# From Points to Coalitions: Hierarchical Contrastive Shapley Values for Prioritizing Data Samples

arXiv: https://arxiv.org/abs/2512.19363 · HTML: https://mlsanity.com/paper/2512.19363/

## Key facts

- Cited by 12 papers in the map (data through 14 Oct 2026).
- Builds on 21 of its 45 references that are in the map.
- First posted on arXiv 22 Dec 2025.

## Builds on (most cited first, 21 of 21)

- [A Simple Framework for Contrastive Learning of Visual Representations](https://mlsanity.com/paper/2002.05709/) (2020)
- [Representation Learning with Contrastive Predictive Coding](https://mlsanity.com/paper/1807.03748/) (2018)
- [Data Shapley: Equitable Valuation of Data for Machine Learning](https://mlsanity.com/paper/1904.02868/) (2019)
- [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 Banzhaf: A Robust Data Valuation Framework for Machine Learning](https://mlsanity.com/paper/2205.15466/) (2022)
- [A Principled Approach to Data Valuation for Federated Learning](https://mlsanity.com/paper/2009.06192/) (2020)
- [Data Collection and Quality Challenges in Deep Learning: A Data-Centric AI Perspective](https://mlsanity.com/paper/2112.06409/) (2021)
- [NDC-Scene: Boost Monocular 3D Semantic Scene Completion in Normalized Device Coordinates Space](https://mlsanity.com/paper/2309.14616/) (2023)
- [Active Federated Learning](https://mlsanity.com/paper/1909.12641/) (2019)
- [A Survey on Data Pricing: from Economics to Data Science](https://mlsanity.com/paper/2009.04462/) (2020)
- [Less Is Better: Unweighted Data Subsampling via Influence Function](https://mlsanity.com/paper/1912.01321/) (2019)
- [Swift Sampler: Efficient Learning of Sampler by 10 Parameters](https://mlsanity.com/paper/2410.05578/) (2024)
- [Improving Fairness for Data Valuation in Horizontal Federated Learning](https://mlsanity.com/paper/2109.09046/) (2021)
- [Machine Learning Data Practices through a Data Curation Lens: An Evaluation Framework](https://mlsanity.com/paper/2405.02703/) (2024)
- [Data Valuation and Detections in Federated Learning](https://mlsanity.com/paper/2311.05304/) (2023)
- [Variance reduced Shapley value estimation for trustworthy data valuation](https://mlsanity.com/paper/2210.16835/) (2022)
- [DU-Shapley: A Shapley Value Proxy for Efficient Dataset Valuation](https://mlsanity.com/paper/2306.02071/) (2023)
- [MemeBLIP2: A novel lightweight multimodal system to detect harmful memes](https://mlsanity.com/paper/2504.21226/) (2025)
- [A Survey of Data Pricing for Data Marketplaces](https://mlsanity.com/paper/2303.04810/) (2023)

## Built on by (most cited first, 12 of 12)

- [EEO-TFV: Escape-Explore Optimizer for Web-Scale Time-Series Forecasting and Vision Analysis](https://mlsanity.com/paper/2602.02551/) (2026)
- [TimeSAF: Towards LLM-Guided Semantic Asynchronous Fusion for Time Series Forecasting](https://mlsanity.com/paper/2604.12648/) (2026)
- [Curvature-Adaptive Consistency Flow Matching: Autonomous Trajectory Optimization via Reinforcement Learning](https://mlsanity.com/paper/2606.22394/) (2026)
- [Time-TK: A Multi-Offset Temporal Interaction Framework Combining Transformer and Kolmogorov-Arnold Networks for Time Series Forecasting](https://mlsanity.com/paper/2602.11190/) (2026)
- [MedTri: A Platform for Structured Medical Report Normalization to Enhance Vision-Language Pretraining](https://mlsanity.com/paper/2602.22143/) (2026)
- [Sharpness-Aware Minimization for Generalized Embedding Learning in Federated Recommendation](https://mlsanity.com/paper/2603.11503/) (2026)
- [Taming the Long Tail: Efficient Item-wise Sharpness-Aware Minimization for LLM-based Recommender Systems](https://mlsanity.com/paper/2603.12752/) (2026)
- [MHMamba: Multi-Head Mamba for 3D Brain Tumor Segmentation](https://mlsanity.com/paper/2605.16464/) (2026)
- [Foundation-Assisted Active Learning for Object Detection Annotation](https://mlsanity.com/paper/2607.16671/) (2026)
- [Scope3Trace: Evidence-Based Identification and Extraction of Scope 3 GHG Emissions from Sustainability Reports](https://mlsanity.com/paper/2607.17122/) (2026)
- [AsyncCouple-Flow: Asynchronous Cross-Modal Coupling and Flow Matching for Spatio-Temporal Forecasting](https://mlsanity.com/paper/2609.16573/) (2026)
- [CoRe: Coherence and Relational Alignment for Multivariate Time Series Forecasting](https://mlsanity.com/paper/2609.19670/) (2026)

## Abstract (arXiv)

How should we quantify the value of each training example when datasets are large, heterogeneous, and geometrically structured? Classical Data-Shapley answers in principle, but its O(n!) complexity and point-wise perspective are ill-suited to modern scales. We propose Hierarchical Contrastive Data Valuation (HCDV), a three-stage framework that (i) learns a contrastive, geometry-preserving representation, (ii) organizes the data into a balanced coarse-to-fine hierarchy of clusters, and (iii) assigns Shapley-style payoffs to coalitions via local Monte-Carlo games whose budgets are propagated downward. HCDV collapses the factorial burden to O(T sum_{l} K_{l}) = O(T K_max log n), rewards examples that sharpen decision boundaries, and regularizes outliers through curvature-based smoothness. We prove that HCDV approximately satisfies the four Shapley axioms with surplus loss O(eta log n), enjoys sub-Gaussian coalition deviation tilde O(1/sqrt{T}), and incurs at most k epsilon_infty regret for top-k selection. Experiments on four benchmarks--tabular, vision, streaming, and a 45M-sample CTR task--plus the OpenDataVal suite show that HCDV lifts accuracy by up to +5 pp, slashes valuation time by up to 100x, and directly supports tasks such as augmentation filtering, low-latency streaming updates, and fair marketplace payouts.