Convergence of Smoothed Empirical Measures, with ML Applications by Dr. Kristjan Greenewald

Abstract: Statistical distances, such as the KL divergence and Wasserstein distances, are powerful tools for measuring differences between probability distributions. Unfortunately, the sample complexity of estimating these distances often scales prohibitively poorly with increasing dimension. In this work, we study the convergence of the empirical measure smoothed by a Gaussian kernel to the true measure convolved with a Gaussian, as measured by various statistical distances.

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