| Package | Description |
|---|---|
| weka.classifiers.functions |
| Modifier and Type | Class and Description |
|---|---|
class |
Logistic
Class for building and using a multinomial logistic
regression model with a ridge estimator.
There are some modifications, however, compared to the paper of leCessie and van Houwelingen(1992): If there are k classes for n instances with m attributes, the parameter matrix B to be calculated will be an m*(k-1) matrix. The probability for class j with the exception of the last class is Pj(Xi) = exp(XiBj)/((sum[j=1..(k-1)]exp(Xi*Bj))+1) The last class has probability 1-(sum[j=1..(k-1)]Pj(Xi)) = 1/((sum[j=1..(k-1)]exp(Xi*Bj))+1) The (negative) multinomial log-likelihood is thus: L = -sum[i=1..n]{ sum[j=1..(k-1)](Yij * ln(Pj(Xi))) +(1 - (sum[j=1..(k-1)]Yij)) * ln(1 - sum[j=1..(k-1)]Pj(Xi)) } + ridge * (B^2) In order to find the matrix B for which L is minimised, a Quasi-Newton Method is used to search for the optimized values of the m*(k-1) variables. |
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