Year: 2026
Type: preprint
Abstract: Csiszar's formulation of the $f$-divergence introduced a vast family of functionals for quantifying dissimilarity between probability distributions. However, many applications in statistics and information theory rely only on a few $f$-divergences, such as the Kullback-Leibler divergence, the $χ^2$-divergence, and the squared Hellinger distance. These divergences are especially useful because they admit simple compositional formulas under product measures, a property sometimes referred to as tensorization. In this work, we refine a formalism of tensorization previously introduced in the literature. Then, we show that any possible tensorization formula has a multi-affine form characterized by a single parameter, and identify all tensorizable $f$-divergences under our adopted notion of tensorization.
Source: arXiv (Cornell University)
Authors: Cruz, Rodrigo, Calmon, Flavio P., Yu, Qian
Institutions: Harvard University, University of California, Santa Barbara
Language: English
Subfield: Applied Mathematics
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W7204808564