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import numpy as np
from scipy.special import expit
from scipy.optimize import minimize
from sklearn.base import BaseEstimator, ClassifierMixin
from sklearn.metrics import accuracy_score
from sklearn.cross_validation import KFold
from sklearn import preprocessing
import seaborn
import matplotlib.pyplot as plt
from math import exp
import sys
seaborn.set_style("white")
class LogReg(BaseEstimator, ClassifierMixin):
def __init__(self, sigmas=1.):
self.sigmas = sigmas
def fit(self, x, y):
w = np.zeros(x.shape[1])
def aux(w):
return l_gradient(w, x, y, self.sigmas)
self.w = minimize(aux, w, jac=True, method='L-BFGS-B',
options={'disp': False, 'gtol': 1e-10}).x
return self
def predict(self, x):
pred = np.dot(x, self.w)
return (pred > 0).astype(int)
def l(w, x, y, sigmas):
x2 = np.dot(x, w)
l = (-np.log(expit(x2)).sum() + np.inner(1-y, x2)
+ 1 / (2 * sigmas) * np.inner(w, w))
return l
def l_gradient(w, x, y, sigmas):
x2 = np.dot(x, w)
l = (-np.log(expit(x2)).sum() + np.inner(x2, (1 - y))
+ 1 / (2 * sigmas) * np.inner(w, w))
grad = (np.sum(-x * expit(-x2)[:, None], axis=0)
+ np.sum(x * (1 - y)[:, None], axis=0) + 1 / sigmas * w)
return l, grad
def test_gradient(w, x, y, sigmas):
eps = 1e-10
_, g = l_gradient(w, x, y, sigmas)
for i in xrange(len(g)):
z = np.zeros(len(g))
z[i] = eps
l1 = l(w + z, x, y, sigmas)
z = np.zeros(len(g))
z[i] = -eps
l2 = l(w + z, x, y, sigmas)
print (l1 - l2) / (2 * eps), g[i]
def cross_validation(x, y):
for sigmas in [10 ** i for i in xrange(-8, 9)]:
train_scores = []
test_scores = []
for train, test in KFold(n=x.shape[0], n_folds=10, shuffle=True):
mod = LogReg(sigmas=sigmas)
x_train_f = x[train]
y_train_f = y[train]
x_test_f = x[test]
y_test_f = y[test]
mod = mod.fit(x_train_f, y_train_f)
train_scores.append(accuracy_score(y_test_f,
mod.predict(x_test_f)))
test_scores.append(accuracy_score(y_test, mod.predict(x_test)))
print np.mean(train_scores), np.mean(test_scores)
def plot_scores():
plt.figure(figsize=(9, 6))
values = [map(float, line.strip().split())
for line in open(sys.argv[1])]
y1, y2 = zip(*values)
x = xrange(-8, 9)
y1 = 1 - np.array(y1)
y2 = 1 - np.array(y2)
plt.plot(x, y1, label='CV error')
plt.plot(x, y2, label='Test error')
plt.legend()
plt.xlabel("log(sigma^2)")
plt.ylabel("Error")
plt.savefig(sys.argv[1] + ".pdf")
def three(x, y):
sigmas = exp(2)
mod = LogReg(sigmas=sigmas)
mod.fit(x, y)
print 1 - accuracy_score(y, mod.predict(x))
print 1 - accuracy_score(y_test, mod.predict(x_test))
print mod.w
def norm(x):
for i in [54, 55, 56]:
x[:, i] = np.log(1 + x[:, i])
return x
if __name__ == "__main__":
data_train = np.loadtxt("spam.train.dat")
x_train = data_train[:, :-1]
y_train = data_train[:, -1].astype(int)
data_test = np.loadtxt("spam.test.dat")
x_test = data_test[:, :-1]
y_test = data_test[:, -1].astype(int)
#x_train = preprocessing.scale(x_train)
#x_test = preprocessing.scale(x_test)
#x_train = norm(x_train)
#x_test = norm(x_test)
cross_validation(x_train, y_train)
#plot_scores()
#three(x_train, y_train)
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