Pith Number

pith:ESGERUKY

pith:2026:ESGERUKYJUNB2P3LZBI5Y77ORK

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Generalized Functional ANOVA in Closed-Form: A Unified View of Additive Explanations

Baptiste Ferrere, Fabrice Gamboa, Jean-Michel Loubes, Nicolas Bousquet

Hilbert space methods yield an explicit Riesz basis for generalized functional ANOVA on continuous dependent inputs

arxiv:2605.18422 v1 · 2026-05-18 · stat.ML · cs.LG · math.ST · stat.TH

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Record completeness

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Claims

C1strongest claim

By combining Hilbert space methods with the generalized functional ANOVA, we build an explicit decomposition Riesz Basis allowing to easily compute the decomposition. Our formulation recovers the classical independent case and its associated orthogonal decomposition.

C2weakest assumption

The construction assumes that the input variables are continuous and that a suitable Riesz basis exists in the underlying Hilbert space so that the decomposition remains both explicit and estimable from finite samples.

C3one line summary

Introduces a Riesz basis for explicit generalized functional ANOVA decomposition under input dependence and an associated data-driven estimation procedure.

References

62 extracted · 62 resolved · 2 Pith anchors

[1] Agarwal, R., Melnick, L., Frosst, N., Zhang, X., Lengerich, B., Caruana, R., and Hinton, G. E. (2021). Neural additive models: Interpretable machine learning with neural nets.Advances in neural inform 2021

[2] I., Salaün, T., and Brunel, N 2022

[3] Apley, D. W. and Zhu, J. (2020). Visualizing the effects of predictor variables in black box super- vised learning models.Journal of the Royal Statistical Society Series B: Statistical Methodology, 82 2020

[4] Arzamasov, V ., Böhm, K., and Jochem, P. (2018). Towards concise models of grid stability. In 2018 IEEE international conference on communications, control, and computing technologies for smart grids 2018

[5] Bach, S., Binder, A., Montavon, G., Klauschen, F., Müller, K.-R., and Samek, W. (2015). On pixel-wise explanations for non-linear classifier decisions by layer-wise relevance propagation. PloS one, 10 2015

Formal links

2 machine-checked theorem links

Receipt and verification

First computed	2026-05-20T00:06:00.022543Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

248c48d1584d1a1d3f6bc851dc7fee8a8869a22331c6d9f4890019dcef1093c4

Aliases

arxiv: 2605.18422 · arxiv_version: 2605.18422v1 · doi: 10.48550/arxiv.2605.18422 · pith_short_12: ESGERUKYJUNB · pith_short_16: ESGERUKYJUNB2P3L · pith_short_8: ESGERUKY

Agent API

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Verify this Pith Number yourself

curl -sH 'Accept: application/ld+json' https://pith.science/pith/ESGERUKYJUNB2P3LZBI5Y77ORK \
  | 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: 248c48d1584d1a1d3f6bc851dc7fee8a8869a22331c6d9f4890019dcef1093c4

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "d5c3d76f93e48f5231f530eb773866c9e5766b9245cb809c437302bc97c0b4ec",
    "cross_cats_sorted": [
      "cs.LG",
      "math.ST",
      "stat.TH"
    ],
    "license": "http://creativecommons.org/licenses/by/4.0/",
    "primary_cat": "stat.ML",
    "submitted_at": "2026-05-18T13:56:10Z",
    "title_canon_sha256": "cdd19d0b35f35a2d94dfbd7e76f4634d10b858719c8777dfb7205cc74bd18ebc"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2605.18422",
    "kind": "arxiv",
    "version": 1
  }
}