Continuous Sweep for Binary Quantification Learning

Journal of Classification, vol. 43, pp. 554–584

Abstract

Abstract A quantifier is a supervised machine learning algorithm that focuses on estimating the class prevalence in a data set rather than labeling its individual observations. We introduce continuous sweep, a new parametric binary quantifier inspired by the well-performing median sweep, which is an ensemble method based on adjusted count estimators. We modified two aspects of median sweep: (1) using parametric class distributions instead of empirical distributions for the true and false positive rates; (2) using the mean instead of the median of a set of adjusted count estimates. These two modifications allow for a theoretical analysis of the bias and variance of the continuous sweep. Furthermore, the expressions of bias and variance can be used to define optimal decision boundaries of the set of adjusted count estimates to be used in the ensemble. In three simulation studies, we show that continuous sweep outperforms the quantifiers in the group classify, count, and correct, including median sweep, and is competitive with the two best quantifiers in the group distribution matchers. Also, an empirical data set is analyzed with these quantifiers, showing similar performances.

Authors 5

1. Kevin Kloos corresponding Aachen Faculty of Social and Behavioural Sciences Institute of Psychology, Methodology and Statistics Unit

   Leiden University

   Affiliation as printed

   Faculty of Social and Behavioural Sciences, Institute of Psychology, Methodology and Statistics Unit, Leiden University, Wassenaarseweg 52, Leiden, 2233 AK, The Netherlands

2. Julian David Karch Aachen Faculty of Social and Behavioural Sciences Institute of Psychology, Methodology and Statistics Unit

   Leiden University

   Affiliation as printed

   Faculty of Social and Behavioural Sciences, Institute of Psychology, Methodology and Statistics Unit, Leiden University, Wassenaarseweg 52, Leiden, 2233 AK, The Netherlands

3. Quinten Meertens

   University of Amsterdam

   Affiliation as printed

   Amsterdam School of Economics, Center for Nonlinear Dynamics in Economics and Finance, University of Amsterdam, Roetersstraat 11, Amsterdam, 1018 WB, The Netherlands

4. Sander Scholtus

   Centraal Bureau voor de Statistiek

   Affiliation as printed

   Department of Methodology, Statistics Netherlands, Henri Faasdreef 312, Den Haag, 2492 JP, The Netherlands

5. Mark de Rooij Aachen Faculty of Social and Behavioural Sciences Institute of Psychology, Methodology and Statistics Unit

   Leiden University

   Affiliation as printed

   Faculty of Social and Behavioural Sciences, Institute of Psychology, Methodology and Statistics Unit, Leiden University, Wassenaarseweg 52, Leiden, 2233 AK, The Netherlands