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I read in several places that SVM is a discriminative model, but SVM has no statistical aspects per se, by that I mean that is does not estimate any probablity, specifically the postirior distribution as a discriminative model should do.

Shouldn't SVM be considered as nirther disciminative nor genreative, rather it finds a disciminative hyperplane in the feature space.

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  • $\begingroup$ Not all discriminative models estimate the posterior distribution, some just estimate decision boundaries between classes, like SVM and decision trees. Discriminative models just enable "discriminating" between classes. $\endgroup$ Commented Dec 30, 2021 at 15:46

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Support Vector Machines are discriminative because they fit a hyperplane which separates two classes. So it learns a decision boundary which is the definition of discriminative methods.

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  • $\begingroup$ Well, according to Bishop's PRML (p 43 microsoft.com/en-us/research/uploads/prod/2006/01/… ) "Approaches that model the posterior probabilities directly are called discriminative models.", this is why I am confused $\endgroup$ Commented Jan 8, 2022 at 22:26
  • $\begingroup$ According to Jebara, Tony (2004). Machine Learning: Discriminative and Generative: Even if a classification does not use any probability it is still discriminative. But still: Franc et al. (icml.cc/Conferences/2011/papers/386_icmlpaper.pdf) can show that SVM are a Probabilistic Model with conditional probabilities which meets your definition of Bishop and the general one as well. $\endgroup$ Commented Jan 9, 2022 at 8:08

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