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The optimal predictor for a linear dynamical system (with hidden state and Gaussian noise) takes the form of an autoregressive linear filter, namely the Kalman filter.
“A new approach to linear filtering and prediction problems”
Rudolph Kalman · 1960
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“Effective construction of linear state-variable models from input/output functions”
BL Ho and Rudolph Kalman · 1966
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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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“System identification: Theory for the User”
Lennart Ljung · 1998
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“Introduction to optimal estimation”
Edward Kamen and Jonathan Su · 1999
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“A unifying review of linear Gaussian models”
Sam Roweis and Zoubin Ghahramani · 1999
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“Adaptive estimation of a quadratic functional by model selection”
Beatrice Laurent and Pascal Massart · 2000
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“A large-deviation inequality for vector-valued martingales”
Thomas Hayes · 2005
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“Time Series: Theory and Methods”
P. Brockwell and R. Davis · 2009
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“Subspace Identification for Linear Systems”
Peter Van and BL De · 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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Badri Bhaskar, Gongguo Tang and Benjamin Recht · 2013
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“Approximation theory and approximation practice”
Lloyd Trefethen · 2013
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“Learning Linear Dynamical Systems via Spectral Filtering”
Elad Hazan, Karan Singh and Cyril Zhang · 2017
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“Non-Asymptotic Analysis of Robust Control from Coarse-Grained Identification”
Stephen Tu, Ross Boczar, Andrew Packard and Benjamin Recht · 2017
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“Finite-Data Performance Guarantees for the Output-Feedback Control of an Unknown System”
Ross Boczar, Nikolai Matni and Benjamin Recht · 2018
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“Spectral Filtering for General Linear Dynamical Systems”
Elad Hazan et al · 2018
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“Non-asymptotic identification of lti systems from a single trajectory”
Samet Oymak and Necmiye Ozay · 2018
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Moritz Hardt, Tengyu Ma and Benjamin Recht · 2016
Cited alongside, same era.
“On the sample complexity of the linear quadratic regulator”
Sarah Dean et al · 2017
Cited alongside, same era.
Later among the works it cites.
“Learning Without Mixing: Towards A Sharp Analysis of Linear System Identification”
Max Simchowitz et al · 2018
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“High-dimensional probability: An introduction with applications in data science”
Roman Vershynin · 2018
Later among the works it cites.
“Learning Linear Dynamical Systems with Semi-Parametric Least Squares”
Max Simchowitz, Ross Boczar and Benjamin Recht · 2019
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