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Maximum Entropy code.
Uses Improved Iterative Scaling.


MaxEntropy Hold information for a Maximum Entropy classifier. 























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Calculate the log of the probability for each class. me is a MaxEntropy object that has been trained. observation is a vector representing the observed data. The return value is a list of unnormalized log probabilities for each class. 
Evaluate a feature function on every instance of the training set and class (PRIVATE). fn is a callback function that takes two parameters: a training instance and a class. Return a dictionary of (training set index, class index) > nonzero value. Values of 0 are not stored in the dictionary. 
Calculate the expectation of each function from the data (PRIVATE). This is the constraint for the maximum entropy distribution. Return a list of expectations, parallel to the list of features. 
Calculate the expectation of each feature from the model (PRIVATE). This is not used in maximum entropy training, but provides a good function for debugging. 
Calculate conditional probability P(yx) (PRIVATE). y is the class and x is an instance from the training set. Return a XSxCLASSES matrix of probabilities. 
Train a maximum entropy classifier, returns MaxEntropy object. Train a maximum entropy classifier on a training set. training_set is a list of observations. results is a list of the class assignments for each observation. feature_fns is a list of the features. These are callback functions that take an observation and class and return a 1 or 0. update_fn is a callback function that is called at each training iteration. It is passed a MaxEntropy object that encapsulates the current state of the training. The maximum number of iterations and the convergence criterion for IIS are given by max_iis_iterations and iis_converge, respectively, while max_newton_iterations and newton_converge are the maximum number of iterations and the convergence criterion for Newton's method. 
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