# Equivalence of Graphical model selection algorithms

Suppose, a jointly Gaussian random vector is denoted by $X \in \mathbb{R}^{p}$ and $X$ has a distribution given by $\mathcal{N}(\mu,\Sigma)$. It is known that estimating the graphical model that defines this random vector is equivalent to estimating the sparsity pattern of the inverse covariance matrix, i.e. $\Sigma ^{-1}$. Suppose the sparsity pattern is in the form of a tree. It is well known that Chou Liu's algorithm can be applied to recover that graphical model structure in this case. How can be prove that this algorithm will recover the sparsity pattern of the $\Sigma^{-1}$ ?

• Please do not simultaneously cross-post at multiple SE sites, as you did here cstheory.stackexchange.com/questions/31208 . It fragments the discussion and leads to duplication of effort. Apr 20 '15 at 21:02
• Thanks for notifying me. I will remove the question here. Apr 20 '15 at 21:10
• I changed my mind and thought it is more suitable for this forum. I have deleted the version of this question on theory cs stack exchange. Apr 21 '15 at 3:46