def figure_5_3():
""" Reproduces figure 5.3 in ESLii displaying the pointwise variance curves
for different spline bases
"""
def pv(D):
cv = np.linalg.inv(np.dot(D.transpose(), D))
return [np.dot(D[i, :].transpose(), np.dot(cv, D[i, :]))
for i in range(D.shape[0])]
n = 50
X = np.sort([random.random() for i in range(n)])
l_X = np.ndarray((n, 2))
l_X[:, 0] = np.ones(n)
l_X[:, 1] = X
l_pv = pv(l_X)
c_X = np.ndarray((n, 4))
c_X[:, 0:2] = l_X
c_X[:, 2] = [x**2 for x in X]
c_X[:, 3] = [x**3 for x in X]
c_pv = pv(c_X)
cs_X = np.ndarray((n, 6))
cs_X[:, 0:4] = c_X
cs_X[:, 4] = [max(0, (x - .33)**3) for x in X]
cs_X[:, 5] = [max(0, (x - .66)**3) for x in X]
cs_pv = pv(cs_X)
ncs_X = splines.ns_basis(X, knots=[0.1, 0.26, 0.42, 0.58, 0.74, 0.9],
intercept=True)
ncs_pv = pv(ncs_X)
plt.plot(X, l_pv)
plt.plot(X, c_pv)
plt.plot(X, cs_pv)
plt.plot(X, ncs_pv)
def figure_5_4():
"""Reproduces figure 5.4 in ESLii displaying the fitted natural spline for
each term
"""
data = eslii.read_sa_heart_data()
data.drop(["adiposity", "typea", "alcohol"], axis=1, inplace=True)
y = data["chd"]
X = data.drop("chd", axis=1)
X["famhist"] = pandas.get_dummies(X["famhist"])["Present"]
N = np.ndarray((X.shape[0], 21))
q = [0, 25, 50, 75, 100]
N[:, 0:4] = splines.ns_basis(X["sbp"],
knots=np.percentile(X["sbp"], q),
intercept=False)
N[:, 4:8] = splines.ns_basis(X["tobacco"],
knots=np.percentile(X["tobacco"], q),
intercept=False)
N[:, 8:12] = splines.ns_basis(X["ldl"],
knots=np.percentile(X["ldl"], q),
intercept=False)
N[:, 12] = X["famhist"]
N[:, 13:17] = splines.ns_basis(X["obesity"],
knots=np.percentile(X["obesity"], q),
intercept=False)
N[:, 17:21] = splines.ns_basis(X["age"],
knots=np.percentile(X["age"], q),
intercept=False)
lr = LogisticRegression(C=1e50).fit(N, y)
N -= N.mean(axis=0)
fig = plt.figure()
fig.add_subplot(321).scatter(X["sbp"], np.dot(N[:, 0:4], lr.coef_[0][0:4]))
fig.add_subplot(322).scatter(X["tobacco"], np.dot(N[:, 4:8], lr.coef_[0][4:8]))
fig.add_subplot(323).scatter(X["ldl"], np.dot(N[:, 8:12], lr.coef_[0][8:12]))
fig.add_subplot(324).scatter(X["famhist"], np.dot(N[:, 12:13], lr.coef_[0][12:13]))
fig.add_subplot(325).scatter(X["obesity"], np.dot(N[:, 13:17], lr.coef_[0][13:17]))
fig.add_subplot(326).scatter(X["age"], np.dot(N[:, 17:21], lr.coef_[0][17:21]))
plt.show()
def figure_5_5():
"""Reproduces figure 5.5 in ESLii displaying the results of fitting a spline
to the phoneme classification result
"""
phoneme = eslii.read_phoneme_data()
aa = phoneme[phoneme['g'] == 'aa']
aa_train = aa[map(lambda s: s.find("train") == 0, aa['speaker'])]
aa_train = aa_train.reset_index()
aa_test = aa[map(lambda s: s.find("test") == 0, aa['speaker'])]
aa_test = aa_test.reset_index()
ao = phoneme[phoneme['g'] == 'ao']
ao_train = ao[map(lambda s: s.find("train") == 0, ao['speaker'])]
ao_train = ao_train.reset_index()
ao_test = ao[map(lambda s: s.find("test") == 0, ao['speaker'])]
ao_test = ao_test.reset_index()
# Print some examples of the data
fit = plt.figure()
for i in range(15):
fit.add_subplot(211).plot(range(1, 257), aa_train.ix[i][1:257], c='green')
fit.add_subplot(211).plot(range(1, 257), ao_train.ix[i][1:257], c='red')
# Separate out train and test data/labels
train_X = np.concatenate((aa_train[aa_train.columns[1:257]],
ao_train[ao_train.columns[1:257]]))
train_y = [0 if i < aa_train.shape[0]
else 1 for i in range(train_X.shape[0])]
test_X = np.concatenate((aa_test[aa_test.columns[1:257]],
ao_test[ao_test.columns[1:257]]))
test_y = [0 if i < aa_test.shape[0] else 1 for i in range(test_X.shape[0])]
# Train raw classifier
lr = LogisticRegression(C=1e50).fit(train_X, train_y)
print "Raw errors: {:.2f} {:.2f}".format(1 - lr.score(train_X, train_y),
1 - lr.score(test_X, test_y))
# Train regularized classifier
N = splines.ns_basis(range(1, 257), [1, 21, 42, 64, 85, 106, 128, 149, 170,
192, 213, 234, 256])
lr2 = LogisticRegression(C=1e50).fit(np.dot(train_X, N), train_y)
print "Reg errors: {:.2f} {:.2f}".format(1 - lr2.score(np.dot(train_X, N),
train_y),
1 - lr2.score(np.dot(test_X, N),
test_y))
fit.add_subplot(212).plot(range(1, 257), lr.coef_[0],
range(1, 257), np.dot(N, lr2.coef_[0]))