title: Probability machines: consistent probability estimation using nonparametric learning machines.
abstract: 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.
  
  
  OBJECTIVE
  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.
authors.affiliation: Center for Computational Bioscience, Center for Information Technology, National Institutes of Health, Bethesda, USA.
authors.forename: J D
authors.initials: JD
authors.lastname: Malley
authors.forename: J
authors.initials: J
authors.lastname: Kruppa
authors.forename: A
authors.initials: A
authors.lastname: Dasgupta
authors.forename: K G
authors.initials: KG
authors.lastname: Malley
authors.forename: A
authors.initials: A
authors.lastname: Ziegler
mesh_terms: D001185:Artificial Intelligence; D003198:Computer Simulation; D006801:Humans; D007858:Learning; D016015:Logistic Models; D015233:Models, Statistical; D011336:Probability; D013223:Statistics as Topic / Q000379:methods; D018709:Statistics, Nonparametric