# A Generalized Bias-Variance Decomposition for Bregman Divergences

arXiv: https://arxiv.org/abs/2511.08789 · HTML: https://mlsanity.com/paper/2511.08789/

## Key facts

- Cited by 8 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 11 Nov 2025.

## Built on by (most cited first, 8 of 8)

- [The Hot Mess of AI: How Does Misalignment Scale With Model Intelligence and Task Complexity?](https://mlsanity.com/paper/2601.23045/) (2026)
- [When Does Predictive Inverse Dynamics Outperform Behavior Cloning?](https://mlsanity.com/paper/2601.21718/) (2026)
- [Loss-Driven Bayesian Active Learning](https://mlsanity.com/paper/2604.11995/) (2026)
- [Subjective Risk Decomposition: A New View for Uncertainty Quantification](https://mlsanity.com/paper/2607.15196/) (2026)
- [A Ground-Truth Framework for Uncertainty Disentanglement with Posterior Risk](https://mlsanity.com/paper/2608.05995/) (2026)
- [Calibeating for general proper losses: A Bregman divergence approach](https://mlsanity.com/paper/2605.17269/) (2026)
- [A Bregman Perspective on Classification and Regression Trees](https://mlsanity.com/paper/2606.13984/) (2026)
- [Elimination Geometry](https://mlsanity.com/paper/2608.17646/) (2026)

## Abstract (arXiv)

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.