Estimate Conditional Probabilies for SVM

Promising Approaches from Paper
Stefan Rüping, A Simple Method For Estimating Conditional Probabilities For SVMs.
Milgram, J., Mohamed Cheriet, Sabourin, R.,  Estimating accurate multi-class probabilities with support vector machines
Ben Van Calster1, Jan Luts1, Johan A. K. Suykens1, George Condous2, Tom Bourne3, Dirk Timmerman4 and Sabine Van Huffel1 , Comparing Methods for Multi-class Probabilities in Medical Decision Making Using LS-SVMs and Kernel Logistic Regression

Some of them ordering by its effective

KLR (Kernel Logistic Regression): optimization problem is similar to SVM except exponential loss function is used instead of L1 loss
     P(y|x) = \frac{1}{1 + e^{-y(w*x-b}}
drawback typically all \alpha_i are non zero, all examples play a role in estimating, whereas only support vectors are needed in SVM. Hence, computational cost.
SVM-Platt:    \sigma_{a,b}(z) = \frac{1}{1+e^{-az+b}}
     with a>0 to obtain monotonically increasing function
     a,b are found by minimization of the cross-entropy (CRE) error over a subset of the data which has not been used for training
     CRE = \sum_i y_ilog(z_i) + (1-y_i)log(1-z_i)
SVM-Beta: \sigma(z) = \beta^{-1}_{\alpha1,\beta1} \beta_{\alpha1,\beta1}(z)
     \beta_{\alpha,\beta} is a beta distribution [garczarek02classification]
SVM-Softmax:   \sigma_{softmax}(z) = \frac{e^{\gamma z}}{\sum_{j=1}^k exp^{\gamma z}}
  \gamma is derived by minimizing the negative log-likelihood of training data which takes form:
  -\sum_{i=1}^{n}\sum_{j=1}{c}(t_i^j log(z_i))
     monotonously map decision function value to interval [0,1]
     with the objective  to exploit the outputs of all SVMs to estimate overall probabilities, the softmax function is presented.
     it can be regarded as a generalization of the sigmoid for multi-class case
                    

Bibtex:
@inproceedings{ruping04simple,
author    = {Stefan R{\"u}ping},
title     = {A Simple Method For Estimating Conditional Probabilities
          For SVMs},
booktitle = {LWA 2004: Lernen - Wissensentdeckung - Adaptivit{\"a}t},
year      = {2004},
pages     = {206-210},
crossref  = {DBLP:conf/lwa/2004},
bibsource = {DBLP, http://dblp.uni-trier.de}
}