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Seminar
FIELD AI and Natural Sciences: Principle of AI
DATE August 10 (Wed), 2022
TIME 14:00-16:00
PLACE Online
SPEAKER Ryu, Jongha
HOST Lee, Sungyoon
INSTITUTE UCSD
TITLE [AI 그룹 세미나] Nearest neighbor density functional estimation from inverse Laplace transform (2)
ABSTRACT

https://arxiv.org/abs/1805.08342

A new approach to L2-consistent estimation of a general density functional using k-nearest neighbor distances is proposed, where the functional under consideration is in the form of the expectation of some function f of the densities at each point. The estimator is designed to be asymptotically unbiased, using the convergence of the normalized volume of a k-nearest neighbor ball to a Gamma distribution in the large-sample limit, and naturally involves the inverse Laplace transform of a scaled version of the function f. Some instantiations of the proposed estimator recover existing k-nearest neighbor based estimators of Shannon and Rényi entropies and Kullback--Leibler and Rényi divergences, and discover new consistent estimators for many other functionals such as logarithmic entropies and divergences. The L2-consistency of the proposed estimator is established for a broad class of densities for general functionals, and the convergence rate in mean squared error is established as a function of the sample size for smooth, bounded densities.

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