Logit function

Show in the plot is how the logistic regression would, in this synthetic dataset, classify values as either 0 or 1, i.e. class one or two, using the logit-curve.

Python source code: plot_logistic.py

print __doc__


# Code source: Gael Varoqueux
# License: BSD

import numpy as np
import pylab as pl

from scikits.learn import linear_model

# this is our test set, it's just a straight line with some
# gaussian noise
xmin, xmax = -5, 5
n_samples = 100
np.random.seed(0)
X = np.random.normal(size=n_samples)
y = (X > 0).astype(np.float)
X[X>0] *= 4
X += .3*np.random.normal(size=n_samples)

X = X[:, np.newaxis]
# run the classifier
clf = linear_model.LogisticRegression(C=1e5)
clf.fit(X, y)

# and plot the result
pl.figure(1, figsize=(4, 3))
pl.clf()
pl.scatter(X.ravel(), y, color='black', zorder=20)
X_test = np.linspace(-5, 10, 300)
def model(x):
    return 1/(1+np.exp(-x))
loss = model(X_test*clf.coef_ + clf.intercept_).ravel()
pl.plot(X_test, loss, color='blue', linewidth=3)

ols = linear_model.LinearRegression()
ols.fit(X, y)
pl.plot(X_test, ols.coef_*X_test + ols.intercept_, linewidth=1)
pl.axhline(.5, color='.5')

pl.ylabel('y')
pl.xlabel('X')
pl.xticks(())
pl.yticks(())
pl.ylim(-.25, 1.25)
pl.xlim(-4, 10)

pl.show()