Methods Inf Med 2012; 51(01): 74-81
DOI: 10.3414/ME00-01-0052
Original Articles
Schattauer GmbH

Probability Machines[*]

Consistent Probability Estimation Using Nonparametric Learning Machines
J. D. Malley
1   Center for Computational Bioscience, Center for Information Technology, National Institutes of Health, Bethesda, USA
,
J. Kruppa
2   Institut für Medizinische Biometrie und Statistik, Universität zu Lübeck, Universitätsklinikum Schleswig-Holstein, Campus Lübeck, Germany
,
A. Dasgupta
3   Clinical Sciences Section, National Institute of Arthritis and Musculoskeletal and Skin Diseases, National Institutes of Health, Bethesda, USA
,
K. G. Malley
4   Malley Research Programming, Rockville, USA
,
A. Ziegler
2   Institut für Medizinische Biometrie und Statistik, Universität zu Lübeck, Universitätsklinikum Schleswig-Holstein, Campus Lübeck, Germany
› Author Affiliations
Further Information

Publication History

received:15 June 2011

accepted:05 July 2011

Publication Date:
20 January 2018 (online)

Summary

Background: Most machine learning approaches only provide a classification for binary responses. However, probabilities are required for risk estimation using individual patient characteristics. It has been shown recently that every statistical learning machine known to be consistent for a nonparametric regression problem is a probability machine that is provably consistent for this estimation problem.

Objectives: The aim of this paper is to show how random forests and nearest neighbors can be used for consistent estimation of individual probabilities.

Methods: Two random forest algorithms and two nearest neighbor algorithms are described in detail for estimation of individual probabilities. We discuss the consistency of random forests, nearest neighbors and other learning machines in detail. We conduct a simulation study to illustrate the validity of the methods. We exemplify the algorithms by analyzing two well-known data sets on the diagnosis of appendicitis and the diagnosis of diabetes in Pima Indians.

Results: Simulations demonstrate the validity of the method. With the real data application, we show the accuracy and practicality of this approach. We provide sample code from R packages in which the probability estimation is already available. This means that all calculations can be performed using existing software.

Conclusions: Random forest algorithms as well as nearest neighbor approaches are valid machine learning methods for estimating individual probabilities for binary responses. Freely available implementations are available in R and may be used for applications.

* Supplementary material published on our website www.methods-online.com