|On Learning Parametric Non-Smooth Continuous Distributions
|Sudeep Kamath, PDT Partners, United States; Alon Orlitsky, University of California San Diego, United States; Venkatadheeraj Pichapati, Apple Inc., United States; Ehsan Zobeidi, University of California San Diego, United States
|L.4: Distribution Learning
|Statistics and Learning Theory
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|With the eventual goal of better understanding learning rates of general continuous distributions, we derive the first essentially min-max optimal estimators and learning rates for several natural classes of parametric non-smooth continuous distributions under KL divergence. In particular, we show that unlike the folk theorem of 1/2n learning-rate increase per distribution parameter, non-smooth distribution exhibit a wide range of learning rates.