# Error Estimate and Convergence Analysis for Data Valuation

arXiv: https://arxiv.org/abs/2511.06463 · HTML: https://mlsanity.com/paper/2511.06463/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 6 of its 15 references that are in the map.
- First posted on arXiv 9 Nov 2025.

## Builds on (most cited first, 6 of 6)

- [Data Shapley: Equitable Valuation of Data for Machine Learning](https://mlsanity.com/paper/1904.02868/) (2019)
- [Datamodels: Predicting Predictions from Training Data](https://mlsanity.com/paper/2202.00622/) (2022)
- [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 Survey on Data Pricing: from Economics to Data Science](https://mlsanity.com/paper/2009.04462/) (2020)

## Abstract (arXiv)

Data valuation quantifies data importance, but existing methods cannot ensure validity in a single training process. The neural dynamic data valuation (NDDV) method [3] addresses this limitation. Based on NDDV, we are the first to explore error estimation and convergence analysis in data valuation. Under Lipschitz and smoothness assumptions, we derive quadratic error bounds for loss differences that scale inversely with time steps and quadratically with control variations, ensuring stability. We also prove that the expected squared gradient norm for the training loss vanishes asymptotically, and that the meta loss converges sublinearly over iterations. In particular, NDDV achieves sublinear convergence.