SIF 4th Cohort Fellows - Jack Storror Carter, Pompeu Fabra University Barcelona

• Education

• Experience

• Publications/Research achievements

Gaussian graphical models (GGMs) are a useful statistical tool for visualising dependencies among continuous random variables. Applications of GGMs include genetics, computer vision and causal inference. GGMs are commonly learned from data through sparse estimation of the precision matrix because zeros in the matrix correspond to conditional independencies between the variables. However, the precision matrix entries measure not only dependence but also dispersion, as they depend on both partial correlations and partial variances, hampering interpretation. I addressed this point during my PhD by directly modelling partial correlations, which lead to improved model selection in the case of l1 penalised likelihood estimation. A further issue hampering interpretation is that the diagonal entries (partial variances) depend on both the dispersion of the variable (through the marginal variance) and the dependence between variables (stronger dependence means smaller partial variances). I propose exploring reparameterisations of partial variances which decouple these two concepts. A first research line is to devise penalised likelihood and Bayesian methods for estimating GGMs under the reparameterisations. A second line is to study the explainability of GGM data analysis methods under the reparameterization. Here explainability refers to tuning parameters having a simple interpretation, so that their choice can be understood and guided by humans. The proposed decoupling can aid explainability because each parameter corresponds to a separate property of the distribution and so can be interpreted individually. This is particularly relevant in Bayesian methods, a hallmark of which is the interpretation of the prior distribution and the ability to incorporate expert knowledge.