Triangular-Reference Schr\"odinger Bridges for Time Series Generation

2026-06-18 · Source: stat.ML updates on arXiv.org · Field: Technology & Digital — Artificial Intelligence & Machine Learning, Data Science & Analytics · Depth: Expert, extended

Summary

Triangular-Reference Schr"odinger Bridges for Time Series (TR-SBTS) is a novel generative model that extends the SBTS framework by replacing the standard Brownian reference with an intervalwise frozen, possibly degenerate diffusion reference. This reference is triangular across a hierarchy of latent volatility levels, allowing the model to capture complex temporal and cross-sectional dependencies, including stochastic volatility and rank-deficient covariance structures. The construction involves a single entropy projection on an augmented state space, preserving the SBTS variational core where the entropy minimiser is an h-transform of the reference. It employs a logarithmic-gradient drift formula and a finite-dimensional conditioning map, realized through block PCR, a reference-aware Mahalanobis kernel, and a past-window WLS drift regressor, coupled with a state–covariance bridge step. Numerical experiments demonstrate its robustness in high-dimensional settings and its ability to recover Heston model parameters like variance-of-variance and leverage, which traditional Brownian-reference SBTS models fail to capture.

Key takeaway

For Machine Learning Engineers or Data Scientists building generative models for complex time series, especially in finance, TR-SBTS offers a robust solution. If your current models struggle with stochastic volatility, tail behavior, or high-dimensional data, consider implementing TR-SBTS. Its adaptive, hierarchical reference process can significantly improve the fidelity of synthetic paths, reproducing critical distributional and temporal characteristics that fixed-reference models miss.

Key insights

TR-SBTS enhances time series generation by using a hierarchical, adaptive volatility reference for improved fidelity.

Principles

• Entropy minimiser is the h-transform of the reference.
• Optimal dynamics admit a logarithmic-gradient drift formula.
• Triangular structure allows bottom-up implementation of augmented bridges.

Method

TR-SBTS constructs a finite-dimensional conditioning map using block PCR, a reference-aware Mahalanobis kernel, and a past-window WLS drift regressor, coupled with a state–covariance bridge step.

In practice

• Use block PCR for global past summary or reference-aware Mahalanobis kernel for local spectral comparison.
• Employ a past-window WLS drift regressor for stable conditional drift estimation.

Topics

• Schrödinger Bridges
• Time Series Generation
• Stochastic Volatility
• Generative Models
• Kernel Regression
• Financial Modeling

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

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Editorial summary, takeaway, and curation by AIssential. Original article published by stat.ML updates on arXiv.org.