Both discriminative and generative models have the ability to learn model parameters in a classification setting, but they are based on entirely different mechanisms and serve different purposes.
Pros: Well-designed for multiclass problems
Cons: Assumes multivariate normality among features, though it is relatively robust to this assumption
Both QDA and GMM are based on the premise that the underlying data is generated from two or more Gaussian distributions, but QDA is usually used in the supervised learning context, while GMM is used in the unsupervised context.
LDA assumes heterogeneity among class variances, while QDA allows for each class to have its own variance.
Discriminant analysis is a dimension reduction approach similar to principal components analysis but applied in a classification context.
Pros: Relatively fast computational time due to kernel trick
Cons:Performance of algorithm is sensitive to the choice of kernel
While SVM is used most often in classification scenarios, it can be extended to regression cases by allowing the user to provide a maximum margin of error allowed for any observation.
Hinge loss adds an increased penalty to misclassifications that are off by a large amount, since the cost function increases linearly as the decision function output moves further away from the actual label.
The hinge loss function uses the distance between observations and the hyperplane that separates classes in the SVM algorithm in order to quantify the magnitude of error.
C (regularization parameter), Kernel Function, Gamma (RBF kernel)