Kernel Density Estimation for Multiclass Quantification

TL;DR

This paper introduces KDEy, a kernel density estimation-based method for multiclass quantification that outperforms existing distribution-matching approaches and EM-based methods in estimating class prevalences under label shift.

Contribution

The paper proposes a novel multivariate density representation using KDE for multiclass quantification, improving upon histogram-based methods and integrating with maximum likelihood frameworks.

Findings

KDEy outperforms previous distribution-matching methods in quantification accuracy.

KDEy shows superior performance compared to EM-based methods in experiments.

The KDE-based approach effectively models inter-class information in multiclass data.

Abstract

Several disciplines, like the social sciences, epidemiology, sentiment analysis, or market research, are interested in knowing the distribution of the classes in a population rather than the individual labels of the members thereof. Quantification is the supervised machine learning task concerned with obtaining accurate predictors of class prevalence, and to do so particularly in the presence of label shift. The distribution-matching (DM) approaches represent one of the most important families among the quantification methods that have been proposed in the literature so far. Current DM approaches model the involved populations by means of histograms of posterior probabilities. In this paper, we argue that their application to the multiclass setting is suboptimal since the histograms become class-specific, thus missing the opportunity to model inter-class information that may exist in the data. We propose a new representation mechanism based on multivariate densities that we model via kernel density estimation (KDE). The experiments we have carried out show our method, dubbed KDEy, yields superior quantification performance with respect to previous DM approaches. We also investigate the KDE-based representation within the maximum likelihood framework and show KDEy often shows superior performance with respect to the expectation-maximization method for quantification, arguably the strongest contender in the quantification arena to date.