When Does Data Value Reduce to Class Balance? A Coverage View of Per-Point Data Valuation
Abstract
Per-point data-valuation scores -- Data Shapley, influence, leverage -- are routinely used to select training data: keep the points with the top k scores. We argue that top-k by a fixed, mode-blind per-point score is the wrong selection rule precisely in the regime where data selection matters. The reason is that a point's value is not a fixed number but depends on what else has been selected -- a near-duplicate of an already-chosen point adds almost nothing, however high its score -- and a per-point scalar cannot express this interaction. The theory quantifies this failure exactly: in an equal latent-mode model, fixed top-k selection incurs a closed-form excess risk over adaptive coverage because it repeatedly spends budget on already-covered modes. The gap is largest when the budget is tight, the learner representation is redundant, and missing a mode is costly. The practical rule is simple: use balance when the labels available at selection identify the learner's modes, and use explicit coverage when they do not. On standard classification tasks with strong pretrained features, class-balancing the same per-point scores recovers the missing coverage and matches or outperforms generic set coverage across our datasets. Without labels, label-free coverage improves accuracy by up to +0.20 while raw top-k can fall below random; when labels are coarser than the modes, coverage within coarse strata performs best. We turn this distinction into a pre-specified diagnostic and validate it across both favorable and stress-test settings. The limits are part of the claim: the advantage is representation-relative. Coverage fails when the relevant modes are not expressed in the learner geometry, as with spurious subgroups, or when data quality varies independently of coverage -- exactly as the theory predicts.
Related
- The 2-Adic Valuation of the Order of the All-Ones Class in the Sandpile Group of a Square
- On the Value Function for a Class of Set Motion Problems
- Extension of valuation rings as limits of complete intersection algebras
- Coherence and the Hilbert-syzygy identity for power series over valuation domains
- Frobenius splitting of valuation rings revisited
BibTeX
@misc{bai2026when,
title = {{When Does Data Value Reduce to Class Balance? A Coverage View of Per-Point Data Valuation}},
author = {Yingjie Bai and Weiming Zhi},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.34801},
eprint = {2610.34801},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.34801},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - When Does Data Value Reduce to Class Balance? A Coverage View of Per-Point Data Valuation
AU - Yingjie Bai
AU - Weiming Zhi
PY - 2026
DA - 2026/10/26
PB - arXiv
DO - 10.48550/arxiv.2610.34801
UR - https://arxiv.org/abs/2610.34801
AB - Per-point data-valuation scores -- Data Shapley, influence, leverage -- are routinely used to select training data: keep the points with the top k scores. We argue that top-k by a fixed, mode-blind per-point score is the wrong selection rule precisely in the regime where data selection matters. The reason is that a point's value is not a fixed number but depends on what else has been selected -- a near-duplicate of an already-chosen point adds almost nothing, however high its score -- and a per-point scalar cannot express this interaction. The theory quantifies this failure exactly: in an equal latent-mode model, fixed top-k selection incurs a closed-form excess risk over adaptive coverage because it repeatedly spends budget on already-covered modes. The gap is largest when the budget is tight, the learner representation is redundant, and missing a mode is costly. The practical rule is simple: use balance when the labels available at selection identify the learner's modes, and use explicit coverage when they do not. On standard classification tasks with strong pretrained features, class-balancing the same per-point scores recovers the missing coverage and matches or outperforms generic set coverage across our datasets. Without labels, label-free coverage improves accuracy by up to +0.20 while raw top-k can fall below random; when labels are coarser than the modes, coverage within coarse strata performs best. We turn this distinction into a pre-specified diagnostic and validate it across both favorable and stress-test settings. The limits are part of the claim: the advantage is representation-relative. Coverage fails when the relevant modes are not expressed in the learner geometry, as with spurious subgroups, or when data quality varies independently of coverage -- exactly as the theory predicts.
ER -