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Efficient two-sample functional estimation and the super-oracle phenomenon
TL;DR: In this paper, the estimation of two-sample integral functionals with unknown probability densities is studied, and a weighted nearest neighbor estimator is proposed to achieve the local asymptotic minimax lower bound.
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Abstract: We consider the estimation of two-sample integral functionals, of the type that occur naturally, for example, when the object of interest is a divergence between unknown probability densities. Our first main result is that, in wide generality, a weighted nearest neighbour estimator is efficient, in the sense of achieving the local asymptotic minimax lower bound. Moreover, we also prove a corresponding central limit theorem, which facilitates the construction of asymptotically valid confidence intervals for the functional, having asymptotically minimal width. One interesting consequence of our results is the discovery that, for certain functionals, the worst-case performance of our estimator may improve on that of the natural `oracle' estimator, which is given access to the values of the unknown densities at the observations.
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Variance Reduction for Estimation of Shapley Effects and Adaptation to Unknown Input Distribution
TL;DR: The Shapley effects are global sensitivity indices: they quantify the impact of each input variable on the output variable in a model as discussed by the authors, and the Shapley effect is defined as a global sensitivity index.
58
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Local nearest neighbour classification with applications to semi-supervised learning
TL;DR: A new asymptotic expansion for the global excess risk of a local-$k$-nearest neighbour classifier is derived, where the choice of $k$ may depend upon the test point, and it is proved that, provided the $d$-dimensional marginal distribution of the features has a finite $\rho$th moment, a local choice of k can yield a rate of convergence of the excessrisk of $O(n^{-4/(d+4)})$.
38
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Variance reduction for estimation of Shapley effects and adaptation to unknown input distribution
TL;DR: This work investigates the already existing estimator of Shapley effects and suggests a new one with a lower variance, and extends these estimators when the distribution of the inputs is unknown.
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Minimax Optimal Estimation of KL Divergence for Continuous Distributions
Puning Zhao,Lifeng Lai +1 more
TL;DR: In this article, the convergence rates of the bias and variance of the kNN estimator were analyzed and a lower bound of the minimax mean square error was derived, and it was shown that kNN method is asymptotically rate optimal.
Ensemble Estimation of Generalized Mutual Information with Applications to Genomics
TL;DR: This work derives the mean squared error convergence rates of kernel density-based plug-in estimators of general mutual information measures between two multidimensional random variables and proposes an ensemble estimator called GENIE, the first nonparametric mutual information estimator known to achieve the parametric convergence rate for the mixture case.
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