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pith:7JVW7MQ7

pith:2026:7JVW7MQ7KD7ONX7VG6APWPLAXY

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Statistical Unlearning of Distributions: A Hypothesis Testing Approach

Aaradhya Pandey, Sanjeev Kulkarni

A hypothesis test comparing edited data to desired and unwanted distributions supplies a criterion for choosing which samples to remove when unlearning entire domains.

arxiv:2605.16645 v1 · 2026-05-15 · math.ST · cs.IT · cs.LG · math.IT · stat.ML · stat.TH

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Claims

C1strongest claim

We formalize this using a hypothesis test of the edited data with the desired and unwanted domains, leading to an interpretable and robust criterion for selecting samples to remove. Within this statistical framework, we characterize the fundamental region of the allowable edited data distributions and the removal-preservation Pareto frontier for a broad class of distribution families.

C2weakest assumption

Domains of information can be accurately modeled as probability distributions, and a hypothesis test between the edited dataset and the desired versus unwanted distributions provides a sufficient criterion for sample removal that preserves performance on the target domain.

C3one line summary

A hypothesis testing approach to distributional unlearning that characterizes allowable edited distributions and removal-preservation Pareto frontiers for parametric and nonparametric families including Gaussians, Poisson, and Gaussian white noise.

References

13 extracted · 13 resolved · 0 Pith anchors

[1] Sangamesh Kodge, Gobinda Saha, and Kaushik Roy 2024

[2] Vladimir Koltchinskii and Martin Wahl 2023 · doi:10.1007/978-3-031-26979-0_15

[3] T(t 1 +X, t 2 +X)(x) =F F −1(1−x)−δ =T(t 2 +X, t 1 +X)(x).(25) So,T(t 1 +X, t 2 +X)(x) =T(X, δ+X)(x) =T(δ+X, X)(x)(26)

[4] Thenε 1 ≤ε 2 if and only if fX,ε1(x)≥f X,ε2(x)for allx∈[0,1].(27) Intuition and importance:The proof of this lemma is along the same lines of the proof given in Dong et al 2022

[5] There exists a Markov kernel 3 R : (W,F W)→(W ′,F W ′)such that R◦P=P ′ andR◦Q=Q ′,where for a probability distribution p on (W,F W), we define the probability distribution R◦p as R◦p(A ′) := Z W R(w, 2022

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Receipt and verification

First computed	2026-05-20T00:02:34.135065Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

fa6b6fb21f50fee6dff53780fb3d60be07392612b84d96c983fb42366df961c1

Aliases

arxiv: 2605.16645 · arxiv_version: 2605.16645v1 · doi: 10.48550/arxiv.2605.16645 · pith_short_12: 7JVW7MQ7KD7O · pith_short_16: 7JVW7MQ7KD7ONX7V · pith_short_8: 7JVW7MQ7

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  | 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: fa6b6fb21f50fee6dff53780fb3d60be07392612b84d96c983fb42366df961c1

Canonical record JSON

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    "license": "http://creativecommons.org/licenses/by/4.0/",
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    "submitted_at": "2026-05-15T21:33:38Z",
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