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pith:FAUZONQK

pith:2025:FAUZONQK64KTIQB7CJZVRVCHMN

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Classification Trees with Valid Inference via the Exponential Mechanism

Snigdha Panigrahi, Soham Bakshi

Classification trees fitted via the exponential mechanism produce pivots for asymptotically valid inference on model parameters.

arxiv:2511.15068 v3 · 2025-11-19 · stat.ME · stat.ML

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Claims

C1strongest claim

Our method produces pivots directly from the sampling probabilities in the exponential mechanism. In theory, our pivots allow asymptotically valid inference on the parameters in the predictive fit, and in practice, our method delivers powerful inference without sacrificing predictive accuracy, in contrast to data splitting methods.

C2weakest assumption

That the sampling probabilities from the exponential mechanism, when used to define pivots, correctly account for the adaptivity of the entire tree-growing process and yield asymptotically valid inference for the parameters in the final predictive fit.

C3one line summary

Classification trees built with the exponential mechanism generate asymptotically valid inference pivots from sampling probabilities without major accuracy loss.

References

6 extracted · 6 resolved · 1 Pith anchors

[1] Holistic Evaluation of Language Models 2022 · doi:10.1007/bf01194075

[2] The gain functionsG k h(v)and their first- to third-order derivatives order∇G k h(v),∇2Gk h(v), ∇3Gk h(v)are bounded for allv∈ eDn

[3] The functionf(.), derived from the logarithm of the sampling probabilities based on the gain functions, isL-Lipschitz, i.e.|f(v 1)−f(v 2)| ≤L||v 1 −v 2||for allv 1, v2 ∈ eDn

[4] 49 Firstly, note that the absolute value of each component ofη k h ∈R 8 is uniformly bounded with respect ton

[5] Now, since eachb i,n is uni- 55 formly bounded, i.e., sup n,i |bi,n| ≤ ¯C+ (by Proposition B.1), and the uniform multivariate Berry–Esseen bound in Bentkus [2003] applies, it follows that sup A∈C¯k P( 2003

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Receipt and verification

First computed	2026-07-21T02:21:25.911903Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

282997360af71534403f127358d447634930f29cfb73e4663d5d022b10cf4276

Aliases

arxiv: 2511.15068 · arxiv_version: 2511.15068v3 · doi: 10.48550/arxiv.2511.15068 · pith_short_12: FAUZONQK64KT · pith_short_16: FAUZONQK64KTIQB7 · pith_short_8: FAUZONQK

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curl -sH 'Accept: application/ld+json' https://pith.science/pith/FAUZONQK64KTIQB7CJZVRVCHMN \
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Canonical record JSON

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    "abstract_canon_sha256": "58f98323fd9b294efba0ce73cf9be9ce4deeba5b706a0ea795bb804650526ebf",
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    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "stat.ME",
    "submitted_at": "2025-11-19T03:20:04Z",
    "title_canon_sha256": "31bba1e9ba4c084dd931aa691a0a70448bd41007f18defe1a56b8c02dc51a0d6"
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