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2022 Tight risk bound for high dimensional time series completion
Pierre Alquier, Nicolas Marie, Amélie Rosier
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Electron. J. Statist. 16(1): 3001-3035 (2022). DOI: 10.1214/22-EJS2015

Abstract

Initially designed for independent datas, low-rank matrix completion was successfully applied in many domains to the reconstruction of partially observed high-dimensional time series. However, there is a lack of theory to support the application of these methods to dependent datas. In this paper, we propose a general model for multivariate, partially observed time series. We show that the least-square method with a rank penalty leads to reconstruction error of the same order as for independent datas. Moreover, when the time series has some additional properties such as periodicity or smoothness, the rate can actually be faster than in the independent case.

Funding Statement

This work was partially funded by CY Initiative of Excellence (grant “Investissements d’Avenir” ANR-16-IDEX-0008), Project “EcoDep” PSI-AAP2020-0000000013.

Citation

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Pierre Alquier. Nicolas Marie. Amélie Rosier. "Tight risk bound for high dimensional time series completion." Electron. J. Statist. 16 (1) 3001 - 3035, 2022. https://doi.org/10.1214/22-EJS2015

Information

Received: 1 May 2021; Published: 2022
First available in Project Euclid: 4 May 2022

Digital Object Identifier: 10.1214/22-EJS2015

Subjects:
Primary: 62M20
Secondary: 37A25 , 60B20 , 62H12 , 62H25 , 62M10

Keywords: Concentration inequalities , high-dimensional time series , Matrix completion , matrix factorization , Mixing , Multivariate Time Series Analysis

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Vol.16 • No. 1 • 2022
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