List of likelihood-based classification techniques This is a basic statistical pattern recognition question.
I'm aware of LDA classification, Naive Bayes Classification techniques which give output as a likelihood (of data belonging to a certain class).
What are other likelihood-based supervised classification techniques?
Can all of the supervised classification techniques be expressed as likelihood or likelihood ratio in order to classify given data?
Can anyone point me to articles of notes which can help me out?
 A: It think this has potential to become an interesting list. Maybe we should all either explain or reference how the methods use a likelihood approach.   
A list of additional likelihood classification procedures: 


*

*GLMs for binomial or multinomial data (Logistic Regression, Probit Regression, other Link Functions) McCullagh & Nelder and their regularized extensions Hastie et al.

*The equivalent GAMs Hastie & Tibshirani

*Certain classification and model trees can also be seen as likelihood-based models (Su et al, Loh et al's work , Zeileis et al , Rusch & Zeileis, etc.) 

*Certain types of Boosting may also be seen as likelihood-based Lebanon & Lafferty, Friedman et al. 

*From what I know, Bayesian approaches nearly always use the likelihood as part of the model, hence they are always likelihood based.


If a negative (log)-likelihood for a classification problem is used as the loss function that is minimized to train the model and then predictions from this model are made, I suppose any classification approach following this counts as likelihood-based.   
A: LDA and QDA are likelihood based approaches based on respectively both class-conditional densities are multivariate normal with the same covariance matrix and both class-conditional densities are multivariate normal with different covariance matrices.  In a broad sense kernel discrimination can be considered likelihood based. because if you assumed that the estimated densities were the actual class conditional densities the decision boundary could be considered based on likelihood ratios.  If you put a prior distribution on the class associated with a given feature vector you can get a Bayes rule by any of these approaches under the respective model assumptions.  I like the 1972 book "Pattern Classification and Scene Analysis" by Duda and Hart for a clear description of this.  There is a new addition of this book that came out a few years ago with a third author (Stork, I think).
