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Interpretable Matrix Completion: A Discrete Optimization Approach

Author

Listed:
  • Dimitris Bertsimas

    (Sloan School of Management, Massachusetts Institute of Technology, Cambridge, Massachusetts 02142)

  • Michael Lingzhi Li

    (Technology and Operations Management, Harvard Business School, Boston, Massachusetts 02163)

Abstract

We consider the problem of matrix completion on an n × m matrix. We introduce the problem of interpretable matrix completion that aims to provide meaningful insights for the low-rank matrix using side information. We show that the problem can be reformulated as an optimization problem with a convex objective and binary variables. We design an algorithm called OptComplete, based on a novel concept of stochastic cutting planes to enable efficient scaling of the algorithm up to matrices of sizes n = 10 6 and m = 10 6 . We prove that OptComplete converges to an optimal solution of the interpretable matrix completion problem with exponentially vanishing failure probability. We report experiments on both synthetic and real-world data sets that show that OptComplete has favorable scaling behavior and accuracy when compared with state-of-the-art methods for other types of matrix completion while providing insight on the factors that affect the matrix.

Suggested Citation

  • Dimitris Bertsimas & Michael Lingzhi Li, 2023. "Interpretable Matrix Completion: A Discrete Optimization Approach," INFORMS Journal on Computing, INFORMS, vol. 35(5), pages 952-965, September.
    • Handle: RePEc:inm:orijoc:v:35:y:2023:i:5:p:952-965
    DOI: 10.1287/ijoc.2022.0022
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    References listed on IDEAS

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    1. Bertsimas, Dimitris & Copenhaver, Martin S., 2018. "Characterization of the equivalence of robustification and regularization in linear and matrix regression," European Journal of Operational Research, Elsevier, vol. 270(3), pages 931-942.
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