Inverse Covariance Matrix

An Inverse Covariance Matrix is an Inverse Matrix of a Covariance Matrix.

• AKA: Concentration/Precision Matrix.
• See: Inverse Operation, Inverse Covariance Matrix Estimation.

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References

2009

• http://en.wikipedia.org/wiki/Covariance_matrix#Definition
  • The inverse of this matrix, [math]\displaystyle{ \Sigma^{-1} }[/math], is called the inverse covariance matrix, concentration matrix or precision matrix. The elements of the precision matrix have an interpretation in terms of partial correlations and partial variances.

2007

• (Yuan & Lin, 2007) ⇒ Ming Yuan, and Yi Lin. (2007). “Model Election and Estimation in the Gaussian Graphical Model.” In: Biometrica, 90. doi:10.1093/biomet/asm018.
  • We propose penalized likelihood methods for estimating the concentration matrix in the Gaussian graphical model. The methods lead to a sparse and shrinkage estimator of the concentration matrix that is positive definite, and thus conduct model selection and estimation simultaneously. The implementation of the methods is nontrivial because of the positive definite constraint on the concentration matrix, but we show that the computation can be done effectively by taking advantage of the efficient maxdet algorithm developed in convex optimization.

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