# Eigen-Value: Efficient Domain-Robust Data Valuation via Eigenvalue-Based Approach

arXiv: https://arxiv.org/abs/2510.23409 · HTML: https://mlsanity.com/paper/2510.23409/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 36 of its 63 references that are in the map.
- First posted on arXiv 27 Oct 2025.

## Builds on (most cited first, 30 of 36)

- [Deep Residual Learning for Image Recognition](https://mlsanity.com/paper/1512.03385/) (2015)
- [An Image is Worth 16x16 Words: Transformers for Image Recognition at Scale](https://mlsanity.com/paper/2010.11929/) (2020)
- [RoBERTa: A Robustly Optimized BERT Pretraining Approach](https://mlsanity.com/paper/1907.11692/) (2019)
- [Retrieval-Augmented Generation for Knowledge-Intensive NLP Tasks](https://mlsanity.com/paper/2005.11401/) (2020)
- [Benchmarking Neural Network Robustness to Common Corruptions and Perturbations](https://mlsanity.com/paper/1903.12261/) (2019)
- [The Many Faces of Robustness: A Critical Analysis of Out-of-Distribution Generalization](https://mlsanity.com/paper/2006.16241/) (2020)
- [Understanding Black-box Predictions via Influence Functions](https://mlsanity.com/paper/1703.04730/) (2017)
- [Do ImageNet Classifiers Generalize to ImageNet?](https://mlsanity.com/paper/1902.10811/) (2019)
- [Natural Adversarial Examples](https://mlsanity.com/paper/1907.07174/) (2019)
- [Moment Matching for Multi-Source Domain Adaptation](https://mlsanity.com/paper/1812.01754/) (2018)
- [Learning Robust Global Representations by Penalizing Local Predictive Power](https://mlsanity.com/paper/1905.13549/) (2019)
- [TIES-Merging: Resolving Interference When Merging Models](https://mlsanity.com/paper/2306.01708/) (2023)
- [Robust fine-tuning of zero-shot models](https://mlsanity.com/paper/2109.01903/) (2021)
- [Data Shapley: Equitable Valuation of Data for Machine Learning](https://mlsanity.com/paper/1904.02868/) (2019)
- [What Neural Networks Memorize and Why: Discovering the Long Tail via Influence Estimation](https://mlsanity.com/paper/2008.03703/) (2020)
- [Normalized Loss Functions for Deep Learning with Noisy Labels](https://mlsanity.com/paper/2006.13554/) (2020)
- [Bridging Language and Items for Retrieval and Recommendation: Benchmarking LLMs as Semantic Encoders](https://mlsanity.com/paper/2403.03952/) (2024)
- [Geometric Dataset Distances via Optimal Transport](https://mlsanity.com/paper/2002.02923/) (2020)
- [RankMe: Assessing the downstream performance of pretrained self-supervised representations by their rank](https://mlsanity.com/paper/2210.02885/) (2022)
- [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)
- [Data Valuation using Reinforcement Learning](https://mlsanity.com/paper/1909.11671/) (2019)
- [Large-scale Unsupervised Semantic Segmentation](https://mlsanity.com/paper/2106.03149/) (2021)
- [A Marketplace for Data: An Algorithmic Solution](https://mlsanity.com/paper/1805.08125/) (2018)
- [Distributionally Robust Optimization: A Review](https://mlsanity.com/paper/1908.05659/) (2019)
- [Distributionally Robust Optimization and Generalization in Kernel Methods](https://mlsanity.com/paper/1905.10943/) (2019)
- [LAVA: Data Valuation without Pre-Specified Learning Algorithms](https://mlsanity.com/paper/2305.00054/) (2023)
- [The Price of Fair PCA: One Extra Dimension](https://mlsanity.com/paper/1811.00103/) (2018)
- [DORO: Distributional and Outlier Robust Optimization](https://mlsanity.com/paper/2106.06142/) (2021)
- [OpenDataVal: a Unified Benchmark for Data Valuation](https://mlsanity.com/paper/2306.10577/) (2023)

## Abstract (arXiv)

Data valuation has become central in the era of data-centric AI. It drives efficient training pipelines and enables objective pricing in data markets by assigning a numeric value to each data point. Most existing data valuation methods estimate the effect of removing individual data points by evaluating changes in model validation performance under in-distribution (ID) settings, as opposed to out-of-distribution (OOD) scenarios where data follow different patterns. Since ID and OOD data behave differently, data valuation methods based on ID loss often fail to generalize to OOD settings, particularly when the validation set contains no OOD data. Furthermore, although OOD-aware methods exist, they involve heavy computational costs, which hinder practical deployment. To address these challenges, we introduce Eigen-Value (EV), a plug-and-play data valuation framework for OOD robustness that uses only an ID data subset, including during validation. EV provides a new spectral approximation of domain discrepancy, which is the gap of loss between ID and OOD using ratios of eigenvalues of ID data's covariance matrix. EV then estimates the marginal contribution of each data point to this discrepancy via perturbation theory, alleviating the computational burden. Subsequently, EV plugs into ID loss-based methods by adding an EV term without any additional training loop. We demonstrate that EV achieves improved OOD robustness and stable value rankings across real-world datasets, while remaining computationally lightweight. These results indicate that EV is practical for large-scale settings with domain shift, offering an efficient path to OOD-robust data valuation.