Probabilistic Forecasting of Irregularly Sampled Time Series with Missing Values via Conditional Normalizing Flows

Abstract Probabilistic forecasting of irregularly sampled multivariate time series with missing values is crucial for decision-making in various domains, including health care, astronomy, and climate. State-of-the-art methods estimate only marginal distributions of observations in single channels and at single timepoints, assuming a Gaussian distribution for the data. In this work, we propose a novel model, ProFITi using conditional normalizing flows to learn multivariate conditional distribution: joint distribution of the future values of the time series conditioned on past observations and specific channels and timepoints, without assuming any fixed shape of the underlying distribution. As model components, we introduce a novel invertible triangular attention layer and an invertible non-linear activation function on and onto the whole real line. Through extensive experiments on 4 real-world datasets, ProFITi demonstrates significant improvement, achieving an average log-likelihood gain of 2.0 compared to the previous state-of-the-art method.