Ecosystem of Bregman Divergences and Dualities
FrnkNlsn · x · 2026-09-02
The post highlights the fundamental role of Bregman divergences in information geometry, illustrating dualities with:
- Exponential families
- Quasi-arithmetic centers
- Hessian manifolds
The attached paper, "$k$-MLE: A fast algorithm for learning statistical mixture models" by Frank Nielsen, leverages the duality between exponential families and Bregman divergences to prove the local convergence of the $k$-MLE algorithm, interpreting it as a dual additively weighted Bregman hard clustering.
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