1 files changed, 125 insertions, 0 deletions
diff --git a/hw2/p3.py b/hw2/p3.py
new file mode 100644
index 0000000..f4a3ffa
--- /dev/null
+++ b/hw2/p3.py
@@ -0,0 +1,125 @@
+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)