Global goodness-of-fit and discrepancy statistics can establish that a sample departs from a reference distribution without identifying which observations drive the departure. We develop a framework for this localization problem by assigning to each observation its conditional or marginal contribution across random statistical contexts. This connects resampling diagnostics and data valuation to projection theory and event-level anomaly detection. For symmetric statistics, fixed-size replacement is exactly equivalent to centered conditional localization. For U-statistics, the addition score equals the first Hoeffding/Hájek contribution; for smooth distributional functionals it is related at leading order to the influence function; and for unbiased known-background MMD it reduces exactly to the MMD witness. This viewpoint also yields more efficient estimators. Matched-context subtraction removes fluctuations unrelated to the observation, while for pairwise MMD the event-containing terms give a simple localizer. On the LHC Olympics anomaly-detection benchmark, the pair estimator converges to the direct empirical MMD witness with the predicted 1/(Rm^2) scaling, where m is batch size and R the number of batches. At m=1000 and R=5x106 it reaches correlation 0.9993 with essentially identical AUC. We also ask when context contains information beyond an event's own features. In a shared-latent toy model, the full single-event signal and background distributions are identical by construction, forcing isolated-event AUC=0.5. Discriminating information survives only in cross-event dependence induced by the shared latent parameter; the ensemble recovers this information, whereas an independent-latent control does not. This separates two roles of context: efficient localization of a global discrepancy and genuinely additional class information when the alternative contains shared structure.
Data valuation is a cornerstone of data-centric learning, where prior efforts primarily focus on designing algorithms to classify training samples as either beneficial or detrimental for the learning task. However, leveraging these valuation estimates for subsequent data intervention remains underexplored; conventional approaches typically discard or downweight harmful samples, thereby underutilizing available data resources. In this paper, we present Dynamic Influence-based Valuation and Editing (DIVE), a novel and efficient framework that dynamically estimates sample values at the batch level and transforms detrimental data into beneficial contributions. Rather than altering the raw data, DIVE operates at the optimization level by strategically reversing the gradient directions of harmful samples during training, ensuring seamless integration with standard learning procedures with minimal overhead. Extensive empirical evaluations demonstrate that DIVE consistently improves classification performance, maximizes data efficiency, stabilizes optimization, and effectively generalizes to large language model fine-tuning.
Data Shapley answers which training points are worth what, and its nearest-neighbor specialization is the version actually deployed, shipped by toolkits such as pyDVL and OpenDataVal. Exact algorithms exist for unweighted nearest-neighbor classification and regression, and recently for weighted classification; weighted regression and soft-label prediction have resisted, the only exact method being enumeration exponential in the neighborhood size. The obstruction, in the prior authors' own words, is that the weighted regression prediction is a ratio of two coalition-dependent weighted sums: its normalization denominator blocks the additive and threshold routes, and leaves the counting route exponential in the target resolution. We close this gap with a counting dynamic program over the joint integer state of accumulated weight and weighted target, a minimal sufficient statistic for the ratio; it is exact, pseudo-polynomial, and matched exhaustive enumeration with zero mismatch. We add a certified approximation scheme for continuous weights and targets carrying a machine-checkable per-value certificate, a complexity landscape delimiting the exact problem, and a soft-label extension. We release an open-source, CPU-only library and the first exact weighted-regression ground truth. On mislabel detection our exact values are statistically equivalent to Monte-Carlo Data Shapley; exactness instead buys determinism, a certified bound, and an auditing reference, and it puts a measured price on approximation.
Shapley values are widely used to attribute value to training data based on their marginal contribution to performance on a validation set. Existing practice often assumes these values are stable once the training data and model are fixed. In this work, we uncover a systematic vulnerability: even modest changes to the validation set, such as introducing noises, cause directional shifts in Shapley distributions. As noises are added, Shapley values of training samples compress toward zero. We trace this to a noise-induced neighborhood reshuffling effect: perturbations alter the local rank order between validation and training samples, flattening the valuation landscape. Using the KNN-Shapley framework, we show through synthetic and real data that these shifts are consistent and reproducible. Our findings challenge the assumption of Shapley stability and reveal a new axis of fragility in data valuation. We propose normalization and boundary-aware validation strategies to mitigate these distortions and enable more robust, interpretable valuation in machine learning marketplaces.
Data valuation quantifies the intrinsic quality of individual samples to enable principled data curation, quality control, and robust learning. For time series in critical domains such as healthcare, finance, and industrial monitoring, effective valuation methods are essential yet fundamentally lacking. Existing approaches are either model-dependent, limiting their generalizability, or designed for i.i.d. data and thus fail to capture temporal dependencies, multi-scale patterns, and non-stationary dynamics inherent to sequential data. We introduce TimeLAVA, a learning-agnostic framework that values temporal segments by their marginal contribution to minimizing distributional discrepancy between evaluated and reference data. At its core is a novel Selective Wavelet-based Wasserstein discrepancy combining multi-scale wavelet transforms for temporal localization with unbalanced optimal transport for robustness to distributional shifts. Segment values are efficiently computed via sensitivity analysis without requiring model training and aggregated into point-wise scores. We provide theoretical guarantees linking valuation to model-agnostic generalization and prove bounded sensitivity to outlier contamination. Extensive experiments across anomaly detection, data pruning, and label noise detection demonstrate that TimeLAVA produces significantly more informative value scores than existing methods on diverse real-world datasets.
Guangyi Zhang, Lutz Oettershagen, Lixu Wang +1cs.LG cs.DS
Data valuation, the task of quantifying the contribution of individual data points to model performance, has emerged as a fundamental challenge in machine learning. Game-theoretic approaches, such as the Banzhaf value, offer principled frameworks for fair data valuation; however, they suffer from exponential computational complexity. We address this challenge by developing efficient algorithms specifically tailored for computing Banzhaf values in $k$-nearest neighbor ($k$NN) classifiers. We first establish the theoretical hardness of the problem by proving that it is \#P-hard. Despite this intractability, we exploit the locality properties of $k$NN classifiers to develop practical exact algorithms. Our main contribution is a dynamic programming framework that achieves significant computational improvements: we present a pseudo-polynomial algorithm with $O(Wkn^2)$ time complexity for weighted $k$NN classifiers, where $W$ is the maximum sum of top-$k$ weights, and a specialized algorithm for unweighted $k$NN that achieves $O(nk^2)$ time complexity, that is, linear in the number of data points. We also offer efficient Monte Carlo estimation methods. Extensive experiments on real-world datasets demonstrate the practical efficiency of our approach and its effectiveness in data valuation applications.
Xuan Yang, Hsi-Wen Chen, Ming-Syan Chen +1cs.LG cs.DB cs.GT
Shapley-based data valuation provides a principled way to quantify the contribution of training data, but its high computational cost makes it impractical in dynamic settings where tasks and training players evolve. Existing methods treat Shapley computation as a one-shot process and collapse contributions into aggregated scores, preventing reuse and requiring recomputation under any change. We introduce a new perspective that represents Shapley values as a player-by-task matrix and formulates dynamic valuation as a structured matrix maintenance problem. We exploit the fact that each task depends on a small subset of training players and that similar tasks yield similar valuations, leading to utility locality and coalition locality. Based on these insights, we propose D-Shap, a dynamic valuation framework that enables efficient updates by modifying only a small portion of the matrix: new task valuations are inferred via structure-aware interpolation, while updates induced by new players are confined to affected local matrix blocks. To eliminate the need for pre-specified evaluation tasks, we introduce self-valuation, which constructs the initial matrix directly from training data, supported by scalable subset reuse and coverage-aware anchor selection. Experiments across diverse models show that D-Shap performs task updates in milliseconds and reduces the cost of player updates by up to three orders of magnitude, while achieving valuation quality competitive with full recomputation.
Probabilistic values, including Shapley values and semivalues, provide a model-agnostic framework to attribute the behavior of a black-box model to data points or features, with a wide range of applications including explainable artificial intelligence and data valuation. However, their exact computation requires utility evaluations over exponentially many coalitions, making Monte Carlo approximation essential in modern machine learning applications. Existing estimators are often developed through different identification strategies, including weighted averages, self-normalized weighting, regression adjustment, and weighted least squares. Our key observation is that these seemingly distinct constructions share a common first-order error structure, in which the leading term is an augmented inverse-probability weighted influence term determined by the sampling law and a working surrogate function. This first-order representation yields an explicit expression for the leading mean squared error (MSE), which characterizes how the sampling law and the surrogate jointly determine statistical efficiency. Guided by this criterion, we propose an Efficiency-Aware Surrogate-adjusted Estimator (EASE) that directly chooses the sampling law and surrogate to minimize the first-order MSE. We demonstrate that EASE consistently outperforms state-of-the-art estimators for various probabilistic values.