An interesting exercise would have been to run a Gaussian Graphical Model (like the “graphical lasso”) to sparsify that correlation matrix. In the Gaussian cas

An interesting exercise would have been to run a Gaussian Graphical Model (like the “graphical lasso”) to sparsify that correlation matrix. In the Gaussian case, those methods are able to identify nonzero partial correlations and hence a causal graph. Since there’s multimodality here trust in that interpretation should be lower, but it’s still worthwhile looking at a pseudo/candidate causal structure as part of EDA.