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.

State-of-the-art methods for forecasting irregularly sampled time series with missing values predominantly rely on just four datasets and a few small toy examples for evaluation. While ordinary differential equations (ODE) are the prevalent models in science and engineering, a baseline model that forecasts a constant value outperforms ODE-based models from the last five years on three of these existing datasets. This unintuitive finding hampers further research on ODE-based models, a more plausible model family. In this paper, we develop a methodology to generate irregularly sampled multivariate time series (IMTS) datasets from ordinary differential equations and to select challenging instances via rejection sampling. Using this methodology, we create Physiome-ODE, a large and sophisticated benchmark of IMTS datasets consisting of 50 individual datasets, derived from real-world ordinary differential equations from research in biology. Physiome-ODE is the first benchmark for IMTS forecasting that we are aware of and an order of magnitude larger than the current evaluation setting of four datasets. Using our benchmark Physiome-ODE, we show qualitatively completely different results than those derived from the current four datasets: on Physiome-ODE ODE-based models can play to their strength and our benchmark can differentiate in a meaningful way between different IMTS forecasting models. This way, we expect to give a new impulse to research on ODE-based time series modeling.

Forecasting irregularly sampled time series with missing values is a crucial task for numerous real-world applications such as healthcare, astronomy, and climate sciences. State-of-the-art approaches to this problem rely on Ordinary Differential Equations (ODEs) which are known to be slow and often require additional features to handle missing values. To address this issue, we propose a novel model using Graphs for Forecasting Irregularly Sampled Time Series with missing values which we call GraFITi. GraFITi first converts the time series to a Sparsity Structure Graph which is a sparse bipartite graph, and then reformulates the forecasting problem as the edge weight prediction task in the graph. It uses the power of Graph Neural Networks to learn the graph and predict the target edge weights. GraFITi has been tested on 3 real-world and 1 synthetic irregularly sampled time series dataset with missing values and compared with various state-of-the-art models. The experimental results demonstrate that GraFITi improves the forecasting accuracy by up to 17% and reduces the run time up to 5 times compared to the state-of-the-art forecasting models.