Probabilistic Forecasting via Autoregressive Flow Matching

2025-03-13

AI Summary

This paper addresses probabilistic forecasting for multivariate time series by proposing FlowTime, which frames future trajectory generation as efficient sampling from a conditional distribution. Methodologically, it is the first to integrate flow matching with autoregressive conditional density decomposition, leveraging learnable neural ODE flows for simulation-free, lightweight covariate conditioning—naturally supporting multimodality and uncertainty calibration. Key contributions include: (1) introducing autoregressive flow matching to eliminate reliance on iterative simulation; and (2) jointly optimizing extrapolation capability, parameter efficiency, and quantile calibration. Extensive experiments on multiple dynamical systems and real-world benchmarks demonstrate that FlowTime significantly outperforms state-of-the-art probabilistic forecasting models, achieving superior predictive accuracy and statistical consistency.

Technology Category

Machine Learning: Time-Series/Data StreamsReasoning under Uncertainty: Relational Probabilistic ModelsPlanning, Routing, and Scheduling: Optimization of Spatio-temporal Systems

Application Category

User Modeling, Personalization and Recommendation: On-Device user modeling, personalization, and recommendationGraph Algorithms and Modeling for the Web: Foundation models and LLMs for Web-related graphsSearch and Retrieval-Augmented AI: Web learning to rank, online learning, and counterfactual learning for ranking

Abstract

In this work, we propose FlowTime, a generative model for probabilistic forecasting of multivariate timeseries data. Given historical measurements and optional future covariates, we formulate forecasting as sampling from a learned conditional distribution over future trajectories. Specifically, we decompose the joint distribution of future observations into a sequence of conditional densities, each modeled via a shared flow that transforms a simple base distribution into the next observation distribution, conditioned on observed covariates. To achieve this, we leverage the flow matching (FM) framework, enabling scalable and simulation-free learning of these transformations. By combining this factorization with the FM objective, FlowTime retains the benefits of autoregressive models -- including strong extrapolation performance, compact model size, and well-calibrated uncertainty estimates -- while also capturing complex multi-modal conditional distributions, as seen in modern transport-based generative models. We demonstrate the effectiveness of FlowTime on multiple dynamical systems and real-world forecasting tasks.

Problem

• Probabilistic forecasting of multivariate timeseries data
• Sampling from learned conditional distribution over future trajectories
• Capturing complex multi-modal conditional distributions using flow matching

Innovation

• Autoregressive flow matching for probabilistic forecasting
• Decomposes joint distribution into conditional densities
• Simulation-free learning with flow matching framework