Causal Optimal Coupling for Gaussian Input-Output Distributional Data
Fuente:
arXiv
Saved in:
| Main Authors: | , |
|---|---|
| Format: | Preprint |
| Published: |
2026
|
| Subjects: | |
| Online Access: | |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1866908932868407296 |
|---|---|
| author | Xu, Daran Taghvaei, Amirhossein |
| author_facet | Xu, Daran Taghvaei, Amirhossein |
| contents | We study the problem of identifying an optimal coupling between input-output distributional data generated by a causal dynamical system. The coupling is required to satisfy prescribed marginal distributions and a causality constraint reflecting the temporal structure of the system. We formulate this problem as a Schr"odinger Bridge, which seeks the coupling closest - in Kullback-Leibler divergence - to a given prior while enforcing both marginal and causality constraints. For the case of Gaussian marginals and general time-dependent quadratic cost functions, we derive a fully tractable characterization of the Sinkhorn iterations that converges to the optimal solution. Beyond its theoretical contribution, the proposed framework provides a principled foundation for applying causal optimal transport methods to system identification from distributional data. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2604_01406 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Causal Optimal Coupling for Gaussian Input-Output Distributional Data Xu, Daran Taghvaei, Amirhossein Systems and Control Machine Learning Optimization and Control Probability We study the problem of identifying an optimal coupling between input-output distributional data generated by a causal dynamical system. The coupling is required to satisfy prescribed marginal distributions and a causality constraint reflecting the temporal structure of the system. We formulate this problem as a Schr"odinger Bridge, which seeks the coupling closest - in Kullback-Leibler divergence - to a given prior while enforcing both marginal and causality constraints. For the case of Gaussian marginals and general time-dependent quadratic cost functions, we derive a fully tractable characterization of the Sinkhorn iterations that converges to the optimal solution. Beyond its theoretical contribution, the proposed framework provides a principled foundation for applying causal optimal transport methods to system identification from distributional data. |
| title | Causal Optimal Coupling for Gaussian Input-Output Distributional Data |
| topic | Systems and Control Machine Learning Optimization and Control Probability |
| url | https://arxiv.org/abs/2604.01406 |