On Flow-based Generative Models for Probabilistic Forecasting

Edmond Cunningham, Madalina Fiterau, Daniel Sheldon

Keywords: Flow based generative models, stochastic interpolation, time series, probabilistic forecasting, mean-field variational inference, conditional random fields

TL;DR: We generalize the key elements of flow-based generative models to the time series setting to see if they can be a good fit for probabilistic forecasting.

Abstract: Flow-based generative models (FBGM) have emerged as a dominant approach to generative modeling in many domains for their scalability and controllability, but have notably not made the same impact on autoregressive probabilistic forecasting. Although the methodology behind these models can be applied directly to the time series setting, and in theory offers the potential to apply the advances in generative modeling to time series, this direct approach is difficult to use in practice. In this work, we investigate this methodological gap by generalizing the key elements of flow-based generative modeling to the time series setting to devise a more practical related algorithm. We show that FBGMs based on linear stochastic differential equations are instances of a more general mean-field variational inference algorithm for conditional exponential family distributions that constructs Bayes estimators of natural parameters. This insight yields a family of mean-squared error based latent probabilistic forecasters that contains a discrete time counterpart of FBGMs for time series. We demonstrate that the models we develop inherit the convenient theoretical properties of FBGMs while being easy to work with in practice.

Primary Area: Probabilistic methods (e.g., variational inference, causal inference, Gaussian processes)

Submission Number: 24023