Package weka.classifiers.functions

Class Summary
GaussianProcesses Implements Gaussian processes for regression without hyperparameter-tuning.
LinearRegression Class for using linear regression for prediction.
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.
MultilayerPerceptron A Classifier that uses backpropagation to classify instances.
This network can be built by hand, created by an algorithm or both.
SGD Implements stochastic gradient descent for learning various linear models (binary class SVM, binary class logistic regression and linear regression).
SGDText Implements stochastic gradient descent for learning a linear binary class SVM or binary class logistic regression on text data.
SimpleLinearRegression Learns a simple linear regression model.
SimpleLogistic Classifier for building linear logistic regression models.
SMO Implements John Platt's sequential minimal optimization algorithm for training a support vector classifier.

This implementation globally replaces all missing values and transforms nominal attributes into binary ones.
SMOreg SMOreg implements the support vector machine for regression.
VotedPerceptron Implementation of the voted perceptron algorithm by Freund and Schapire.
 



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