source: arxiv statistics ml: triangular-reference schr\"odinger bridges for time series generation
level: research
the paper introduces triangular-reference schrödinger bridges for time series (tr-sbts), an extension of the sbts framework. instead of a standard brownian reference, it uses an intervalwise frozen diffusion reference that is triangular across a hierarchy of latent volatility levels. this reference can be degenerate, meaning its covariance may be rank-deficient. the construction is a single entropy projection on an augmented state space, with the variational constraint applied jointly over time and latent levels, unfolded hierarchically using the disintegration of relative entropy.
the variational core of sbts is preserved: the entropy minimizer remains the h-transform of the reference. on each frozen interval, the optimal dynamics follow a logarithmic-gradient drift formula on the affine leaves of the active covariance directions. this holds even when the frozen covariance is rank-deficient, which is a key technical contribution. the method thus generalizes previous approaches by allowing more flexible reference processes that can better capture complex time series structures.
the authors establish stability of the frozen approximation and prove convergence of the corresponding regularized kernel. this provides theoretical guarantees for the method's reliability. the approach is designed for time series generation tasks, where modeling dependencies across time and latent factors is crucial. by using a triangular reference, the model can efficiently handle varying volatility regimes and missing data patterns, making it suitable for financial, climate, or other sequential data applications.
why it matters: this method enables more accurate and stable generation of complex time series data, such as financial or climate sequences, by handling degenerate noise structures and latent volatility hierarchies.
source: arxiv statistics ml: triangular-reference schr\"odinger bridges for time series generation