摘要翻译:
本文提出了一种在高维背景下构造逆协方差(浓度)矩阵稀疏估计的方法。该估计器使用惩罚的正态似然方法,并通过使用套索型惩罚强制稀疏性。在Frobenius范数中,当数据维数P$和样本容量N$都允许增长时,我们建立了一个收敛速度,并证明了收敛速度明显依赖于真实集中矩阵的稀疏程度。我们还表明,基于相关的方法在算子范数中表现出更好的速率。我们还导出了一个快速迭代算法来计算估计量,该算法依赖于流行的逆的Cholesky分解,但产生了一个置换不变估计量。在模拟数据和一个利用基因表达数据进行肿瘤组织分类的实际数据上,将该方法与其他估计方法进行了比较。
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英文标题:
《Sparse permutation invariant covariance estimation》
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作者:
Adam J. Rothman, Peter J. Bickel, Elizaveta Levina, Ji Zhu
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最新提交年份:
2008
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分类信息:
一级分类:Mathematics 数学
二级分类:Statistics Theory 统计理论
分类描述:Applied, computational and theoretical statistics: e.g. statistical inference, regression, time series, multivariate analysis, data analysis, Markov chain Monte Carlo, design of experiments, case studies
应用统计、计算统计和理论统计:例如统计推断、回归、时间序列、多元分析、数据分析、马尔可夫链蒙特卡罗、实验设计、案例研究
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一级分类:Statistics 统计学
二级分类:Statistics Theory 统计理论
分类描述:stat.TH is an alias for math.ST. Asymptotics, Bayesian Inference, Decision Theory, Estimation, Foundations, Inference, Testing.
Stat.Th是Math.St的别名。渐近,贝叶斯推论,决策理论,估计,基础,推论,检验。
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英文摘要:
The paper proposes a method for constructing a sparse estimator for the inverse covariance (concentration) matrix in high-dimensional settings. The estimator uses a penalized normal likelihood approach and forces sparsity by using a lasso-type penalty. We establish a rate of convergence in the Frobenius norm as both data dimension $p$ and sample size $n$ are allowed to grow, and show that the rate depends explicitly on how sparse the true concentration matrix is. We also show that a correlation-based version of the method exhibits better rates in the operator norm. We also derive a fast iterative algorithm for computing the estimator, which relies on the popular Cholesky decomposition of the inverse but produces a permutation-invariant estimator. The method is compared to other estimators on simulated data and on a real data example of tumor tissue classification using gene expression data.
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PDF链接:
https://arxiv.org/pdf/801.4837