The `1-regularized Gaussian maximum likelihood estimator (MLE) has been shown to have strong statistical guarantees in recovering a sparse inverse covariance matrix, or alternatively the underlying graph structure of a Gaussian Markov Random Field, from very limited samples. We propose a novel algorithm for solving the resulting optimization problem which is a regularized log-determinant progra...

Two popular approaches to forming bounds in approximate Bayesian inference are local variational methods and minimal KullbackLeibler divergence methods. For a large class of models we explicitly relate the two approaches, showing that the local variational method is equivalent to a weakened form of Kullback-Leibler Gaussian approximation. This gives a strong motivation to develop efficient meth...

The present article derives the minimal number N of observations needed to approximate a Bayesian posterior distribution by Gaussian. derivation is based on an invariance requirement for likelihood . This defined Lie group that leaves src=image/13422860_01.gif> unchanged, when applied both observation(s) src=image/13422860_05.gif> and parameter src=image/13422860_...