Mastodawn

At my work we use kernel density estimation to estimate a density distribution from a set of measured points (we measure the size and refractive index of microparticles in liquid samples). I found a paper that relates kernel density estimation to Gaussian process based approaches. I haven't finished reading the paper yet, but it seems that kernel density estimation is a frequentist approach while Gaussian process techniques take a Bayesian perspective. https://arxiv.org/abs/2506.17366

#frequentist
#bayesian
#kernelDensityEstimation

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Gaussian Processes and Reproducing Kernels: Connections and Equivalences

This monograph studies the relations between two approaches using positive definite kernels: probabilistic methods using Gaussian processes, and non-probabilistic methods using reproducing kernel Hilbert spaces (RKHS). They are widely studied and used in machine learning, statistics, and numerical analysis. Connections and equivalences between them are reviewed for fundamental topics such as regression, interpolation, numerical integration, distributional discrepancies, and statistical dependence, as well as for sample path properties of Gaussian processes. A unifying perspective for these equivalences is established, based on the equivalence between the Gaussian Hilbert space and the RKHS. The monograph serves as a basis to bridge many other methods based on Gaussian processes and reproducing kernels, which are developed in parallel by the two research communities.

arXiv.org