{"paper":{"title":"Entropic Strict Minimum Message Length and Its Connections to PAC-Bayes and NML","license":"http://creativecommons.org/licenses/by/4.0/","headline":"Entropic SMML generalizes strict minimum message length into a tunable family that interpolates between Bayesian and minimax coding.","cross_cats":["stat.TH"],"primary_cat":"math.ST","authors_text":"Daniel F. Schmidt, Enes Makalic","submitted_at":"2026-05-03T23:38:19Z","abstract_excerpt":"We introduce entropic strict minimum message length (SMML), a risk-sensitive generalization of strict minimum message length coding. The proposed criterion replaces expected two-part codelength under the prior predictive distribution with an exponential certainty equivalent, thereby defining a one-parameter family of coding rules that interpolates between Bayesian average-case coding and worst-case minimax coding. We show that ordinary SMML is recovered in the risk-neutral limit, while the extreme risk-sensitive limit yields a minimax codelength criterion; when centered by the oracle maximum l"},"claims":{"count":4,"items":[{"kind":"strongest_claim","text":"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.","source":"verdict.strongest_claim","status":"machine_extracted","claim_id":"C1","attestation":"unclaimed"},{"kind":"weakest_assumption","text":"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.","source":"verdict.weakest_assumption","status":"machine_extracted","claim_id":"C2","attestation":"unclaimed"},{"kind":"one_line_summary","text":"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.","source":"verdict.one_line_summary","status":"machine_extracted","claim_id":"C3","attestation":"unclaimed"},{"kind":"headline","text":"Entropic SMML generalizes strict minimum message length into a tunable family that interpolates between Bayesian and minimax coding.","source":"verdict.pith_extraction.headline","status":"machine_extracted","claim_id":"C4","attestation":"unclaimed"}],"snapshot_sha256":"cb055e2b13d48f69399c2650771879fb50558b86b5d9366068de73cfb85fb815"},"source":{"id":"2605.02099","kind":"arxiv","version":2},"verdict":{"id":"b0d8d8d8-63db-4f65-9622-d5f2c71a9c5d","model_set":{"reader":"grok-4.3"},"created_at":"2026-05-08T18:36:25.767126Z","strongest_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.","one_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.","pipeline_version":"pith-pipeline@v0.9.0","weakest_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.","pith_extraction_headline":"Entropic SMML generalizes strict minimum message length into a tunable family that interpolates between Bayesian and minimax coding."},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2605.02099/integrity.json","findings":[],"available":true,"detectors_run":[{"name":"doi_compliance","ran_at":"2026-05-19T16:40:11.652073Z","status":"completed","version":"1.0.0","findings_count":0}],"snapshot_sha256":"e212b1dae4db6e6d3b8118052cb7499db5e42d25b8a0ca3e0c133ab9341bcb17"},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":3,"snapshot_sha256":"d94df8091ecbe77559d3eb3f23d5b130ba926bf6168773176b72a6709bc542eb"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"}