Publication

MATHICSE Technical Report : Density estimation in RKHS with application to Korobov spaces in high dimensions

Fabio Nobile
2021
Working Papers

Abstract

A kernel method for estimating a probability density function (pdf) from an i.i.d. sample drawn from such density is presented. Our estimator is a linear combination of kernel functions, the coefficients of which are determined by a linear equation. An error analysis for the mean integrated squared error is established in a general reproducing kernel Hilbert space setting. The theory developed is then applied to estimate pdfs belonging to weighted Korobov spaces, for which a dimension independent convergence rate is established. Under a suitable smoothness assumption, our method attains a rate arbitrarily close to the optimal rate. Numerical results support our theory.

Official source

https://infoscience.epfl.ch/entities/publication/49a7adae-a8ac-4ca6-9f37-399b1e4dc720

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Fabio Nobile
2021
Working Papers

Abstract

Official source

https://infoscience.epfl.ch/entities/publication/49a7adae-a8ac-4ca6-9f37-399b1e4dc720

About this result

Related concepts (32)

Kernel (statistics)

The term kernel is used in statistical analysis to refer to a window function. The term "kernel" has several distinct meanings in different branches of statistics. In statistics, especially in Bayesian statistics, the kernel of a probability density function (pdf) or probability mass function (pmf) is the form of the pdf or pmf in which any factors that are not functions of any of the variables in the domain are omitted. Note that such factors may well be functions of the parameters of the pdf or pmf.

Kernel method

In machine learning, kernel machines are a class of algorithms for pattern analysis, whose best known member is the support-vector machine (SVM). These methods involve using linear classifiers to solve nonlinear problems. The general task of pattern analysis is to find and study general types of relations (for example clusters, rankings, principal components, correlations, classifications) in datasets.

Probability density function

In probability theory, a probability density function (PDF), density function, or density of an absolutely continuous random variable, is a function whose value at any given sample (or point) in the sample space (the set of possible values taken by the random variable) can be interpreted as providing a relative likelihood that the value of the random variable would be equal to that sample.

Related publications (32)

MATHICSE Technical Report : Density estimation in RKHS with application to Korobov spaces in high dimensions

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