论文标题
通过渐进式凸松弛进行洗牌线性回归
Shuffled linear regression through graduated convex relaxation
论文作者
论文摘要
改组的线性回归问题旨在恢复数据集中的线性关系，其中输入和输出之间的对应关系未知。这个问题出现在包括调查数据在内的广泛应用程序中，在这些应用程序中，人们需要在其中确定响应的匿名性，同时揭示重大统计连接。在这项工作中，我们提出了一种基于高斯噪声的后验最大化目标函数的新型优化算法，用于洗牌线性回归。我们将我们的方法与现有的合成和真实数据进行比较。我们表明，我们的方法在实现经验的运行时间改进的同时竞争性能。此外，我们证明了我们的算法能够以种子的形式利用侧面信息，最近在相关问题中引起了人们的突出。
The shuffled linear regression problem aims to recover linear relationships in datasets where the correspondence between input and output is unknown. This problem arises in a wide range of applications including survey data, in which one needs to decide whether the anonymity of the responses can be preserved while uncovering significant statistical connections. In this work, we propose a novel optimization algorithm for shuffled linear regression based on a posterior-maximizing objective function assuming Gaussian noise prior. We compare and contrast our approach with existing methods on synthetic and real data. We show that our approach performs competitively while achieving empirical running-time improvements. Furthermore, we demonstrate that our algorithm is able to utilize the side information in the form of seeds, which recently came to prominence in related problems.
