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A fast trans-lasso algorithm with penalized weighted score function

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  • Fan, Xianqiu
  • Cheng, Jun
  • Wang, Hailing
  • Zhang, Bin
  • Chen, Zhenzhen

Abstract

An efficient transfer learning algorithm for high-dimensional sparse logistic regression models is proposed using penalized weighted score function based on square root Lasso, which intends to prespecify the tuning parameter. Three different choices of the tuning parameter are considered in the case of fixed design matrix. With a novel weight construction, the estimator of the regression vector is showed to be consistent when the inequality with respect to the Karush-Kuhn-Tucker (KKT) optimality conditions holds with high probability and the sparsity assumption for the regression vectors is required. There is information from source data to fit target data such that with high probability tending to 1-α, which is sharper than the corresponding probability bound without using the auxiliary samples, the KKT optimality conditions hold for the asymptotic choice. To detect which sources are transferable, an efficient data-driven method is proposed, which helps avoid negative transfer in practice. Simulation studies are carried out to demonstrate the numerical performance of the proposed procedure and their superiority over some existing methods. The procedures are also illustrated by analyzing the China Migrants Dynamic Survey dataset with binary outcomes concerning the associations among different provinces.

Suggested Citation

  • Fan, Xianqiu & Cheng, Jun & Wang, Hailing & Zhang, Bin & Chen, Zhenzhen, 2024. "A fast trans-lasso algorithm with penalized weighted score function," Computational Statistics & Data Analysis, Elsevier, vol. 192(C).
    • Handle: RePEc:eee:csdana:v:192:y:2024:i:c:s0167947323002104
    DOI: 10.1016/j.csda.2023.107899
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    References listed on IDEAS

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    1. Lukas Meier & Sara Van De Geer & Peter Bühlmann, 2008. "The group lasso for logistic regression," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 70(1), pages 53-71, February.
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    3. A. Belloni & V. Chernozhukov & L. Wang, 2011. "Square-root lasso: pivotal recovery of sparse signals via conic programming," Biometrika, Biometrika Trust, vol. 98(4), pages 791-806.
    4. Tingni Sun & Cun-Hui Zhang, 2012. "Scaled sparse linear regression," Biometrika, Biometrika Trust, vol. 99(4), pages 879-898.
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