V2EX influence function

Influence Function

定义 Definition

influence function(影响函数):统计学与稳健统计中的一个概念,用来描述某个估计量/统计量对数据中单个观测点发生微小扰动时的敏感程度;常用于衡量离群点对结果的影响、分析估计的稳健性。(在机器学习与因果推断等领域也常借用这一思想。)

发音 Pronunciation (IPA)

/nfluns fkn/

例句 Examples

The influence function shows how much one data point can affect the estimate.
影响函数展示了单个数据点会在多大程度上影响估计结果。

In robust statistics, researchers often study the influence function to design estimators that resist outliers and remain stable under small data contamination.
在稳健统计中,研究者常通过分析影响函数来设计能抵抗离群点、并在数据受到小幅“污染”时仍保持稳定的估计量。

词源 Etymology

influence 源自拉丁语 influere(意为“流入、产生影响”),后来引申为“对某事产生作用”。function 源自拉丁语 functio(意为“执行、履行的活动/作用”)。合在一起,influence function字面意思就是“用来刻画影响作用的函数”。

相关词 Related Words

文学与著作中的用例 Literary Works

  • Robust Statistics: The Approach Based on Influence Functions(Hampel, Ronchetti, Rousseeuw, Stahel)
  • Robust Statistics(Peter J. Huber)
  • Robust Statistics: Theory and Methods(Maronna, Martin, Yohai)
  • The Elements of Statistical Learning(Hastie, Tibshirani, Friedman)(在讨论稳健方法/诊断思想时会涉及相关概念)
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