Green's function based unparameterised multi-dimensional kernel density and likelihood ratio estimator

TL;DR

This paper presents a novel Green's function-based density estimator that reconstructs differentiable probability densities and is applicable to classification tasks, addressing issues like mis-modeling and overtraining.

Contribution

It introduces a new kernel density estimation method based on Green's functions, requiring only differentiability of the density, and applies it to likelihood ratio estimation for classification.

Findings

Effective reconstruction of differentiable densities

Addresses mis-modeling and overtraining issues

Applicable to binary classification tasks

Abstract

This paper introduces a probability density estimator based on Green's function identities. A density model is constructed under the sole assumption that the probability density is differentiable. The method is implemented as a binary likelihood estimator for classification purposes, so issues such as mis-modeling and overtraining are also discussed. The identity behind the density estimator can be interpreted as a real-valued, non-scalar kernel method which is able to reconstruct differentiable density functions.