Softmax Regression

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(Introduction)
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<math>\{ (x^{(1)}, y^{(1)}), \ldots, (x^{(m)}, y^{(m)}) \}</math>
<math>\{ (x^{(1)}, y^{(1)}), \ldots, (x^{(m)}, y^{(m)}) \}</math>
of <math>m</math> labeled examples, where the input features are <math>x^{(i)} \in \Re^{n+1}</math>.   
of <math>m</math> labeled examples, where the input features are <math>x^{(i)} \in \Re^{n+1}</math>.   
-
We had considered the binary classification setting, so the labels  
+
(In these set of notes, we will use the notational convention of letting <math>x^{(i)}</math> be
 +
<math>n+1</math> dimensional, with <math>x_0 = 1</math> corresponding to the intercept term.)
 +
With logistic regression, we were in the binary classification setting, so the labels  
were <math>y^{(i)} \in \{0,1\}</math>.  Our hypothesis took the form:
were <math>y^{(i)} \in \{0,1\}</math>.  Our hypothesis took the form:

Revision as of 18:28, 10 May 2011

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