Sparse spectral estimation with missing and corrupted measurements
Sparse spectral estimation with missing and corrupted measurements
复制标题
测量缺失和损坏的稀疏光谱估计
作者：
A. Elsener;S. Geer
具有缺失数据的监督学习方法已经得到了广泛的研究，这不仅仅是因为与低秩矩阵完成相关的技术。此外，在无监督学习中，人们通常依赖于估算方法。事实上，缺失值会导致各种估计量（如样本协方差矩阵）的偏差。本文将稀疏子空间估计的一种凸方法推广到观测值丢失和损坏的情况。这是通过校正偏倚而不是插补缺失值来完成的。然后将估计量用作非凸过程的初始值，以提高整体统计性能。方法和理论框架适用于广泛的统计问题。其中包括稀疏主成分分析与不同类型的随机缺失数据。最后，在合成数据上展示了统计性能。
Supervised learning methods with missing data have been extensively studied not just due to the techniques related to low‐rank matrix completion. Also, in unsupervised learning, one often relies on imputation methods. As a matter of fact, missing values induce a bias in various estimators such as the sample covariance matrix. In the present paper, a convex method for sparse subspace estimation is extended to the case of missing and corrupted measurements. This is done by correcting the bias instead of imputing the missing values. The estimator is then used as an initial value for a nonconvex procedure to improve the overall statistical performance. The methodological and theoretical frameworks are applied to a wide range of statistical problems. These include sparse principal component analysis with different types of randomly missing data. Finally, the statistical performance is demonstrated on synthetic data.