一种针对含缺失数据的椭圆分布混合模型的鲁棒且灵活的 EM 算法
A Robust and Flexible EM Algorithm for Mixtures of Elliptical Distributions with Missing Data
AI总结：
针对含噪声和非高斯数据的缺失值插补问题，提出一种用于椭圆分布混合模型的新EM算法，通过简化为Angular Gaussian分布估计并利用多元t分布条件，实现了对异常值的鲁棒性和极具竞争力的插补性能。
摘要：
本文解决了针对含噪声和非高斯数据的缺失数据插补问题。与其他流行的插补方法（例如基于 k 近邻或通过链式方程进行多重插补的方法）相比，一种经典的插补方法——用于高斯混合模型的期望最大化（EM）算法，已经展现出了有趣的特性。然而，已知高斯混合模型对异构数据不具有鲁棒性，当数据被异常值污染或遵循非高斯分布时，这可能导致较差的估计性能。为了克服这一问题，本文研究了一种新的 EM 算法，用于具有处理潜在缺失数据特性的椭圆分布混合模型。本文表明，在一般假设下（即每个样本均抽取自一个椭圆分布混合模型，且不同样本之间可能存在差异），该问题可简化为 Angular Gaussian 分布混合模型的估计问题。在这种情况下，得益于其条件分布（被证明是一种多元 $t$-分布），与椭圆分布混合模型相关的完整数据似然非常适合带有缺失数据的 EM 框架。在合成数据上的实验结果表明，所提出的算法对异常值具有鲁棒性，并且可用于非高斯数据。此外，在真实世界数据集上进行的实验表明，与其他经典的插补方法相比，该算法极具竞争力。
英文摘要：
This paper tackles the problem of missing data imputation for noisy and non-Gaussian data. A classical imputation method, the Expectation Maximization (EM) algorithm for Gaussian mixture models, has shown interesting properties when compared to other popular approaches such as those based on k-nearest neighbors or on multiple imputations by chained equations. However, Gaussian mixture models are known to be non-robust to heterogeneous data, which can lead to poor estimation performance when the data is contaminated by outliers or follows non-Gaussian distributions. To overcome this issue, a new EM algorithm is investigated for mixtures of elliptical distributions with the property of handling potential missing data. This paper shows that this problem reduces to the estimation of a mixture of Angular Gaussian distributions under generic assumptions (i.e., each sample is drawn from a mixture of elliptical distributions, which is possibly different for one sample to another). In that case, the complete-data likelihood associated with mixtures of elliptical distributions is well adapted to the EM framework with missing data thanks to its conditional distribution, which is shown to be a multivariate $t$-distribution. Experimental results on synthetic data demonstrate that the proposed algorithm is robust to outliers and can be used with non-Gaussian data. Furthermore, experiments conducted on real-world datasets show that this algorithm is very competitive when compared to other classical imputation methods.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
