High-dimensional covariance estimation based on Gaussian graphical models

Statistics – Machine Learning

Scientific paper

Rate now

  [ 0.00 ] – not rated yet Voters 0   Comments 0

Details

50 Pages, 6 figures. Major revision

Scientific paper

Undirected graphs are often used to describe high dimensional distributions. Under sparsity conditions, the graph can be estimated using $\ell_1$-penalization methods. We propose and study the following method. We combine a multiple regression approach with ideas of thresholding and refitting: first we infer a sparse undirected graphical model structure via thresholding of each among many $\ell_1$-norm penalized regression functions; we then estimate the covariance matrix and its inverse using the maximum likelihood estimator. We show that under suitable conditions, this approach yields consistent estimation in terms of graphical structure and fast convergence rates with respect to the operator and Frobenius norm for the covariance matrix and its inverse. We also derive an explicit bound for the Kullback Leibler divergence.

No associations

LandOfFree

Say what you really think

Search LandOfFree.com for scientists and scientific papers. Rate them and share your experience with other people.

Rating

High-dimensional covariance estimation based on Gaussian graphical models does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with High-dimensional covariance estimation based on Gaussian graphical models, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and High-dimensional covariance estimation based on Gaussian graphical models will most certainly appreciate the feedback.

Rate now

     

Profile ID: LFWR-SCP-O-683862

All data on this website is collected from public sources. Our data reflects the most accurate information available at the time of publication.