Estimators based on influence functions (IFs) have been shown to be effective in many settings, especially when combined with machine learning techniques. By focusing on estimating a specific target of interest (e.g., the average effect of a treatment), rather than on estimating the full underlying data generating distribution, IF-based estimators are often able to achieve asymptotically optimal mean-squared error. Still, many researchers find IF-based estimators to be opaque or overly technical, which makes their use less prevalent and their benefits less available. To help foster understanding and trust in IF-based estimators, we present tangible, visual illustrations of when and how IF-based estimators can outperform standard ``plug-in'' estimators. The figures we show are based on connections between IFs, gradients, linear approximations, and Newton-Raphson.

中文翻译：

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影响功能的视觉传达和教学直觉

基于影响函数 (IF) 的估计器已被证明在许多环境中都是有效的，尤其是在与机器学习技术相结合时。通过专注于估计感兴趣的特定目标（例如，治疗的平均效果），而不是估计完整的基础数据生成分布，基于 IF 的估计器通常能够实现渐近最优的均方误差。尽管如此，许多研究人员发现基于 IF 的估算器不透明或过于技术化，这使得它们的使用不那么普遍，而且它们的好处也较少。为了帮助促进对基于 IF 的估计器的理解和信任，我们提供了基于 IF 的估计器何时以及如何超越标准“插件”估计器的有形的、直观的说明。我们展示的数字基于 IF、梯度、