Sinkhorn algorithms for entropic vector quantile regression
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arXiv
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| Format: | Preprint |
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2026
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| _version_ | 1866915882986373120 |
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| author | Kato, Kengo Wang, Boyu |
| author_facet | Kato, Kengo Wang, Boyu |
| contents | Vector quantile regression (VQR) is an optimal transport (OT)-based framework that extends linear quantile regression to vector-valued response variables and can be formulated as an OT problem with a mean-independence constraint. In this paper, we study two Sinkhorn-type algorithms for VQR with entropic regularization, building on our previous work on its duality theory. The first is a direct adaptation of the classical Sinkhorn iteration based on solving the full Schrödinger-type system characterizing the dual potentials, which requires solving an implicit functional equation at each iteration. The second algorithm, which is new in the literature, replaces the implicit update with a projected gradient step, resulting in a modified scheme that is computationally more practical. For both algorithms, and for general compactly supported marginals, we establish linear convergence in both the dual objective value and the iterates. A key innovation in our analysis is the derivation of explicit quantitative bounds on the dual potentials and Sinkhorn iterates. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2603_21554 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Sinkhorn algorithms for entropic vector quantile regression Kato, Kengo Wang, Boyu Optimization and Control Statistics Theory 49Q22, 62G08, 90C25 Vector quantile regression (VQR) is an optimal transport (OT)-based framework that extends linear quantile regression to vector-valued response variables and can be formulated as an OT problem with a mean-independence constraint. In this paper, we study two Sinkhorn-type algorithms for VQR with entropic regularization, building on our previous work on its duality theory. The first is a direct adaptation of the classical Sinkhorn iteration based on solving the full Schrödinger-type system characterizing the dual potentials, which requires solving an implicit functional equation at each iteration. The second algorithm, which is new in the literature, replaces the implicit update with a projected gradient step, resulting in a modified scheme that is computationally more practical. For both algorithms, and for general compactly supported marginals, we establish linear convergence in both the dual objective value and the iterates. A key innovation in our analysis is the derivation of explicit quantitative bounds on the dual potentials and Sinkhorn iterates. |
| title | Sinkhorn algorithms for entropic vector quantile regression |
| topic | Optimization and Control Statistics Theory 49Q22, 62G08, 90C25 |
| url | https://arxiv.org/abs/2603.21554 |