Gaussian Mixture Copula Processes for Irregular Time Series

We introduce Gaussian Mixture Copula Processes (GMCP), a conditional copula process for irregularly sampled multivariate time series (IMTS) that is expressive and marginalization consistent at the same time. Existing conditional copula processes achieve only one of the two. Gaussian copula processes are consistent by construction but confined to elliptical dependence, whereas attentional copulas such as TACTiS-2 are far more expressive but neither preserve the marginals they are built on nor guarantee that integrating out a target point returns the joint over the remaining ones. GMCP closes this gap by inferring the parameters of a Gaussian Mixture Copula from the context in a way that guarantees consistent marginalization. This yields a non-elliptical copula process with tractable likelihood and consistency guarantees. Our experiments show that copulas equipped with MargFlow, a normalizing-flow model for the univariate marginals fitted in isolation, outperform jointly trained baselines in probabilistic IMTS forecasting. We further provide evidence that GMCP is more expressive than Gaussian copula processes, and on par with the inconsistent TACTiS-2.