Pith Number

pith:Q4AMPNU5

pith:2026:Q4AMPNU5KYXMJCSZ6TPV4I2BXS

not attested not anchored not stored refs pending

Bayesian online learning in the one-pass regime: Frequentist validity and uncertainty quantification

Dongguen Kim, Jeyong Lee, Junhyeok Choi, Minwoo Chae

A Bayesian algorithm for one-pass online learning achieves optimal posterior convergence and an online Bernstein-von Mises theorem.

arxiv:2604.27442 v2 · 2026-04-30 · math.ST · stat.ML · stat.TH

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\usepackage{pith}
\pithnumber{Q4AMPNU5KYXMJCSZ6TPV4I2BXS}

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4 Citations open

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The bundle contains the canonical record plus signed events. A mirror can host it anywhere and recompute the same current state with the deterministic merge algorithm.

Claims

C1strongest claim

For this algorithm, we show that the sequentially updated posterior attains the optimal convergence rate. Building on this, we establish an online analogue of the Bernstein-von Mises theorem, which guarantees valid uncertainty quantification without diverging mini-batch sample sizes.

C2weakest assumption

The analysis assumes that a warm-start phase can be incorporated to ensure stable sequential updates in the one-pass regime without violating the single-pass constraint or requiring additional conditions that may not hold for general data streams.

C3one line summary

A one-pass Bayesian online learner with warm-start achieves optimal posterior convergence and satisfies an online Bernstein-von Mises theorem for uncertainty quantification.

Receipt and verification

First computed	2026-06-11T01:09:36.571493Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

8700c7b69d562ec48a59f4df5e2341bcb08d22352d974d6ba751f97729f773b0

Aliases

arxiv: 2604.27442 · arxiv_version: 2604.27442v2 · doi: 10.48550/arxiv.2604.27442 · pith_short_12: Q4AMPNU5KYXM · pith_short_16: Q4AMPNU5KYXMJCSZ · pith_short_8: Q4AMPNU5

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Verify this Pith Number yourself

curl -sH 'Accept: application/ld+json' https://pith.science/pith/Q4AMPNU5KYXMJCSZ6TPV4I2BXS \
  | 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: 8700c7b69d562ec48a59f4df5e2341bcb08d22352d974d6ba751f97729f773b0

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "c52da6ac5ca8b93c632b6dcbb546e27924dccc2ffeae31588d763db780edd4f0",
    "cross_cats_sorted": [
      "stat.ML",
      "stat.TH"
    ],
    "license": "http://creativecommons.org/licenses/by/4.0/",
    "primary_cat": "math.ST",
    "submitted_at": "2026-04-30T05:29:06Z",
    "title_canon_sha256": "f45db0a01905c0764b6d6c64779a2956ea26c73ef25365783754f7ba3bb7c606"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2604.27442",
    "kind": "arxiv",
    "version": 2
  }
}