# GMM model of the joint distribution from multivariate marginals

I have two multivariate Gaussian variables $$X \sim \mathcal{N}(\boldsymbol {\mu}_X \in \mathcal R^d,\boldsymbol {\Sigma}_X \in \mathcal R^{d \times d})$$ and $$Y \sim \mathcal{N}(\boldsymbol {\mu}_Y \in \mathcal R^d,\boldsymbol {\Sigma}_Y \in \mathcal R^{d \times d})$$. $$X$$ and $$Y$$ are not independent. I want to model their joint distribution $$(X,Y)$$ as a Gaussian Mixture GMM. Does this make sense? Any insights on how to do it? Thanks

• Can you show some plots? – user2974951 Jan 8 at 9:44