Higher-Order Series Expansion of f-Divergence
FrnkNlsn · x · 2026-07-13
This content discusses an expansion perspective on the Ali-Silvey-Csiszar f-divergence:
- Reviews the definition of f-divergence:
\( If(p:q)=\int p\, f(q/p)\, d\mu \)
- Explains that common divergences are encompassed in this framework, such as Kullback-Leibler, Jeffreys, and Jensen-Shannon.
- The core viewpoint: f-divergence can be written as a Taylor series of higher-order chi divergence.
- Provides sufficient conditions for the convergence of this series.
Overall, this is a theoretical statistics/information theory result, ideal for those interested in divergence functions, optimization, or probability distance representations.
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