Robust Sparse Principal Component Regression under the High Dimensional Elliptical Model
Robust Sparse Principal Component Regression under the High Dimensional Elliptical Model
复制标题
高维椭圆模型下的鲁棒稀疏主成分回归
DOI：
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发表时间：
2013
期刊：
影响因子：
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通讯作者：
Han Liu
中科院分区：
文献类型：
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作者：
Fang Han;Han Liu
在本文中，我们着重于主要成分回归及其在高维非高斯数据中的应用。主要贡献是两个折。首先，在低维度和高斯模型下，通过借用最小值最佳主成分估计的最新发展强度，我们首先急剧地描述了经典主体组件回归的潜在优势，而不是最小二乘估计。其次，我们建议和分析高维椭圆形分布数据上的新的鲁棒稀疏主组件回归。椭圆形分布是高斯的半参数概括，其中包括许多众所周知的分布，例如多元高斯，缺乏等级的高斯，T，库奇和逻辑。它允许随机矢量沉重，并具有尾部依赖性。这些额外的灵活性使其非常适合对金融和生物医学成像数据进行建模。在椭圆模型下，我们证明我们的方法可以估计最佳参数速率的回归系数，因此是基于高斯方法的良好替代方法。进行了合成和现实世界数据的实验，以说明该方法的经验实用性。
In this paper we focus on the principal component regression and its application to high dimension non-Gaussian data. The major contributions are two folds. First, in low dimensions and under the Gaussian model, by borrowing the strength from recent development in minimax optimal principal component estimation, we first time sharply characterize the potential advantage of classical principal component regression over least square estimation. Secondly, we propose and analyze a new robust sparse principal component regression on high dimensional elliptically distributed data. The elliptical distribution is a semiparametric generalization of the Gaussian, including many well known distributions such as multivariate Gaussian, rank-deficient Gaussian, t, Cauchy, and logistic. It allows the random vector to be heavy tailed and have tail dependence. These extra flexibilities make it very suitable for modeling finance and biomedical imaging data. Under the elliptical model, we prove that our method can estimate the regression coefficients in the optimal parametric rate and therefore is a good alternative to the Gaussian based methods. Experiments on synthetic and real world data are conducted to illustrate the empirical usefulness of the proposed method.