A Generalized Bias-Variance Decomposition for Bregman Divergences

• URL: http://arxiv.org/abs/2511.08789v1
• Date: Thu, 13 Nov 2025 01:07:54 GMT
• Title: A Generalized Bias-Variance Decomposition for Bregman Divergences
• Authors: David Pfau,
• Abstract summary: We present a generalization of the bias-variance decomposition where the prediction error is a Bregman divergence.<n>While the result is already known, there was not previously a clear, standalone derivation, so we provide one for pedagogical purposes.
• Score: 1.9483779836489397
• License: http://creativecommons.org/licenses/by/4.0/
• 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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