Local Shapley: Model-Induced Locality and Optimal Reuse in Data Valuation

TL;DR

This paper introduces Local Shapley, a model-induced locality framework for efficient data valuation, reducing retraining costs by focusing on influential support sets and proposing algorithms that leverage this structure for speedups.

Contribution

It formalizes model-induced locality in Shapley value computation, providing a structured approach and algorithms that significantly reduce retraining in data valuation tasks.

Findings

Substantial reduction in retraining operations achieved.

Algorithms maintain high valuation accuracy.

Speedups demonstrated across multiple model types.

Abstract

The Shapley value provides a principled foundation for data valuation, but exact computation is #P-hard due to the exponential coalition space. Existing accelerations remain global and ignore a structural property of modern predictors: for a given test instance, only a small subset of training points influences the prediction. We formalize this model-induced locality through support sets defined by the model's computational pathway (e.g., neighbors in KNN, leaves in trees, receptive fields in GNNs), showing that Shapley computation can be projected onto these supports without loss when locality is exact. This reframes Shapley evaluation as a structured data processing problem over overlapping support-induced subset families rather than exhaustive coalition enumeration. We prove that the intrinsic complexity of Local Shapley is governed by the number of distinct influential subsets, establishing an information-theoretic lower bound on retraining operations. Guided by this result, we propose LSMR (Local Shapley via Model Reuse), an optimal subset-centric algorithm that trains each influential subset exactly once via support mapping and pivot scheduling. For larger supports, we develop LSMR-A, a reuse-aware Monte Carlo estimator that remains unbiased with exponential concentration, with runtime determined by the number of distinct sampled subsets rather than total draws. Experiments across multiple model families demonstrate substantial retraining reductions and speedups while preserving high valuation fidelity.