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Unformatted text preview: .statgun.com/tutorials/logistic regression.html) , [16] (http://etd.library.pitt.edu/ETD/available/etd 04122006102254/unrestricted/realfinalplus_ETD2006.pdf)
Exte ns ion
When we are dealing with a problem with more than two classes, we need to generalize our logistic regression to a Multinomial Logit model
(http://en.wikipedia.org/wiki/Multinomial_logit) .
Limitations of Logistic Regression:
1. We know that there is no assumptions are made about the distributions of the features of the data (i.e. the explanatory variables). However, the features should not
be highly correlated with one another because this could cause problems with estimation.
2. Large number of data points (i.e.the sample sizes) are required for logistic regression to provide sufficient numbers in both classes. The more number of
features/dimensions of the data, the larger the sample size required. Logistic Regression(2)  October 19, 2009
Logis tic Regres s ion Model
Recall that in the last lecture, we learned the logistic regression model. wikicour senote.com/w/index.php?title= Stat841&pr intable= yes 29/74 10/09/2013 Stat841  Wiki Cour se Notes Find
Crite ria: find a that maximizes the conditional likelihood of Y given X using the training data. From above, we have the first derivative of the log likelihood: Newton Raphson algorithm:
If we want to find
such that If we want to maximize or minimize , then solve for The Newton Raphson algorithm (http://en.wikipedia.org/wiki/Newton%27s_method) requires the second derivative or Hessian matrix
(http://en.wikipedia.org/wiki/Hessian_matrix) . (note : you can check it here (http://www.ee.ic.ac.uk/hp/staff/dmb/matrix/intro.html) , it's a very useful website including a Matrix Reference Manual that you can find information about linear algebra and the properties of real and complex matrices.) (by cancellation) (since and ) The same second derivative can be achieved if we reduce the occurrences of beta to 1 by the identity And solving Starting with , the Newt...
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