Non-asymptotic error controlled sparse high dimensional precision matrix estimation

Bayesian estimation of a sparse precision matrix

We consider the problem of estimating a sparse precision matrix of a multivariate Gaussian distribution, including the case where the dimension p is large. Gaussian graphical models provide an important tool in describing conditional independence through presence or absence of the edges in the underlying graph. A popular non-Bayesian method of estimating a graphical structure is given by the gr...

Sparse Precision Matrix Estimation with Calibration

We propose a semiparametric method for estimating sparse precision matrix of high dimensional elliptical distribution. The proposed method calibrates regularizations when estimating each column of the precision matrix. Thus it not only is asymptotically tuning free, but also achieves an improved finite sample performance. Theoretically, we prove that the proposed method achieves the parametric ...

Approaches to High-Dimensional Covariance and Precision Matrix Estimation

High-dimensional bolstered error estimation

MOTIVATION In small-sample settings, bolstered error estimation has been shown to perform better than cross-validation and competitively with bootstrap with regard to various criteria. The key issue for bolstering performance is the variance setting for the bolstering kernel. Heretofore, this variance has been determined in a non-parametric manner from the data. Although bolstering based on thi...

Sparse Precision Matrix Estimation via Lasso Penalized D-Trace Loss

We introduce a constrained empirical loss minimization framework for estimating highdimensional sparse precision matrices and propose a new loss function, called the D-trace loss, for that purpose. A novel sparse precision matrix estimator is defined as the minimizer of the lasso penalized D-trace loss under a positive-definiteness constraint. Under a new irrepresentability condition, the lasso...