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  • title: Linear Convergence of Gradient Methods for Estimating Structured Transition Matrices in High-dimensional Vector Autoregressive Models
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            Linear Convergence of Gradient Methods for Estimating Structured Transition Matrices in High-dimensional Vector Autoregressive Models
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            Linear Convergence of Gradient Methods for Estimating Structured Transition Matrices in High-dimensional Vector Autoregressive Models

            Dec 6, 2021

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            Xiao Lv

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            Wei Cui

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            YL

            Yulong Liu

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            In this paper, we present non-asymptotic optimization guarantees of gradient descent methods for estimating structured transition matrices in high-dimensional vector autoregressive (VAR) models. We adopt the projected gradient descent (PGD) for single-structured transition matrices and the alternating projected gradient descent (AltPGD) for superposition-structured ones. Our analysis demonstrates that both gradient algorithms converge linearly to the statistical error even though the strong conv…

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