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The Alternating Direction Method of Multipliers for Sufficient Dimension Reduction

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  • Sheng Ma
  • Qin Jiang
  • Zaiqiang Ku
  • Barbara Martinucci

Abstract

The minimum average variance estimation (MAVE) method has proven to be an effective approach to sufficient dimension reduction. In this study, we apply the computationally efficient optimization algorithm named alternating direction method of multipliers (ADMM) to a particular approach (MAVE or minimum average variance estimation) to the problem of sufficient dimension reduction (SDR). Under some assumptions, we prove that the iterative sequence generated by ADMM converges to some point of the associated augmented Lagrangian function. Moreover, that point is stationary. It also presents some numerical simulations on synthetic data to demonstrate the computational efficiency of the algorithm.

Suggested Citation

  • Sheng Ma & Qin Jiang & Zaiqiang Ku & Barbara Martinucci, 2024. "The Alternating Direction Method of Multipliers for Sufficient Dimension Reduction," Journal of Mathematics, Hindawi, vol. 2024, pages 1-8, May.
    • Handle: RePEc:hin:jjmath:3692883
    DOI: 10.1155/2024/3692883
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