# Geometric Data Valuation via Leverage Scores

arXiv: https://arxiv.org/abs/2511.02100 · HTML: https://mlsanity.com/paper/2511.02100/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 15 of its 29 references that are in the map.
- First posted on arXiv 3 Nov 2025.

## Builds on (most cited first, 15 of 15)

- [Understanding Black-box Predictions via Influence Functions](https://mlsanity.com/paper/1703.04730/) (2017)
- [Data Shapley: Equitable Valuation of Data for Machine Learning](https://mlsanity.com/paper/1904.02868/) (2019)
- [LESS: Selecting Influential Data for Targeted Instruction Tuning](https://mlsanity.com/paper/2402.04333/) (2024)
- [BatchBALD: Efficient and Diverse Batch Acquisition for Deep Bayesian Active Learning](https://mlsanity.com/paper/1906.08158/) (2019)
- [TRAK: Attributing Model Behavior at Scale](https://mlsanity.com/paper/2303.14186/) (2023)
- [Towards Efficient Data Valuation Based on the Shapley Value](https://mlsanity.com/paper/1902.10275/) (2019)
- [Beta Shapley: a Unified and Noise-reduced Data Valuation Framework for Machine Learning](https://mlsanity.com/paper/2110.14049/) (2021)
- [Efficient Task-Specific Data Valuation for Nearest Neighbor Algorithms](https://mlsanity.com/paper/1908.08619/) (2019)
- [Data Shapley in One Training Run](https://mlsanity.com/paper/2406.11011/) (2024)
- [A Marketplace for Data: An Algorithmic Solution](https://mlsanity.com/paper/1805.08125/) (2018)
- [Data-OOB: Out-of-bag Estimate as a Simple and Efficient Data Value](https://mlsanity.com/paper/2304.07718/) (2023)
- [Active Learning for Speech Recognition: the Power of Gradients](https://mlsanity.com/paper/1612.03226/) (2016)
- [Provably Accurate Shapley Value Estimation via Leverage Score Sampling](https://mlsanity.com/paper/2410.01917/) (2024)
- [Regression-adjusted Monte Carlo Estimators for Shapley Values and Probabilistic Values](https://mlsanity.com/paper/2506.11849/) (2025)
- [ActiveMatch: End-to-end Semi-supervised Active Representation Learning](https://mlsanity.com/paper/2110.02521/) (2021)

## Abstract (arXiv)

Shapley data valuation provides a principled, axiomatic framework for assigning importance to individual datapoints, and has gained traction in dataset curation, pruning, and pricing. However, it is a combinatorial measure that requires evaluating marginal utility across all subsets of the data, making it computationally infeasible at scale. We propose a geometric alternative based on statistical leverage scores, which quantify each datapoint's structural influence in the representation space by measuring how much it extends the span of the dataset and contributes to the effective dimensionality of the training problem. We show that our scores satisfy the dummy, efficiency, and symmetry axioms of Shapley valuation and that extending them to ridge leverage scores yields strictly positive marginal gains that connect naturally to classical A- and D-optimal design criteria. We further show that training on a leverage-sampled subset produces a model whose parameters and predictive risk are within O(varepsilon) of the full-data optimum, thereby providing a rigorous link between data valuation and downstream decision quality. Finally, we conduct an active learning experiment in which we empirically demonstrate that ridge-leverage sampling outperforms standard baselines without requiring access gradients or backward passes.