Abstract Magnitude-preserving ranking (MPRank) under Tikhonov regularization framework has shown competitive performance on information retrial besides theoretical advantages for computation feasibility and statistical guarantees. In this paper, we further characterize the learning rate and asymptotic bias of MPRank, and then propose a new debiased ranking algorithm. In terms of the operator representation and approximation techniques, we establish their convergence rates and bias characterizations. These theoretical results demonstrate that the new model has smaller asymptotic bias than MPRank, and can achieve the satisfactory convergence rate under appropriate conditions. In addition, some empirical examples are provided to verify the effectiveness of our debiased strategy.

中文翻译：

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去偏差量级保持排名：学习率和偏差特征

摘要 Tikhonov 正则化框架下的幅度保持排序 (MPRank) 除了在计算可行性和统计保证方面的理论优势外，还显示出在信息重试方面的竞争性能。在本文中，我们进一步表征了 MPRank 的学习率和渐近偏差，然后提出了一种新的去偏差排序算法。在算子表示和近似技术方面，我们建立了它们的收敛速度和偏差特征。这些理论结果表明，新模型比 MPRank 具有更小的渐近偏差，并且在适当的条件下可以达到令人满意的收敛速度。此外，还提供了一些实证示例来验证我们的去偏策略的有效性。