Gaussian Graphical Model exploration and selection in high dimension low sample size setting
This work addresses a specific bottleneck in statistical modeling for fields like neuroscience and biology where sample sizes are limited, offering an incremental improvement over existing methods.
The authors tackled the problem of Gaussian Graphical Model selection in high-dimensional, low-sample-size settings, where existing methods produce graphs with too few or too many edges. They proposed a composite procedure that explores graphs with a nodewise scheme and selects one using a likelihood criterion, demonstrating on synthetic data that it yields graphs closer to the truth with better KL divergence, and applied it to brain imaging and nephrology data with results aligning better with domain knowledge.
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.