def figure_6_14():
"""Reproduces figure 6.14 in ESLii displaying a density estimate for sbp
levels in chd/no-chd groups using a Gaussian kernel density estimate
"""
sa = eslii.read_sa_heart_data()
sbp = sa["sbp"]
sbp_chd = sa[sa["chd"] == 1]["sbp"].copy()
sbp_chd.sort()
sbp_no_chd = sa[sa["chd"] == 0]["sbp"].copy()
sbp_no_chd.sort()
kde_chd = KernelDensity(kernel='gaussian', bandwidth=7.5).fit(
sbp_chd.reshape(len(sbp_chd), 1))
chd_log_dens = kde_chd.score_samples(sbp_chd.reshape((len(sbp_chd), 1)))
plt.subplot(121)
plt.plot(sbp_chd, np.exp(chd_log_dens), label="CHD")
kde_no_chd = KernelDensity(kernel='gaussian', bandwidth=7.5).fit(
sbp_no_chd.reshape(len(sbp_no_chd), 1))
no_chd_log_dens = kde_no_chd.score_samples(
sbp_no_chd.reshape((len(sbp_no_chd), 1)))
plt.plot(sbp_no_chd, np.exp(no_chd_log_dens), label="no CHD")
plt.legend(loc='best')
sbp_range = np.linspace(min(sbp), max(sbp), 100).reshape((100, 1))
chd_dens = np.exp(kde_chd.score_samples(sbp_range))
no_chd_dens = np.exp(kde_no_chd.score_samples(sbp_range))
p_chd = float(len(sbp_chd))/(len(sbp_chd) + len(sbp_no_chd))
posterior_est = [p_chd * chd_dens[i] /
(p_chd * chd_dens[i] + (1 - p_chd) * no_chd_dens[i])
for i in range(len(sbp_range))]
plt.subplot(122)
plt.plot(sbp_range, posterior_est)
plt.show()
def figure_4_13():
"""Reproduces figure 4.13 in ESLii showing the coefficients of an
L1-regularized logistic regression fit to the South African heart disease
data as a function of the L1 length of beta
TODO: this doesn't match
"""
data = eslii.read_sa_heart_data()
data.drop([u"adiposity", u"typea"], axis=1, inplace=True)
y = data["chd"]
X = data.drop("chd", axis=1)
X["famhist"] = pandas.get_dummies(X["famhist"])["Present"]
X = eslii.standardize_data(X, demeanCols=[])
beta_norms = []
coefs = {}
for column in X.columns:
coefs[column] = []
alphas = [1e-3, 1e-2, 2e-2, 3e-2, 4e-2, 5e-2, 6e-2, 7e-2, 8e-2, 9e-2, 1e-1,
.5, 1.0, 10.0]
for alpha in alphas:
lr = LogisticRegression(penalty="l1", C=alpha).fit(X, y)
beta_norms.append(sum(abs(lr.coef_[0])))
for (i, column) in enumerate(X.columns):
coefs[column].append(lr.coef_[0][i])
for column in X.columns:
plt.plot(beta_norms, coefs[column])
def tables_4_2_and_4_3():
"""Reproduces table 4.2 and 4.3 in ESLii showing the results of a logistic
regression fit to selected predictors of the South African heart disease
data
"""
data = eslii.read_sa_heart_data()
data.drop([u"adiposity", u"typea"], axis=1, inplace=True)
y = data["chd"]
X = data.drop("chd", axis=1)
X["famhist"] = pandas.get_dummies(X["famhist"])["Present"]
lr = LogisticRegression(C=1e30).fit(X, y)
print "(Intercept) {:.3f}".format(lr.intercept_[0])
for (i, column) in enumerate(X.columns):
print "{} {:.3f}".format(column, lr.coef_[0][i])
print "\n"
X.drop(["sbp", "obesity", "alcohol"], axis=1, inplace=True)
lr = LogisticRegression(C=1e30).fit(X, y)
print "(Intercept) {:.3f}".format(lr.intercept_[0])
for (i, column) in enumerate(X.columns):
print "{} {:.3f}".format(column, lr.coef_[0][i])
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()
