多分类判别指数的高效方差估计
Efficient Variance Estimation for the Polytomous Discrimination Index
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中文总结 AI 辅助
针对多分类判别指数方差估计需密集计算的局限，提出基于U统计量理论与组合数学的渐近方差估计量，经模拟验证高效，还成功应用于脑图像分析以评估不同深度神经网络的准确性。
中文摘要 AI 辅助
评估多类别结局的诊断准确性仍是一项重大挑战，主要源于现有性能指标存在计算局限性。多分类判别指数（Polytomous Discrimination Index, PDI）作为一种与顺序无关的解决方案，适用于名义分类，但由于缺乏高效实现，尤其是其方差估计通常需要计算密集型的自助法程序，限制了它的更广泛应用。本研究针对这一局限，提出了一种新的PDI渐近方差估计量，该方法将经典U统计量理论与组合数学的最新进展相结合，提供了一种可扩展且有理论依据的替代方案。为评估所提方法的性能，我们开展了广泛的模拟研究，观察到计算时间显著减少；还将该方法应用于使用深度神经网络作为诊断工具的真实脑图像分析中，可高效报告不同深度规格神经网络的准确性。
英文摘要
Evaluating diagnostic accuracy for multi-category outcomes remains a significant challenge, primarily due to computational limitations in existing performance metrics. The Polytomous Discrimination Index (PDI) has emerged as an order-agnostic solution suitable for nominal classifications. However, its broader adoption has been constrained by the lack of efficient implementation, especially for its variance estimation, which typically would require computationally intensive bootstrapping procedures. In this work, we address this limitation by proposing a novel asymptotic variance estimator for the PDI. Our method integrates classical $U$-statistic theory with recent advances in combinatorics, offering a scalable and theoretically grounded alternative. To assess the performance of the proposed approach, we conduct extensive simulation studies and observe remarkable gain in computing time. We further apply our method to a real-world brain image analysis where deep neural networks are used as a diagnostic tool. We can efficiently report the accuracy of the neural networks with different depth specifications.
