Nonparametric generative modeling for time series via Schr{\"{o}}dinger bridge

2025-12-31 · Source: JMLR · Field: Technology & Digital — Artificial Intelligence & Machine Learning, Data Science & Analytics · Depth: Expert, quick

Summary

A novel generative model for time series, developed by Mohamed Hamdouche, Pierre Henry-Labordère, and Huyên Pham and published in 27(58):1−23, 2026, utilizes the Schrödiger bridge (SB) approach. This method performs entropic interpolation through optimal transport between a reference probability measure on path space and a target measure aligned with the time series' joint data distribution. The model's solution is characterized by a stochastic differential equation (SDE) with a path-dependent drift function, which inherently respects the temporal dynamics of the time series. The drift function is estimated nonparametrically from data samples, often using kernel regression. New synthetic time series data are then generated by simulating the SB diffusion. The model's efficacy is demonstrated through numerical experiments on autoregressive models, GARCH models, and fractional Brownian motion, assessing accuracy via marginal, temporal dependency, and predictive scores. Additionally, SB-generated synthetic samples are applied to deep hedging tasks on real-world datasets.

Key takeaway

For Machine Learning Engineers developing generative models for time series, this Schrödiger bridge approach provides a robust nonparametric method to capture complex temporal dynamics. You should consider integrating this SDE-based technique for generating high-fidelity synthetic data, particularly when working with financial time series or evaluating advanced hedging strategies. This can improve model training and robustness by providing diverse, realistic data samples.

Key insights

Schrödiger bridge offers a nonparametric generative model for time series by interpolating probability measures via optimal transport.

Principles

• Entropic interpolation via optimal transport can generate time series.
• Path-dependent drift functions in SDEs capture temporal dynamics.

Method

Estimate the path-dependent drift function nonparametrically using kernel regression from data samples, then simulate the Schrödiger bridge diffusion to yield new synthetic time series.

In practice

• Test generative models with autoregressive and GARCH models.
• Use SB-generated synthetic samples for deep hedging applications.

Topics

• Nonparametric Generative Models
• Time Series
• Schrödiger Bridge
• Stochastic Differential Equations
• Deep Hedging
• Optimal Transport

Best for: Research Scientist, AI Scientist, Machine Learning Engineer

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Editorial summary, takeaway, and curation by AIssential. Original article published by JMLR.