ProFITi: Probabilistic Forecasting of Irregular Time Series via Conditional Flows

Abstract

Probabilistic forecasting of irregularly sampled multivariate time series with missing values is an important problem in many fields, including astronomy, finance, and healthcare. Traditional methods for this task often rely on differential equations based models and make an assumption on the target distribution. In recent years, normalizing flow models have emerged as a promising approach for density estimation and uncertainty quantification, offering a flexible framework that can capture complex dependencies. In this work, we propose a novel model ProFITi for probabilistic forecasting of irregular time series with missing values using conditional normalizing flows. In this approach, the model learns a {joint} probability distribution over the future values of the time series conditioned on the past observations and query (future) time-channel information. As components of our model, we introduce a novel invertible triangular attention layer, and an invertible non-linear activation function on and onto the whole real line. We conduct extensive experiments on $3$ datasets, and demonstrate that the proposed model, ProFITi, provides significantly better forecasting likelihoods compared to the existing baseline models. Specifically, on average, ProFITi provides $4$ times higher likelihood over the previously best model.