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Relative Entropy Derivative Bounds
Universidad de los Andes, Facultad de Ingeniería y Ciencias Aplicadas, Monseñor Álvaro del Portillo 12455, Las Condes, Santiago, Chile
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Received: 24 May 2013; in revised form: 12 July 2013 / Accepted: 16 July 2013 / Published: 23 July 2013
Abstract: We show that the derivative of the relative entropy with respect to its parameters is lower and upper bounded. We characterize the conditions under which this derivative can reach zero. We use these results to explain when the minimum relative entropy and the maximum log likelihood approaches can be valid. We show that these approaches naturally activate in the presence of large data sets and that they are inherent properties of any density estimation process involving large numbers of random variables.
Keywords: relative entropy; Kullback-Leibler divergence; Shannon differential entropy; asymptotic equipartition principle; typical set; Fisher information; maximum log likelihood
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MDPI and ACS Style
Zegers, P.; Fuentes, A.; Alarcón, C. Relative Entropy Derivative Bounds. Entropy 2013, 15, 2861-2873.
Zegers P, Fuentes A, Alarcón C. Relative Entropy Derivative Bounds. Entropy. 2013; 15(7):2861-2873.
Zegers, Pablo; Fuentes, Alexis; Alarcón, Carlos. 2013. "Relative Entropy Derivative Bounds." Entropy 15, no. 7: 2861-2873.