Pith Number

pith:VTWKRKFV

pith:2026:VTWKRKFVZPFARD3EPS2KQJM4GS

not attested not anchored not stored refs resolved

To discretize continually: Mean shift interacting particle systems for Bayesian inference

Ayoub Belhadji, Daniel Sharp, Youssef M. Marzouk

Mean shift interacting particle systems approximate expectations from unnormalized densities by minimizing maximum mean discrepancy.

arxiv:2605.14142 v1 · 2026-05-13 · stat.ML · cs.LG · stat.CO

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Record completeness

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2 Internet Archive

3 Author claim open · sign in to claim

4 Citations open

5 Replications 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

The resulting mean shift interacting particle systems converge quickly, capture anisotropy and multi-modality, avoid mode collapse, and scale to high dimensions.

C2weakest assumption

That the proposed MMD-minimizing dynamics, when applied to unnormalized densities, produce particle configurations whose weighted averages accurately approximate the true expectations for the target distribution across the claimed regimes.

C3one line summary

Mean shift interacting particle systems generate weighted samples approximating expectations under unnormalized densities by minimizing MMD through normalizing-constant-invariant dynamics.

References

78 extracted · 78 resolved · 2 Pith anchors

[1] I. Arasaratnam and S. Haykin. Cubature Kalman Filters.IEEE Transactions on Automatic Control, 54(6):1254–1269, June 2009. ISSN 0018-9286, 1558-2523. doi: 10.1109/TAC.2009. 2019800 2009 · doi:10.1109/tac.2009

[2] M. Arbel, A. Korba, A. Salim, and A. Gretton. Maximum mean discrepancy gradient flow. Advances in Neural Information Processing Systems, 32, 2019 2019

[3] D. Aristoff and W. Bangerth. A Benchmark for the Bayesian Inversion of Coefficients in Partial Differential Equations.SIAM Review, 65(4):1074–1105, November 2023. ISSN 0036-1445, 1095-7200 2023

[4] F. Bach. On the equivalence between kernel quadrature rules and random feature expansions. The Journal of Machine Learning Research, 18(1):714–751, 2017 2017

[5] F. Bach, S. Lacoste-Julien, and G. Obozinski. On the equivalence between herding and condi- tional gradient algorithms. InProceedings of the 29th International Coference on International Conference on 2012

Formal links

2 machine-checked theorem links

Receipt and verification

First computed	2026-05-17T23:39:11.674632Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

aceca8a8b5cbca088f647cb4a8259c34b7c1f6e871f7c2d08e906e71441bbaaa

Aliases

arxiv: 2605.14142 · arxiv_version: 2605.14142v1 · doi: 10.48550/arxiv.2605.14142 · pith_short_12: VTWKRKFVZPFA · pith_short_16: VTWKRKFVZPFARD3E · pith_short_8: VTWKRKFV

Agent API

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Verify this Pith Number yourself

curl -sH 'Accept: application/ld+json' https://pith.science/pith/VTWKRKFVZPFARD3EPS2KQJM4GS \
  | 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: aceca8a8b5cbca088f647cb4a8259c34b7c1f6e871f7c2d08e906e71441bbaaa

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "46145b591dadf3cf1ec66b843547dfc7e36fdff69f1862c4b2b8259da133d419",
    "cross_cats_sorted": [
      "cs.LG",
      "stat.CO"
    ],
    "license": "http://creativecommons.org/licenses/by-sa/4.0/",
    "primary_cat": "stat.ML",
    "submitted_at": "2026-05-13T21:48:00Z",
    "title_canon_sha256": "12265a45de3a5c7e16e0b39f26f4bb3ed2e53f88486f17d273b4008645d7d17e"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2605.14142",
    "kind": "arxiv",
    "version": 1
  }
}