# QUadratic Inverse Covariance estimation

### Description

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

### Usage

1 2 |

### Arguments

`S` |
Covariance matrix. A |

`rho` |
Regularization parameter. It can be a |

`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. |

### Author(s)

Matyas A. Sustik (package maintainer), Cho-Jui Hsieh, Inderjit S. Dhillon, Pradeep Ravikumar

### 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