8.1. Getting started with scikit-learn¶
import numpy as np
import scipy.stats as st
import sklearn.linear_model as lm
import matplotlib.pyplot as plt
%matplotlib inline
def f(x):
return np.exp(3 * x)
x_tr = np.linspace(0., 2, 200)
y_tr = f(x_tr)
x = np.array([0, .1, .2, .5, .8, .9, 1])
y = f(x) + 2 * np.random.randn(len(x))
fig, ax = plt.subplots(1, 1, figsize=(6, 3))
ax.plot(x_tr, y_tr, '--k')
ax.plot(x, y, 'ok', ms=10)
ax.set_xlim(0, 1.5)
ax.set_ylim(-10, 80)
ax.set_title('Generative model')
# We create the model.
lr = lm.LinearRegression()
# We train the model on our training dataset.
lr.fit(x[:, np.newaxis], y)
# Now, we predict points with our trained model.
y_lr = lr.predict(x_tr[:, np.newaxis])
fig, ax = plt.subplots(1, 1, figsize=(6, 3))
ax.plot(x_tr, y_tr, '--k')
ax.plot(x_tr, y_lr, 'g')
ax.plot(x, y, 'ok', ms=10)
ax.set_xlim(0, 1.5)
ax.set_ylim(-10, 80)
ax.set_title("Linear regression")
lrp = lm.LinearRegression()
fig, ax = plt.subplots(1, 1, figsize=(6, 3))
ax.plot(x_tr, y_tr, '--k')
for deg, s in zip([2, 5], ['-', '.']):
lrp.fit(np.vander(x, deg + 1), y)
y_lrp = lrp.predict(np.vander(x_tr, deg + 1))
ax.plot(x_tr, y_lrp, s,
label=f'degree {deg}')
ax.legend(loc=2)
ax.set_xlim(0, 1.5)
ax.set_ylim(-10, 80)
# Print the model's coefficients.
print(f'Coefficients, degree {deg}:\n\t',
' '.join(f'{c:.2f}' for c in lrp.coef_))
ax.plot(x, y, 'ok', ms=10)
ax.set_title("Linear regression")
ridge = lm.RidgeCV()
fig, ax = plt.subplots(1, 1, figsize=(6, 3))
ax.plot(x_tr, y_tr, '--k')
for deg, s in zip([2, 5], ['-', '.']):
ridge.fit(np.vander(x, deg + 1), y)
y_ridge = ridge.predict(np.vander(x_tr, deg + 1))
ax.plot(x_tr, y_ridge, s,
label='degree ' + str(deg))
ax.legend(loc=2)
ax.set_xlim(0, 1.5)
ax.set_ylim(-10, 80)
# Print the model's coefficients.
print(f'Coefficients, degree {deg}:',
' '.join(f'{c:.2f}' for c in ridge.coef_))
ax.plot(x, y, 'ok', ms=10)
ax.set_title("Ridge regression")
