Reliable Probabilistic Forecasting of Irregular Time Series through Marginalization-Consistent Flows

Probabilistic forecasting of joint distributions for irregular time series with missing values is an underexplored area in machine learning. Existing models, such as Gaussian Process Regression and ProFITi, are limited: while ProFITi is highly expressive due to its use of normalizing flows, it often produces unrealistic predictions because it lacks marginalization consistency—marginal distributions of subsets of variables may not match those predicted directly, leading to inaccurate marginal forecasts when trained on joints. We propose MOSES (Mixtures of Separable Flows), a novel model that parametrizes a stochastic process via a mixture of normalizing flows, where each component combines a latent multivariate Gaussian with separable univariate transformations. This design allows MOSES to be analytically marginalized, enabling accurate and reliable predictions for various probabilistic queries. Experiments on four datasets show that MOSES achieves highly accurate joint and marginal predictions. Thanks to its inherent marginalization consistency, MOSES significantly outperforms all baselines—including ProFITi—on marginal predictions. For joint predictions, it beats all other consistent models and performs close to or slightly worse than ProFITi.