Custom Orthogonal Weight functions (COWs) for Event Classification

TL;DR

This paper introduces Custom Orthogonal Weight functions (COWs), a generalization of the sWeights method, enabling better separation of signal and background in data analysis even when variables are dependent.

Contribution

It extends the sWeights method to a broader class of problems using COWs, allowing for effective signal-background separation with dependent variables.

Findings

COWs generalize sWeights for dependent variables.

Closed-form formulas for parameter covariance matrices.

Practical applications demonstrate improved performance.

Abstract

A common problem in data analysis is the separation of signal and background. We revisit and generalise the so-called $sWeights$ method, which allows one to calculate an empirical estimate of the signal density of a control variable using a fit of a mixed signal and background model to a discriminating variable. We show that $sWeights$ are a special case of a larger class of Custom Orthogonal Weight functions (COWs), which can be applied to a more general class of problems in which the discriminating and control variables are not necessarily independent and still achieve close to optimal performance. We also investigate the properties of parameters estimated from fits of statistical models to $sWeights$ and provide closed formulas for the asymptotic covariance matrix of the fitted parameters. To illustrate our findings, we discuss several practical applications of these techniques.