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Covariate-Assisted Matrix Completion with Multiple Structural Breaks

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Abstract

In matrix completion, additional covariates often provide valuable information for completing the unobserved entries of a high-dimensional low-rank matrix A. In this paper, the authors consider the matrix recovery problem when there are multiple structural breaks in the coefficient matrix β under the column-space-decomposition model A = Xβ + B. A cumulative sum (CUSUM) statistic is constructed based on the penalized estimation of β. Then the CUSUM is incorporated into the Wild Binary Segmentation (WBS) algorithm to consistently estimate the location of breaks. Consequently, a nearly-optimal recovery of A is fulfilled. Theoretical findings are further corroborated via numerical experiments and a real-data application.

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Author notes

  1. These authors contributed equally: MENG Jing and FENG Long.

Authors and Affiliations

  1. School of Statistics and Data Science, KLMDASR, LEBPS, and LPMC, Nankai University, Tianjin, 300071, China

    Jing Meng, Long Feng, Changliang Zou & Zhaojun Wang

Authors
  1. Jing Meng
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  2. Long Feng
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  3. Changliang Zou
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  4. Zhaojun Wang
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Corresponding author

Correspondence to Zhaojun Wang.

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The authors declare no conflict of interest.

Additional information

This research was supported by the National Natural Science Foundation of China under Grant Nos. 12226007, 12271271, 11925106, 12231011, 11931001 and 11971247, the Fundamental Research Funds for the Central Universities under Grant No. ZB22000105 and the China National Key R&D Program under Grant Nos. 2022YFA1003703, 2022YFA1003800, and 2019YFC1908502.

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Meng, J., Feng, L., Zou, C. et al. Covariate-Assisted Matrix Completion with Multiple Structural Breaks. J Syst Sci Complex 37, 692–728 (2024). https://doi.org/10.1007/s11424-023-2342-2

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  • DOI: https://doi.org/10.1007/s11424-023-2342-2

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