  Gaussian Graphical Models (GGM) are often used to describe the conditional
correlations between the components of a random vector. In this article, we
compare two families of GGM inference methods: nodewise edge selection and
penalised likelihood maximisation. We demonstrate on synthetic data that, when
the sample size is small, the two methods produce graphs with either too few or
too many edges when compared to the real one. As a result, we propose a
composite procedure that explores a family of graphs with an nodewise numerical
scheme and selects a candidate among them with an overall likelihood criterion.
We demonstrate that, when the number of observations is small, this selection
method yields graphs closer to the truth and corresponding to distributions
with better KL divergence with regards to the real distribution than the other
two. Finally, we show the interest of our algorithm on two concrete cases:
first on brain imaging data, then on biological nephrology data. In both cases
our results are more in line with current knowledge in each field.
