A Generalized Bias-Variance Decomposition for Bregman Divergences

David Pfau

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arXiv · 2511.08789

A Generalized Bias-Variance Decomposition for Bregman Divergences

David Pfau

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Abstract

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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David Pfau. 2025-11-11. A Generalized Bias-Variance Decomposition for Bregman Divergences. https://arxiv.org/abs/2511.08789

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