Pith Number

pith:6YRNMN2E

pith:2026:6YRNMN2EMSFQYAU4PK56DEF5GU

not attested not anchored not stored refs pending

Entropic Strict Minimum Message Length and Its Connections to PAC-Bayes and NML

Daniel F. Schmidt, Enes Makalic

Entropic SMML generalizes strict minimum message length into a tunable family that interpolates between Bayesian and minimax coding.

arxiv:2605.02099 v2 · 2026-05-03 · math.ST · stat.TH

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Claims

C1strongest claim

We show that entropic SMML admits a variational characterization as a Kullback--Leibler-regularized worst-case expected codelength, giving it a PAC--Bayes-type interpretation. We establish a joint asymptotic theory linking the sample size n and the risk parameter τ, showing that in regular parametric models the transition between Bayesian, robust, and minimax coding regimes occurs on a logarithmic scale.

C2weakest assumption

The joint asymptotic theory and the affine partition property hold only under the assumption of regular parametric models and regular exponential families; the paper does not specify how the results degrade when these regularity conditions are violated.

C3one line summary

Entropic SMML defines a risk-sensitive family of coding rules bridging Bayesian MML, PAC-Bayes, and NML minimax-regret via exponential certainty equivalents and tilted centroids in exponential families.

Formal links

3 machine-checked theorem links

Receipt and verification

First computed	2026-05-20T01:05:15.187082Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

f622d63744648b0c029c7abbe190bd3509cdcb552d119461be6200bd923aa7ef

Aliases

arxiv: 2605.02099 · arxiv_version: 2605.02099v2 · doi: 10.48550/arxiv.2605.02099 · pith_short_12: 6YRNMN2EMSFQ · pith_short_16: 6YRNMN2EMSFQYAU4 · pith_short_8: 6YRNMN2E

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Verify this Pith Number yourself

curl -sH 'Accept: application/ld+json' https://pith.science/pith/6YRNMN2EMSFQYAU4PK56DEF5GU \
  | 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: f622d63744648b0c029c7abbe190bd3509cdcb552d119461be6200bd923aa7ef

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "87d39ae688331f7d4099c11e22b306fff206253ef0a9180a56f9552ebed52ad2",
    "cross_cats_sorted": [
      "stat.TH"
    ],
    "license": "http://creativecommons.org/licenses/by/4.0/",
    "primary_cat": "math.ST",
    "submitted_at": "2026-05-03T23:38:19Z",
    "title_canon_sha256": "84873b3a30d08b4f73d3cb7a54b01efa0e77edb25746b829ac58c66a564750f1"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2605.02099",
    "kind": "arxiv",
    "version": 2
  }
}