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A Convenient Generalization of Schlick’s Bias and Gain Functions

Class for boosting a classifier using the MultiBoosting method. MultiBoosting is an extension to the highly successful AdaBoost technique for forming decision committees. MultiBoosting can be viewed as combining AdaBoost with wagging. It is able to harness both AdaBoost's high bias and variance reduction with wagging's superior variance reduction. Using C4.5 as the base learning algorithm, Multi-boosting is demonstrated to produce decision committees with lower error than either AdaBoost or wagging significantly more often than the reverse over a large representative cross-section of UCI data sets. It offers the further advantage over AdaBoost of suiting parallel execution. For more information, see Geoffrey I. Webb (2000). MultiBoosting: A Technique for Combining Boosting and Wagging. Machine Learning. Vol.40(No.2).

This package currently contains classes for training multilayer perceptrons with one hidden layer, where the number of hidden units is user specified. MLPClassifier can be used for classification problems and MLPRegressor is the corresponding class for numeric prediction tasks. The former has as many output units as there are classes, the latter only one output unit. Both minimise a penalised squared error with a quadratic penalty on the (non-bias) weights, i.e., they implement "weight decay", where this penalised error is averaged over all training instances. The size of the penalty can be determined by the user by modifying the "ridge" parameter to control overfitting. The sum of squared weights is multiplied by this parameter before added to the squared error. Both classes use BFGS optimisation by default to find parameters that correspond to a local minimum of the error function. but optionally conjugated gradient descent is available, which can be faster for problems with many parameters. Logistic functions are used as the activation functions for all units apart from the output unit in MLPRegressor, which employs the identity function. Input attributes are standardised to zero mean and unit variance. MLPRegressor also rescales the target attribute (i.e., "class") using standardisation. All network parameters are initialised with small normally distributed random values.