Residual Stopping and Pointwise Inference for Nonuniform Entropic Self-Transport
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Abstract
We study observable residual stopping for the half-self-Sinkhorn iteration with samples from a fixed positive smooth density on the one- or two-dimensional torus. Under stated bandwidth and tolerance conditions, the first residual hit preserves the pointwise Gaussian limit of the exactly scaled empirical score. We determine the leading stopping count, bound the attained residual, and give an obstruction at the upper tolerance exponent. The proof controls the common empirical trajectory and nonuniform initialization.
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- Residual_Stopping_and_Pointwise_Inference.pdf140.3 KiB · pdf
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Research details
- Subjects
- Mathematics · Probability and Statistics
- Keywords
- entropic self-transport, Sinkhorn iteration, statistical stopping, score estimation, pointwise inference
- Manuscript date
- 2026-10-18
- Reader reuse
- No additional permission granted
Scope
Fixed positive C⁶ density, dimensions one and two, and a fixed query under sufficient asymptotic bandwidth windows. The result concerns the first residual hit. A separate follow-up to Residual Certificates and Empirical Sharpness for Entropic Self-Transport Scores.
Reproduction
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