Pith Number

pith:PLIPPGXA

pith:2026:PLIPPGXA6C5TWV3G7G3QJ6X7SR

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Nearest-Neighbor Radii under Dependent Sampling

Yilong Hou, Yuanyuan Gao, Zhexiao Lin

Nearest-neighbor radii converge almost surely to zero under polynomial strong mixing, with moment bounds controlled by local intrinsic dimension rather than ambient dimension.

arxiv:2605.14343 v1 · 2026-05-14 · cs.LG · math.ST · stat.ML · stat.TH

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Claims

C1strongest claim

We establish distribution-free almost sure convergence under polynomial mixing and sharp non-asymptotic moment bounds under geometric mixing. The moment bounds depend on the local intrinsic dimension rather than the ambient dimension.

C2weakest assumption

The observations satisfy strong mixing conditions (polynomial or geometric decay of dependence) whose rate is known or estimable; if mixing is slower than assumed, the convergence and moment bounds may fail.

C3one line summary

Nearest-neighbor radii converge almost surely and obey local-dimension moment bounds under polynomial and geometric mixing dependence.

References

59 extracted · 59 resolved · 0 Pith anchors

[1] Convergence of distributions generated by stationary stochastic processes , volume =

[2] The Functional Law of the Iterated Logarithm for Stationary Strongly Mixing Sequences , volume =

[3] A distribution-free theory of nonparametric regression , year =

[4] Non-asymptotic uniform rates of consistency for k-nn regression , volume =

[5] Strong convergence of sums of -mixing random variables with applications to density estimation , volume =

Formal links

2 machine-checked theorem links

Receipt and verification

First computed	2026-05-17T23:39:08.163688Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

7ad0f79ae0f0bb3b5766f9b704faff9446500116d5080806571cec296e475086

Aliases

arxiv: 2605.14343 · arxiv_version: 2605.14343v1 · doi: 10.48550/arxiv.2605.14343 · pith_short_12: PLIPPGXA6C5T · pith_short_16: PLIPPGXA6C5TWV3G · pith_short_8: PLIPPGXA

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Verify this Pith Number yourself

curl -sH 'Accept: application/ld+json' https://pith.science/pith/PLIPPGXA6C5TWV3G7G3QJ6X7SR \
  | jq -c '.canonical_record' \
  | python3 -c "import sys,json,hashlib; b=json.dumps(json.loads(sys.stdin.read()), sort_keys=True, separators=(',',':'), ensure_ascii=False).encode(); print(hashlib.sha256(b).hexdigest())"
# expect: 7ad0f79ae0f0bb3b5766f9b704faff9446500116d5080806571cec296e475086

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "dbeeafad118edaa16d5df6f48da3d1f297b733c56ca99e57ddf3e5eeac559c89",
    "cross_cats_sorted": [
      "math.ST",
      "stat.ML",
      "stat.TH"
    ],
    "license": "http://creativecommons.org/licenses/by/4.0/",
    "primary_cat": "cs.LG",
    "submitted_at": "2026-05-14T04:07:05Z",
    "title_canon_sha256": "029cd14806f76fe33b03f42200133e528ef06c390685d94992b7abb5e113fb70"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2605.14343",
    "kind": "arxiv",
    "version": 1
  }
}