提出数据生产价值评估方法,可实现数据定价最优收益。
An Instrumental Value for Data Production and its Application to Data Pricing
- 基于决策上下文和已有信息,量化数据对模型的辅助价值
- 在贝叶斯线性回归中,价值等价于信息增益,可实现完全利润提取
- 即使数据来源受限,仍能逼近最优收益,适用于多臂老虎机场景
数据或数据生产过程对希望用数据辅助决策的代理而言具有何种价值?这是理解数据价值及进一步定价的核心问题。本文提出一种捕捉数据生产过程工具价值的方法,考虑两个关键因素:(a) 代理决策问题的上下文;(b) 代理已有的先验数据或信息。通过与信息经济学中的信息设计与信号理论对接,为估值概念提供微观基础。在贝叶斯线性回归场景下,该价值自然对应信息增益。基于此价值模型,研究了一个基本的卖方垄断定价场景:买方希望购买特定特征方向的标注数据以改进贝叶斯回归模型。结果表明,若卖方可完全定制任意数据请求,则能从任何买方群体中提取第一级价格歧视下的最优收入(即全部剩余)。若卖方只能出售来自现有数据池的数据,其定制能力受限,通常无法达到最优收入。但本文设计了一种机制,使卖方收入最多比最优值低 $\\(log (κ)$,其中 $κ$ 为数据矩阵的条件数。作为推论,卖方在多臂老虎机特例中可提取最优收入。
原文摘要 · Abstract (English)
How much value does a dataset or a data production process have to an agent who wishes to use the data to assist decision-making? This is a fundamental question towards understanding the value of data as well as further pricing of data. This paper develops an approach for capturing the instrumental value of data production processes, which takes two key factors into account: (a) the context of the agent's decision-making problem; (b) prior data or information the agent already possesses. We ''micro-found'' our valuation concepts by showing how they connect to classic notions of information design and signals in information economics. When instantiated in the domain of Bayesian linear regression, our value naturally corresponds to information gain. Based on our designed data value, we then study a basic monopoly pricing setting with a buyer looking to purchase from a seller some labeled data of a certain feature direction in order to improve a Bayesian regression model. We show that when the seller has the ability to fully customize any data request, she can extract the first-best revenue (i.e., full surplus) from any population of buyers, i.e., achieving first-degree price discrimination. If the seller can only sell data that are derived from an existing data pool, this limits her ability to customize, and achieving first-best revenue becomes generally impossible. However, we design a mechanism that achieves seller revenue at most $\log (κ)$ less than the first-best revenue, where $κ$ is the condition number associated with the data matrix. A corollary of this result is that the seller can extract the first-best revenue in the multi-armed bandits special case.
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