Discovering Sparse Covariance Structures With the Isomap
نویسندگان
چکیده
منابع مشابه
Discovering Sparse Covariance Structures with the Isomap
Regularization of covariance matrices in high dimensions is usually either based on a known ordering of variables or ignores the ordering entirely. This paper proposes a method for discovering meaningful orderings of variables based on their correlations using the Isomap, a non-linear dimension reduction technique designed for manifold embeddings. These orderings are then used to construct a sp...
متن کاملCovariance Estimation via Sparse Kronecker Structures
The problem of estimating covariance matrices is central to statistical analysis and is extensively addressed when data are vectors. This paper studies a novel Kronecker-structured approach for estimating such matrices when data are matrices and arrays. Focusing on matrix-variate data, we present simple approaches to estimate the row and the column correlation matrices, formulated separately vi...
متن کاملSparse inverse covariance estimation with the lasso
We consider the problem of estimating sparse graphs by a lasso penalty applied to the inverse covariance matrix. Using a coordinate descent procedure for the lasso, we develop a simple algorithm— the Graphical Lasso— that is remarkably fast: it solves a 1000 node problem (∼ 500, 000 parameters) in at most a minute, and is 30 to 4000 times faster than competing methods. It also provides a concep...
متن کاملSparse Multivariate Regression With Covariance Estimation.
We propose a procedure for constructing a sparse estimator of a multivariate regression coefficient matrix that accounts for correlation of the response variables. This method, which we call multivariate regression with covariance estimation (MRCE), involves penalized likelihood with simultaneous estimation of the regression coefficients and the covariance structure. An efficient optimization a...
متن کاملSparse Covariance Matrix Estimation With Eigenvalue Constraints.
We propose a new approach for estimating high-dimensional, positive-definite covariance matrices. Our method extends the generalized thresholding operator by adding an explicit eigenvalue constraint. The estimated covariance matrix simultaneously achieves sparsity and positive definiteness. The estimator is rate optimal in the minimax sense and we develop an efficient iterative soft-thresholdin...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Journal of Computational and Graphical Statistics
سال: 2009
ISSN: 1061-8600,1537-2715
DOI: 10.1198/jcgs.2009.08021