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  • 1.
    Gammerman, Alexander
    et al.
    Royal Holloway Univ London, Egham, Surrey, England..
    Vovk, Vladimir
    Royal Holloway Univ London, Egham, Surrey, England..
    Boström, Henrik
    KTH, School of Electrical Engineering and Computer Science (EECS), Software and Computer systems, SCS.
    Carlsson, Lars
    Stena Line AB, Gothenburg, Sweden..
    Conformal and probabilistic prediction with applications: editorial2019In: Machine Learning, ISSN 0885-6125, E-ISSN 1573-0565, Vol. 108, no 3, p. 379-380Article in journal (Other academic)
  • 2.
    Johansson, Ulf
    et al.
    Högskolan i Borås, Institutionen Handels- och IT-högskolan.
    Boström, Henrik
    Högskolan i Borås, Institutionen Handels- och IT-högskolan, Sweden.
    Löfström, Tuve
    Högskolan i Borås, Institutionen Handels- och IT-högskolan.
    Linusson, Henrik
    Högskolan i Borås, Institutionen Handels- och IT-högskolan.
    Regression conformal prediction with random forests2014In: Machine Learning, ISSN 0885-6125, E-ISSN 1573-0565, Vol. 97, no 1-2, p. 155-176Article in journal (Refereed)
    Abstract [en]

    Regression conformal prediction produces prediction intervals that are valid, i.e., the probability of excluding the correct target value is bounded by a predefined confidence level. The most important criterion when comparing conformal regressors is efficiency; the prediction intervals should be as tight (informative) as possible. In this study, the use of random forests as the underlying model for regression conformal prediction is investigated and compared to existing state-of-the-art techniques, which are based on neural networks and k-nearest neighbors. In addition to their robust predictive performance, random forests allow for determining the size of the prediction intervals by using out-of-bag estimates instead of requiring a separate calibration set. An extensive empirical investigation, using 33 publicly available data sets, was undertaken to compare the use of random forests to existing stateof- the-art conformal predictors. The results show that the suggested approach, on almost all confidence levels and using both standard and normalized nonconformity functions, produced significantly more efficient conformal predictors than the existing alternatives.

  • 3.
    Johansson, Ulf
    et al.
    Jonkoping Univ, Dept Comp Sci & Informat, Jonkoping, Sweden..
    Lofstrom, Tuve
    Jonkoping Univ, Dept Comp Sci & Informat, Jonkoping, Sweden..
    Linusson, Henrik
    Univ Boras, Dept Informat Technol, Boras, Sweden..
    Boström, Henrik
    KTH, School of Electrical Engineering and Computer Science (EECS), Software and Computer systems, SCS.
    Efficient Venn predictors using random forests2019In: Machine Learning, ISSN 0885-6125, E-ISSN 1573-0565, Vol. 108, no 3, p. 535-550Article in journal (Refereed)
    Abstract [en]

    Successful use of probabilistic classification requires well-calibrated probability estimates, i.e., the predicted class probabilities must correspond to the true probabilities. In addition, a probabilistic classifier must, of course, also be as accurate as possible. In this paper, Venn predictors, and its special case Venn-Abers predictors, are evaluated for probabilistic classification, using random forests as the underlying models. Venn predictors output multiple probabilities for each label, i.e., the predicted label is associated with a probability interval. Since all Venn predictors are valid in the long run, the size of the probability intervals is very important, with tighter intervals being more informative. The standard solution when calibrating a classifier is to employ an additional step, transforming the outputs from a classifier into probability estimates, using a labeled data set not employed for training of the models. For random forests, and other bagged ensembles, it is, however, possible to use the out-of-bag instances for calibration, making all training data available for both model learning and calibration. This procedure has previously been successfully applied to conformal prediction, but was here evaluated for the first time for Venn predictors. The empirical investigation, using 22 publicly available data sets, showed that all four versions of the Venn predictors were better calibrated than both the raw estimates from the random forest, and the standard techniques Platt scaling and isotonic regression. Regarding both informativeness and accuracy, the standard Venn predictor calibrated on out-of-bag instances was the best setup evaluated. Most importantly, calibrating on out-of-bag instances, instead of using a separate calibration set, resulted in tighter intervals and more accurate models on every data set, for both the Venn predictors and the Venn-Abers predictors.

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