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Pré-Publication, Document De Travail Année : 2022

Stability and upper bounds for statistical estimation of unbalanced transport potentials

Résumé

In this note, we derive upper-bounds on the statistical estimation rates of unbalanced optimal transport (UOT) maps for the quadratic cost. Our work relies on the stability of the semi-dual formulation of optimal transport (OT) extended to the unbalanced case. Depending on the considered variant of UOT, our stability result interpolates between the OT (balanced) case where the semi-dual is only locally strongly convex with respect the Sobolev semi-norm H1 dot and the case where it is locally strongly convex with respect to the H 1 norm. When the optimal potential belongs to a certain class C with sufficiently low metric-entropy, local strong convexity enables us to recover super-parametric rates, faster than 1 / root n.
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Dates et versions

hal-03609629 , version 1 (17-03-2022)
hal-03609629 , version 2 (15-06-2022)

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Citer

Adrien Vacher, François-Xavier Vialard. Stability and upper bounds for statistical estimation of unbalanced transport potentials. 2022. ⟨hal-03609629v1⟩
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