Tutorial on Implied Posterior Probability for SVMs
This is an incremental tutorial for researchers and practitioners using SVMs who need calibrated probability estimates.
This tutorial addresses the problem of estimating and calibrating implied posterior probabilities for Support Vector Machines (SVMs) in binary classification, providing methods to compute these probabilities and map them to expected posterior probabilities using isotonic regression.
Implied posterior probability of a given model (say, Support Vector Machines (SVM)) at a point $\bf{x}$ is an estimate of the class posterior probability pertaining to the class of functions of the model applied to a given dataset. It can be regarded as a score (or estimate) for the true posterior probability, which can then be calibrated/mapped onto expected (non-implied by the model) posterior probability implied by the underlying functions, which have generated the data. In this tutorial we discuss how to compute implied posterior probabilities of SVMs for the binary classification case as well as how to calibrate them via a standard method of isotonic regression.