Comstock Doyle, Keith Glover, et al · 1996
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A fast method to diagonalize a Hankel matrix
Daniel L Boley, Franklin T Luk, and David Vandevoorde · 1998
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System identification: Theory for the User
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A unifying review of linear gaussian models
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Prediction, Learning, and Games
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Logarithmic regret algorithms for online convex optimization
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Regularization techniques for learning with matrices
Sham M Kakade, Shai Shalev-Shwartz, and Ambuj Tewari · 2012
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Online learning for time series prediction
Oren Anava, Elad Hazan, Shie Mannor, and Ohad Shamir · 2013
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A linear dynamical system model for text
David Belanger and Sham Kakade · 2015
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Gradient descent learns linear dynamical systems
Moritz Hardt, Tengyu Ma, and Benjamin Recht · 2016
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On the singular values of matrices with displacement structure
Bernhard Beckermann and Alex Townsend · 2017
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Shai Shalev-Shwartz et al · 2012
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Subspace Identification for Linear Systems
Peter Van Overschee and BL De Moor · 2012
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Ein beitrag zur theorie des legendre’schen polynoms
David Hilbert
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On the sample complexity of the linear quadratic regulator
Sarah Dean, Horia Mania, Nikolai Matni, Benjamin Recht, and Stephen Tu · 2017
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Learning linear dynamical systems via spectral filtering
Elad Hazan, Karan Singh, and Cyril Zhang · 2017
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