将偏差-方差分解拓展至Bregman散度，适用于指数族最大似然估计。
A Generalized Bias-Variance Decomposition for Bregman Divergences
- 用Bregman散度替代平方误差，推导通用偏差-方差分解
- 结果在指数族分布的最大似然估计中具有直接应用价值
- 提供清晰独立的推导过程，适合教学与理论学习
偏差-方差分解是统计学和机器学习中的核心结果，但通常仅针对平方误差给出。本文提出一种推广形式，其中预测误差由Bregman散度衡量，这与指数族分布的最大似然估计密切相关。尽管该结果已有文献记载，但此前缺乏清晰、独立的推导，因此本文为教学目的提供了完整推导。此前版本曾发布于作者个人网站，未附上下文；本文补充了相关文献讨论与背景说明。
原文摘要 · Abstract (English)
The bias-variance decomposition is a central result in statistics and machine learning, but is typically presented only for the squared error. We present a generalization of the bias-variance decomposition where the prediction error is a Bregman divergence, which is relevant to maximum likelihood estimation with exponential families. While the result is already known, there was not previously a clear, standalone derivation, so we provide one for pedagogical purposes. A version of this note previously appeared on the author's personal website without context. Here we provide additional discussion and references to the relevant prior literature.
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