Bound on extended f-divergences for a variety of classes
The concept of f-divergences was introduced by Csiszar in 1963 as measures of the ’hardness’ of a testing problem depending on a convex real valued function f on the interval [0,∞). The choice of this parameter f can be adjusted so as to match the needs for specific applications. The definition and some of the most basic properties of f-divergences are given and five classes of f-divergences are presented. Ostrowski’s inequality and a trapezoid inequality are utilised in order to prove bounds for an extension of the set of f-divergences. All five classes of f-divergences are used in order to investigate limitations and strengths of the inequalities derived.