2014/12/26 by Ashwini Maurya, Maurya, Ashwini
Biochemistry, Genetics and Molecular Biology · Computer Science · Mathematics · #Bayesian Methods and Mixture Models #FOS: Mathematics #Gene expression and cancer classification #Statistical Methods and Bayesian Inference #Statistical Methods and Inference #Statistics Theory (math.ST)
paper · pdf · doi:10.48550/arxiv.1412.7907
openalex publication_date 2014/12/26 · openalex created_date 2019/07/30 · openalex updated_date 2026/07/28
We develop a method for estimating well-conditioned and sparse covariance and\ninverse covariance matrices from a sample of vectors drawn from a sub-gaussian\ndistribution in high dimensional setting. The proposed estimators are obtained\nby minimizing the quadratic loss function and joint penalty of `1 norm and\nvariance of its eigenvalues. In contrast to some of the existing methods of\ncovariance and inverse covariance matrix estimation, where often the interest\nis to estimate a sparse matrix, the proposed method is flexible in estimating\nboth a sparse and well-conditioned covariance matrix simultaneously. The\nproposed estimators are optimal in the sense that they achieve the minimax rate\nof estimation in operator norm for the underlying class of covariance and\ninverse covariance matrices. We give a very fast algorithm for computation of\nthese covariance and inverse covariance matrices which is easily scalable to\nlarge scale data analysis problems. The simulation study for varying sample\nsizes and variables shows that the proposed estimators performs better than\nseveral other estimators for various choices of structured covariance and\ninverse covariance matrices. We also use our proposed estimator for tumor\ntissues classification using gene expression data and compare its performance\nwith some other classification methods.\n