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Divergences are quantities that measure discrepancy between two probability distributions and play an important role in various fields such as statistics and machine learning. Divergences are non-negative and are equal to zero if and only if two distributions are the same. In addition, some important divergences such as the f-divergence have convexity, which we call convex divergence. In this paper, we show new properties of the convex divergences by using integral and differential operators that we introduce. For the convex divergence, the result applied the integral or differential operator is also a divergence. In particular, the integral operator preserves convexity. Furthermore, the results applied the integral operator multiple times constitute a monotonically decreasing sequence of the convex divergences. We derive new sequences of the convex divergences that include the Kullback-Leibler divergence or the reverse Kullback-Leibler divergence from these properties.
We present a unified technique for sequential estimation of convex divergences between distributions, including integral probability metrics like the kernel maximum mean discrepancy, $varphi$-divergences like the Kullback-Leibler divergence, and opti
In this paper, we introduce a sophisticated path loss model into the stochastic geometry analysis incorporating both line-of-sight (LoS) and non-line-of-sight (NLoS) transmissions to study their performance impact in small cell networks (SCNs). Analy
Quantum f-divergences are a quantum generalization of the classical notion of f-divergences, and are a special case of Petz quasi-entropies. Many well known distinguishability measures of quantum states are given by, or derived from, f-divergences; s
Variational representations of divergences and distances between high-dimensional probability distributions offer significant theoretical insights and practical advantages in numerous research areas. Recently, they have gained popularity in machine l
The Bregman divergence (Bregman distance, Bregman measure of distance) is a certain useful substitute for a distance, obtained from a well-chosen function (the Bregman function). Bregman functions and divergences have been extensively investigated du