PDE-Foam - a probability-density estimation method using self-adapting phase-space binning

TL;DR

PDE-Foam introduces a self-adapting binning approach for multivariate probability density estimation, enhancing classification performance and efficiency, especially with small training samples, by dynamically adjusting phase-space partitions.

Contribution

It presents PDE-Foam, a novel PDE method utilizing adaptive binning with Foam, improving density estimation and classification in high-dimensional spaces.

Findings

Enhanced classification with small samples

Reduced computation time

Improved density estimation accuracy

Abstract

Probability Density Estimation (PDE) is a multivariate discrimination technique based on sampling signal and background densities defined by event samples from data or Monte-Carlo (MC) simulations in a multi-dimensional phase space. In this paper, we present a modification of the PDE method that uses a self-adapting binning method to divide the multi-dimensional phase space in a finite number of hyper-rectangles (cells). The binning algorithm adjusts the size and position of a predefined number of cells inside the multi-dimensional phase space, minimising the variance of the signal and background densities inside the cells. The implementation of the binning algorithm PDE-Foam is based on the MC event-generation package Foam. We present performance results for representative examples (toy models) and discuss the dependence of the obtained results on the choice of parameters. The new PDE-Foam shows improved classification capability for small training samples and reduced classification time compared to the original PDE method based on range searching.