Research Article · Preprint Mathematics
Residual Stopping and Pointwise Inference for Nonuniform Entropic Self-Transport
- Primary subject
- Mathematics
- Subject subfields
- Probability and Statistics
- Paper type
- Research Article
- Manuscript stage
- Preprint
- Manuscript
- Archived
- Edition
- 2 · Permanent link
Overview
Abstract
We study observable residual stopping for the half-self-Sinkhorn iteration with iid samples from a fixed positive smooth density on the one- or two-dimensional torus. For the normalized periodic Gaussian, assume that ε→0, nε^(3d/2)→∞, and nε^(d/2+3)→0. Starting from the constant scaling, we stop at the first projective square-root-mass residual below t_n=n^(-1/2)ε^(-γ), where 0<γ<d/4 is fixed. The stopped score has the same pointwise Gaussian limit, centered at the true density score, as the exactly scaled empirical estimator. Its attained residual lies between ct_n and t_n with probability tending to one for every fixed 0<c<1/2, although √(n) t_n→∞. The stopping index is asymptotic to (d/4-γ)log(1/ε)/log2 in probability. For the coefficient-one threshold, uniform sampling already gives a different score limit when γ≥ d/4. The proof retains the iteration-dependent empirical-norm error and uses a normalized-row cancellation to control nonuniform initialization in dimension two.
Keywords entropic self-transport · Sinkhorn iteration · statistical stopping · score estimation · pointwise inference
Scope of the work
Observable first-residual stopping preserves the pointwise Gaussian score limit on one- and two-dimensional tori under the explicit bandwidth and tolerance conditions, with a sharp stopping-count law and tolerance obstruction.
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Scott Schubr. (2026). Residual Stopping and Pointwise Inference for Nonuniform Entropic Self-Transport (Version 2). Luminary Research Archive. https://research.luminaryoddities.com/residual-stopping-pointwise-inference-nonuniform-entropic-self-transport/v/2
BibTeX
@techreport{luminary_residual_stopping_pointwise_inference_nonuniform_entropic_self_transport_v2,
title = {Residual Stopping and Pointwise Inference for Nonuniform Entropic Self-Transport},
author = {Scott Schubr},
year = {2026},
institution = {Luminary Research Archive},
type = {Research Article},
note = {Version 2},
url = {https://research.luminaryoddities.com/residual-stopping-pointwise-inference-nonuniform-entropic-self-transport/v/2}
}Loading discussion…