2021/09/18 by Alankrita Bhatt, Bhatt, Alankrita, Ankit Pensia +1
Mathematics · #FOS: Computer and information sciences #FOS: Mathematics #Information Theory (cs.IT) #Markov Chains and Monte Carlo Methods #Mathematical Approximation and Integration #Statistical Methods and Inference #Statistics Theory (math.ST)
paper · pdf · doi:10.48550/arxiv.2109.09028
openalex publication_date 2021/09/18 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We study the relative entropy between the empirical estimate of a discrete distribution and the true underlying distribution. If the minimum value of the probability mass function exceeds an α> 0 (i.e. when the true underlying distribution is bounded sufficiently away from the boundary of the simplex), we prove an upper bound on the moment generating function of the centered relative entropy that matches (up to logarithmic factors in the alphabet size and α) the optimal asymptotic rates, subsequently leading to a sharp concentration inequality for the centered relative entropy. As a corollary of this result we also obtain confidence intervals and moment bounds for the centered relative entropy that are sharp up to logarithmic factors in the alphabet size and α.