Class RidgeLogisticRegression

source code

             object --+        
                      |        
          BaseEstimator --+    
                          |    
LogisticRegressionEstimator --+
                              |
                             RidgeLogisticRegression

Logistic regression (re-weighted log-likelihood aka. cross-entropy) with
an L2 penalty:

    f(beta) = -loglik / n_samples + (l / 2) * ||beta||²_2,

where

    loglik = Sum wi * (yi * log(pi) + (1 − yi) * log(1 − pi)),

    pi = p(y=1|xi, beta) = 1 / (1 + exp(-xi'*beta)),

    wi = weight of sample i,

    and ||.||²_2 is the squared L2-norm.

Parameters
----------
l : Non-negative float. The L2 regularisation parameter.

algorithm : ExplicitAlgorithm. The algorithm that should be applied.
        Should be one of:
            1. GradientDescent(...)

        Default is GradientDescent(...).

algorithm_params : A dict. The dictionary algorithm_params contains
        parameters that should be set in the algorithm. Passing
        algorithm=MyAlgorithm(**params) is equivalent to passing
        algorithm=MyAlgorithm() and algorithm_params=params. Default is
        an empty dictionary.

class_weight : Dict, 'auto' or None. If 'auto', class weights will be
        given inverse proportional to the frequency of the class in
        the data. If a dictionary is given, keys are classes and values
        are corresponding class weights. If None is given, the class
        weights will be uniform.

penalty_start : Non-negative integer. The number of columns, variables
        etc., to be exempt from penalisation. Equivalently, the first
        index to be penalised. Default is 0, all columns are included.

mean : Boolean. Whether to compute the mean loss or not. Default is True,
        the mean loss.

Examples
--------
>>> import numpy as np
>>> import parsimony.estimators as estimators
>>> import parsimony.algorithms.gradient as gradient
>>> n, p = 10, 16
>>>
>>> np.random.seed(1337)
>>> X = np.random.rand(n, p)
>>> y = np.random.randint(0, 2, (n, 1))
>>> l = 1.0
>>> lr = estimators.RidgeLogisticRegression(l,
...                      algorithm=gradient.GradientDescent(max_iter=1000),
...                      mean=False)
>>> res = lr.fit(X, y)
>>> pred = lr.score(X, y)
>>> print "prediction rate = %.1f" % pred
prediction rate = 0.9