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Generative vs discriminative model

  1. May 8, 2013 #1
    Hello everyone,

    I have a question about generative and discriminative models. As I understand it generative models aim to model the joint distribution p(x,y) of the input x and output y and the discriminative approach estimates the conditional distribution p(y|x). I understand that the generative approach is more complex but I have a small niggle...

    Applying Bayes rule, we have the conditional distribution

    p(y|x) = p(x|y) p(y)/p(x)

    which is equal to:

    P(y|x) = p(x, y)/p(x)

    So it seems when we want to model discriminative modelling, we have to estimate this joint distribution (in he numerator) as well. I am sure this is wrong and I have a flaw in my understanding but I cannot seem to figure it out. Is there something about this modelling process that I am not understanding. Perhaps we do not estimate it in this way?

    Also, a markov random field defined over an undirected graph, is it a joint distribution?

    I would really appreciate any help anyone can give me on this.

    Thanks,
    Luc
     
  2. jcsd
  3. May 9, 2013 #2

    atyy

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    Science Advisor

    P(x|y) has less information than P(x,y), because you can get the former from the latter, but not the latter from the former. For certain data sets, one can estimate parameters for a model of P(x|y) without the intermediate step of modelling P(x,y).

    There is an interesting discussion on the advantages and disadvantages of explicitly learning P(x,y) as an intermediate step in modelling P(x|y) in http://ai.stanford.edu/~ang/papers/nips01-discriminativegenerative.pdf.
     
    Last edited: May 9, 2013
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