Platt scaling
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In machine learning, Platt scaling or Platt calibration is a method of transforming the outputs of a classification model into a probability distribution over classes. The method was invented by John Platt in the context of support vector machines,[1] replacing an earlier method by Vapnik, but can be applied to other classification models.[2] Platt scaling works by fitting a logistic regression model to a classifier's scores.
Description
Let f be a real-valued function that is used as a binary classifier to predict, for examples x, a label y from the set {+1, -1}, as y = sign(f(x)) (disregarding the possibility of a zero output for now). When what is required is instead a probability P(y=1|x), but the model does not provide this (or gives bad probability estimates), Platt scaling can be used. This method produces probabilities
- ,
i.e., a logistic transformation of the classifier scores f(x).
The (scalar) parameters A and B are estimated using a maximum likelihood method. Platt himself suggested using the Levenberg–Marquardt algorithm to optimize the parameters, but a Newton algorithm was later proposed that should be more numerically stable.[3]
See also
- Relevance vector machine: probabilistic alternative to the support vector machine
References
- ^ Platt, John (1999). "Probabilistic outputs for support vector machines and comparisons to regularized likelihood methods" (PDF). Advances in large margin classifiers. 10 (3): 61–74.
- ^ Niculescu-Mizil, Alexandru; Caruana, Rich (2005). Predicting good probabilities with supervised learning (PDF). ICML.
- ^ Lin, Hsuan-Tien; Lin, Chih-Jen; Weng, Ruby C. (2007). "A note on Platt's probabilistic outputs for support vector machines" (PDF). Machine Learning. 68 (3): 267–276.