Linear regression with shuffled labels and with a noisy latent design matrix arises in many correspondence recovery problems. We propose a total least-squares approach to the problem of estimating the underlying true permutation and provide an upper bound to the normalized Procrustes quadratic loss of the estimator. We also provide an iterative algorithm to approximate the estimator and demonstrate its performance on simulated data.

翻译：在许多通信回收问题中,出现了用打乱标签和噪音的潜伏设计矩阵进行线性回归的问题。我们建议对估算底部真实变异问题采取完全最小方位的方法,并为标定仪正常的普罗克鲁斯特二次损耗提供一个上方框。我们还提供了一个迭代算法,以接近测算器,并在模拟数据上展示其性能。