Pith Number

pith:VTHU4UDM

pith:2026:VTHU4UDMXSWBEQFX7HE7R32TD3

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Fenchel-Young Estimators of Perturbed Utility Models

Tianming Liu, Xi Lin, Yafeng Yin

The Fenchel-Young estimator provides a globally convex alternative to maximum likelihood for perturbed utility models.

arxiv:2602.21376 v2 · 2026-02-24 · math.OC · stat.ME

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Claims

C1strongest claim

By leveraging the intrinsic convex conjugate structure of the choice probabilities, we demonstrate that the Fenchel-Young estimator guarantees global convexity, providing a stable alternative to MLE that accommodates both dense and sparse choice kernels. Furthermore, we establish the framework's asymptotic consistency and normality under standard regularity conditions.

C2weakest assumption

Asymptotic consistency and normality hold under standard regularity conditions, and the solution mapping from the inner Fenchel-Young problem can be differentiated under regularity conditions to enable the outer bi-level optimization.

C3one line summary

Fenchel-Young estimators deliver globally convex and asymptotically consistent parameter estimation for perturbed utility models, plus a bi-level parametric basis method to learn perturbation functions, with improved Brier scores over multinomial logit on Swissmetro data.

Formal links

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Receipt and verification

First computed	2026-05-17T23:39:15.967204Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

accf4e506cbcac1240b7f9c9f8ef531eea56797e40120beac542d7b57dc46850

Aliases

arxiv: 2602.21376 · arxiv_version: 2602.21376v2 · doi: 10.48550/arxiv.2602.21376 · pith_short_12: VTHU4UDMXSWB · pith_short_16: VTHU4UDMXSWBEQFX · pith_short_8: VTHU4UDM

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Verify this Pith Number yourself

curl -sH 'Accept: application/ld+json' https://pith.science/pith/VTHU4UDMXSWBEQFX7HE7R32TD3 \
  | 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: accf4e506cbcac1240b7f9c9f8ef531eea56797e40120beac542d7b57dc46850

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "8bf55d7566fff12aa3a4f24a7be7932b5386d52a87209a7a107eda3a0ddd748e",
    "cross_cats_sorted": [
      "stat.ME"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.OC",
    "submitted_at": "2026-02-24T21:14:46Z",
    "title_canon_sha256": "76c6e80596be19a56335058202db98b91bf939686cd77322aee4e8de12fb2da1"
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  "source": {
    "id": "2602.21376",
    "kind": "arxiv",
    "version": 2
  }
}