NH-CROP: Robust Pricing for Governed Language Data Assets under Cost Uncertainty

Traditional data valuation methods based on ``row-count $\times$ quality coefficient'' paradigms fail to capture the nuanced, nonlinear contributions that data makes to Large Language Model (LLM) capabilities. This paper presents a dynamic data valuation framework that transitions from static accounting to utility-based pricing. Our approach operates on three layers: (1) token-level information density metrics using Shannon entropy and Data Quality Scores; (2) empirical training gain measurement through influence functions, proxy model strategies, and Data Shapley values; and (3) cryptographic verifiability through hash-based commitments, Merkle trees, and a tamper-evident training ledger. We provide comprehensive experimental validation on three real domains (instruction following, mathematical reasoning, and code summarization), demonstrating that proxy-based empirical gain achieves near-perfect ranking alignment with realized utility, substantially outperforming row-count and token-count baselines. This framework enables a fair Data-as-a-Service economy where high-reasoning data is priced according to its actual contribution to model intelligence, while providing the transparency and auditability necessary for trustworthy data markets.

High-quality data drives machine learning advances across industries. Recognizing the value of data, data transactions are increasingly common, giving rise to many data marketplaces, e.g., AWS Marketplace, Databricks, and Datarade. However, determining the appropriate prices for data products remains a significant challenge due to the unique properties of data products. Traditional pricing methods in economics can be categorized into the cost approach, the income approach, and the sales comparison approach. The cost approach fails in data pricing due to near-zero marginal cost from data replication, and the income approach fails due to inherently unpredictable data revenue. The sales comparison approach remains viable, yet its application is hindered by the absence of standardized pricing benchmarks for data products across marketplaces. To address this challenge, we introduce \texttt{DaDaDa}, the first dataset for data product pricing, containing metadata for 16,147 data products from 9 major data marketplaces worldwide. \texttt{DaDaDa} enables the training of pricing models, thereby establishing price benchmarks for new data products. In addition, \texttt{DaDaDa} can be utilized for other important tasks in data markets, such as data product classification and retrieval. Experiments and a retrieval prototype demonstrate the effectiveness of \texttt{DaDaDa} for pricing, classification, and retrieval of data products. The dataset and code are available at https://github.com/ZJU-DIVER/DaDaDa.

Data acquisition is a major bottleneck for learning in real-time streams: analysts must decide on the fly which labels to purchase while respecting a rolling budget. However, existing online active learning rarely unifies pricing, information gain, and rolling budget constraints under concept drift. We introduce QueryMarket, a market-inspired framework that queries each incoming data point based on its estimated utility to the model and its price. Within this framework, we propose OVBAL (online variance-based active learning), which integrates data pricing with information-driven selection by estimating each sample's marginal utility via a D-optimality criterion with exponential forgetting and executing cost-aware purchases under rolling budget constraints. OVBAL yields a simple, fully online decision rule that adapts to nonstationary streams and heterogeneous label costs. Experiments on synthetic data and a real-world solar power generation forecasting task show that OVBAL is particularly effective under seller-centric pricing and yields a more favorable long-run error-cost trade-off in the real-world task under both pricing schemes.