Pith Number

pith:YDVSEMJP

pith:2026:YDVSEMJPGCUHHTOZB7FPTVQM7G

not attested not anchored not stored refs resolved

A Majorization-Minimization with Monte Carlo Approach for Hyperparameter Estimation

Arvind K. Saibaba, Elle Buser, Hugo D\'iaz, Julianne Chung

M³C iterates converge with high probability to a critical point of the hyperparameter cost function by majorizing and Monte Carlo approximating the log-determinant.

arxiv:2605.13620 v1 · 2026-05-13 · math.NA · cs.NA

Open paper page JSON Open Graph Bundle Merged state Verified badge What is a Pith Number?

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{YDVSEMJPGCUHHTOZB7FPTVQM7G}

Prints a linked badge after your title and injects PDF metadata. Compiles on arXiv. Learn more · Embed verified badge

Record completeness

1 Bitcoin timestamp

2 Internet Archive

3 Author claim open · sign in to claim

4 Citations open

5 Replications open

✓ Portable graph bundle live · download bundle · merged state

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

we propose a Majorization-Minimization with Monte Carlo approach, which we call M³C, for hyperparameter estimation. ... showing that under certain assumptions, the M³C iterates converge with high probability to a critical point of the original cost function.

C2weakest assumption

The convergence holds under certain assumptions on the validity of the majorization function and the accuracy of the Monte Carlo estimator for the log-determinant term.

C3one line summary

M³C replaces the hard hyperparameter optimization with a sequence of simpler problems using a majorant for the log-determinant approximated via Monte Carlo, with proven high-probability convergence to a critical point under assumptions.

References

189 extracted · 189 resolved · 1 Pith anchors

[1] Inverse Problems , volume=

[2] The Gohberg Anniversary Collection: Volume I: The Calgary Conference and Matrix Theory Papers and Volume II: Topics in Analysis and Operator Theory , pages= 1989

[3] Super-resolution imaging , author=. 2017 , publisher= 2017

[4] High-dimensional probability: An introduction with applications in data science , author=. 2018 , publisher= 2018

[5] Bayesian Statistical Methods: With Applications to Machine Learning , author=. 2026 , publisher= 2026

Formal links

2 machine-checked theorem links

Receipt and verification

First computed	2026-05-18T02:44:17.901364Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

c0eb22312f30a873cdd90fcaf9d60cf9903a08d748852a2bfdf7d270fc8ffb13

Aliases

arxiv: 2605.13620 · arxiv_version: 2605.13620v1 · doi: 10.48550/arxiv.2605.13620 · pith_short_12: YDVSEMJPGCUH · pith_short_16: YDVSEMJPGCUHHTOZ · pith_short_8: YDVSEMJP

Agent API

Resolver JSON Graph JSON Events JSON Schema Signing key

Verify this Pith Number yourself

curl -sH 'Accept: application/ld+json' https://pith.science/pith/YDVSEMJPGCUHHTOZB7FPTVQM7G \
  | 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: c0eb22312f30a873cdd90fcaf9d60cf9903a08d748852a2bfdf7d270fc8ffb13

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "d1ee412eeccaeafc21b97910ad9523d46e09e51eb00ae778a381fb3c54b59782",
    "cross_cats_sorted": [
      "cs.NA"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.NA",
    "submitted_at": "2026-05-13T14:50:12Z",
    "title_canon_sha256": "0b9a5587100759b577ef2fcc47bb18fc0ea32c256e0e56258bcebebb5ec724f1"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2605.13620",
    "kind": "arxiv",
    "version": 1
  }
}