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Concept
Platt scaling
Summary
In machine learning, Platt scaling or Platt calibration is a way 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,
replacing an earlier method by Vapnik,
but can be applied to other classification models.
Platt scaling works by fitting a logistic regression model to a classifier's scores.
Consider the problem of binary classification: for inputs x, we want to determine whether they belong to one of two classes, arbitrarily labeled +1 and −1. We assume that the classification problem will be solved by a real-valued function f, by predicting a class label y = sign(f(x)). For many problems, it is convenient to get a probability , i.e. a classification that not only gives an answer, but also a degree of certainty about the answer. Some classification models do not provide such a probability, or give poor probability estimates.
Platt scaling is an algorithm to solve the aforementioned problem. It produces probability estimates
i.e., a logistic transformation of the classifier scores f(x), where A and B are two scalar parameters that are learned by the algorithm. Note that predictions can now be made according to if the probability estimates contain a correction compared to the old decision function y = sign(f(x)).
The parameters A and B are estimated using a maximum likelihood method that optimizes on the same training set as that for the original classifier f. To avoid overfitting to this set, a held-out calibration set or cross-validation can be used, but Platt additionally suggests transforming the labels y to target probabilities
for positive samples (y = 1), and
for negative samples, y = -1.
Here, N+ and N− are the number of positive and negative samples, respectively. This transformation follows by applying Bayes' rule to a model of out-of-sample data that has a uniform prior over the labels. The constants 1 and 2, on the numerator and denominator respectively, are derived from the application of Laplace smoothing.
Official source
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