QUIC (version 2012.02)

QUIC: QUadratic Inverse Covariance estimation

Description

Estimates a sparse inverse covariance matrix using a combination of Newton's method and coordinate descent.

Usage

QUIC(S, rho, path = NULL, tol = 1e-04, msg = 1, maxIter = 1000, X.init =
NULL, W.init = NULL)

Arguments

S

Covariance matrix. A $p\times p$ symmetric matrix.

rho

Regularization parameter. It can be a $p\times p$ matrix, a vector or scalar.

path

If specified, then rho is scaled with the elements of path and the corresponding inverse covariance matrix estimation is carried out for each value.

tol

Specifes the convergence tolerance.

msg

Controls how verbose messages should be printed during execution. Valid value range: 0--4.

maxIter

Specifies the maximum number of Newton iterations.

X.init

The initial estimate for the regularized inverse covariance matrix.

W.init

The inverse of initial estimate for the regularized inverse covariance matrix.

Value

• X
  Regularized inverse covariance matrix; an array of matrices when path is used.
• W
  Inverse of the matrix X.
• regloglik
  The optimal value for the regularized logarithmic likelihood, an array when path is used.
• opt
  The optimal value of the minimization problem, an array when path is used.
• iter
  The number of Newton iterations executed, an array when path is used.

References

Sparse Inverse Covariance Matrix Estimation Using Quadratic Approximation. Cho-Jui Hsieh, Matyas A. Sustik, Inderjit S. Dhillon, Pradeep Ravikumar, Advances in Neural Information Processing Systems, vol. 24, 2011, p. 2330--2338. http://www.cs.utexas.edu/users/sustik/papers/invcov.pdf