Softmax Regression

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(Introduction)
(Introduction)
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Motivation: One reason for selecting this form of hypotheses comes from connections to linear discriminant analysis. In particular, if one assumes a generative model for the data in the form <math>p(x,y) = p(y) \times p(x | y)</math> and selects for <math>p(x | y)</math> a member of the exponential family (which includes Gaussians, Poissons, etc.) it is possible to show that the conditional probability <math>p(y | x)</math> has the same form as our chosen hypotheses <math>h(x)</math>. For more details, we defer to the [http://www.stanford.edu/class/cs229/notes/cs229-notes2.pdf CS 229 Lecture 2 Notes].
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Motivation: One reason for selecting this form of hypotheses comes from connections to linear discriminant analysis. In particular, if one assumes a generative model for the data in the form <math>p(x,y) = p(y) \times p(x | y)</math> and selects for <math>p(x | y)</math> a member of the exponential family (which includes Gaussians, Poissons, etc.) it is possible to show that the conditional probability <math>p(y | x)</math> has the same form as our chosen hypotheses <math>h(x)</math>. For more details, see the [http://www.stanford.edu/class/cs229/notes/cs229-notes2.pdf CS 229 Lecture 2 Notes].
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Revision as of 07:22, 4 May 2011

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