$f$-Divergence Inequalities via Functional Domination
This work provides theoretical tools for information theory and statistics, but it is incremental as it builds on existing f-divergence frameworks.
The paper tackles the derivation of bounds on f-divergences using functional domination, establishing inequalities based on other f-divergences for probability measures on arbitrary alphabets, with results including bounds under bounded relative information assumptions.
This paper considers derivation of $f$-divergence inequalities via the approach of functional domination. Bounds on an $f$-divergence based on one or several other $f$-divergences are introduced, dealing with pairs of probability measures defined on arbitrary alphabets. In addition, a variety of bounds are shown to hold under boundedness assumptions on the relative information. The journal paper, which includes more approaches for the derivation of f-divergence inequalities and proofs, is available on the arXiv at https://arxiv.org/abs/1508.00335, and it has been published in the IEEE Trans. on Information Theory, vol. 62, no. 11, pp. 5973-6006, November 2016.