Mathematical Aspects of Divergence Based Vector Quantization Using Fr´ echet-Derivatives

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Nonparametric Divergence Estimation with Applications to Machine Learning on Distributions (2011, background): “In the Supplementary material (Póczos et al., 2011), we demonstrate the consistency of the estimators by some numerical experiments as well.”
On the Estimation of α-Divergences (2011, background): “One can see that this is a special case of Csiszár’s f -divergence (Csiszár, 1967) and hence it is always nonnegative.2 Closely related divergences (but not special cases) to (1) are the Rényiα (Rényi, 1961) and the Tsallis-α (Villmann and Haase, 2010) divergences.”
On the Estimation of alpha-Divergences (2011, background): “Further information and useful reviews of several different divergences can be found, e.g., in Villmann and Haase (2010), Cichocki et al. (2009), and Wang et al. (2009b).”
Information theoretical estimators toolbox (2014, background): “…mutual information,1 association, divergence measures and kernels on distributions have found a broad range of applications in many areas of machine learning (Beirlant et al., 1997; Wang et al., 2009; Villmann and Haase, 2010; Basseville, 2013; Póczos et al., 2012; Sriperumbudur et al., 2012).”