标题： 球面回归在不匹配损坏下的应用与自动知识翻译 显示英文标题

标题： Spherical Regression under Mismatch Corruption with Application to Automated Knowledge Translation

摘要： 受数据集成、语言翻译、生物信息学和计算机视觉中一系列应用的启发，我们考虑在响应-预测对中存在少量不匹配的情况下，使用两组单位长度向量进行球面回归。 我们提出了一种三步算法，其中我们通过求解一个正交Procrustes问题来初始化参数，以估计一个忽略不匹配的平移矩阵$\mathbb{W}$。 然后，我们估计一个映射矩阵，旨在通过硬阈值处理来诱导稀疏性以纠正不匹配，同时结合潜在的组信息。 我们最终通过去除估计的不匹配对来获得$\mathbb{W}$的精炼估计。 我们在固定和高维设置中推导了$\mathbb{W}$初始估计的误差界。 我们证明了$\mathbb{W}$的精炼估计的误差率与不存在不匹配时一样好。 我们表明，我们的映射恢复方法不仅能够正确区分一对一和一对多的对应关系，还能一致地识别匹配对并估计组合对应关系的权重向量。 我们通过广泛的模拟研究检查了所提方法的有限样本性能，并应用于使用电子健康记录数据进行医疗代码的无监督翻译。 显示英文摘要

摘要： Motivated by a series of applications in data integration, language translation, bioinformatics, and computer vision, we consider spherical regression with two sets of unit-length vectors when the data are corrupted by a small fraction of mismatch in the response-predictor pairs. We propose a three-step algorithm in which we initialize the parameters by solving an orthogonal Procrustes problem to estimate a translation matrix $\mathbb{W}$ ignoring the mismatch. We then estimate a mapping matrix aiming to correct the mismatch using hard-thresholding to induce sparsity, while incorporating potential group information. We eventually obtain a refined estimate for $\mathbb{W}$ by removing the estimated mismatched pairs. We derive the error bound for the initial estimate of $\mathbb{W}$ in both fixed and high-dimensional setting. We demonstrate that the refined estimate of $\mathbb{W}$ achieves an error rate that is as good as if no mismatch is present. We show that our mapping recovery method not only correctly distinguishes one-to-one and one-to-many correspondences, but also consistently identifies the matched pairs and estimates the weight vector for combined correspondence. We examine the finite sample performance of the proposed method via extensive simulation studies, and with application to the unsupervised translation of medical codes using electronic health records data.