Linear Regression from Strategic Data Sources
Linear Regression from Strategic Data Sources
复制标题
战略数据源的线性回归
DOI：
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发表时间：
2013
期刊：
影响因子：
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通讯作者：
Benjamin Roussillon
中科院分区：
文献类型：
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作者：
Nicolas Gast;Stratis Ioannidis;P. Loiseau;Benjamin Roussillon
线性回归是统计数据分析的基本构建块。统计中的马尔可夫定理指出，概括的最小二乘（GL）是一种所谓的“最佳线性无偏估计器”（蓝色）。面对战略数据来源；例如，提供高精度数据的成本。作为推荐的系统，在本文中产生了准确的估算实体，我们研究了一个功能是公共的，但个人选择了他们向分析师揭示的精度分析师对该数据集进行线性回归，个人受益于此估计的结果，我们将这种情况模型为一个游戏，使个人最小化由两个组成部分组成：（a）高精度数据；（b）（全球）估计代表线性估算中的不准确性这款游戏具有独特的非平凡性NASH等效性，我们研究了这种均等的效率，我们证明了大量披露和估计成本的稳定性范围很紧张。我们表明，总的来说，Aitken的定理在战略数据源下不存在，尽管如果个人有相同的披露费用（最多可达乘法）因素）。
Linear regression is a fundamental building block of statistical data analysis. It amounts to estimating the parameters of a linear model that maps input features to corresponding outputs. In the classical setting where the precision of each data point is fixed, the famous Aitken/Gauss-Markov theorem in statistics states that generalized least squares (GLS) is a so-called “Best Linear Unbiased Estimator” (BLUE). In modern data science, however, one often faces strategic data sources; namely, individuals who incur a cost for providing high-precision data. For instance, this is the case for personal data, whose revelation may affect an individual’s privacy—which can be modeled as a cost—or in applications such as recommender systems, where producing an accurate estimate entails effort. In this article, we study a setting in which features are public but individuals choose the precision of the outputs they reveal to an analyst. We assume that the analyst performs linear regression on this dataset, and individuals benefit from the outcome of this estimation. We model this scenario as a game where individuals minimize a cost composed of two components: (a) an (agent-specific) disclosure cost for providing high-precision data; and (b) a (global) estimation cost representing the inaccuracy in the linear model estimate. In this game, the linear model estimate is a public good that benefits all individuals. We establish that this game has a unique non-trivial Nash equilibrium. We study the efficiency of this equilibrium and we prove tight bounds on the price of stability for a large class of disclosure and estimation costs. Finally, we study the estimator accuracy achieved at equilibrium. We show that, in general, Aitken’s theorem does not hold under strategic data sources, though it does hold if individuals have identical disclosure costs (up to a multiplicative factor). When individuals have non-identical costs, we derive a bound on the improvement of the equilibrium estimation cost that can be achieved by deviating from GLS, under mild assumptions on the disclosure cost functions.
用于统计估计的最佳数据采集
DOI：
10.1145/3219166.3219195
发表时间：
2018
期刊：
ACM Conference on Economics and Computation
影响因子：
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作者：
Chen, Yiling;Immorlica, Nicole;Lucier, Brendan;Syrgkanis, Vasilis;Ziani, Juba
通讯作者：
Ziani, Juba