linear_regression_fit.py

import numpy as np
import matplotlib.pyplot as plt

from sklearn.linear_model import Ridge
from sklearn.preprocessing import PolynomialFeatures
from sklearn.pipeline import make_pipeline

import matplotlib
matplotlib.rcParams['mathtext.fontset'] = 'stix'
matplotlib.rcParams['font.family'] = 'STIXGeneral'
matplotlib.rcParams.update({'font.size': 18})

def f(x):
    """ function to approximate by polynomial interpolation"""
    return 0.5 * x


# generate points used to plot
x_plot = np.linspace(-10, 10, 100)

# generate points and keep a subset of them
x = np.linspace(-10, 10, 100)
rng = np.random.RandomState(0)
rng.shuffle(x)
x = np.sort(x[:10])
noize = [(-2 + np.random.random()*2) for i in range(len(x))]
y = f(x) + noize

# create matrix versions of these arrays
X = x[:, np.newaxis]
X_plot = x_plot[:, np.newaxis]

colors = ['red', 'red']#, 'orange'
lw = 2


type_of_regression = ["linear regression", "regression of degree 10"]
fit = ["fit", "overfit"]
for count, degree in enumerate([1,10]):#, 2, 15
    plt.figure(count)
    axes = plt.gca()
    axes.set_xlim([-10,10])
    axes.set_ylim([-10,10])
    plt.scatter(x, y, color='navy', s=30, marker='o', label="training examples")
    plt.xticks([-10.0, -5.0, 0.0, 5.0, 10.0])
    plt.yticks([-10.0, -5.0, 0.0, 5.0, 10.0])
    model = make_pipeline(PolynomialFeatures(degree), Ridge())
    model.fit(X, y)
    y_plot = model.predict(X_plot)
    plt.plot(x_plot, y_plot, color=colors[count], linewidth=lw,
             label=type_of_regression[count])

    plt.legend(loc='best')
    fig1 = plt.gcf()
    fig1.subplots_adjust(top = 0.98, bottom = 0.1, right = 0.98, left = 0.08, hspace = 0, wspace = 0)
    fig1.savefig('../../Illustrations/linear-regression-' + fit[count] + '.eps', format='eps', dpi=1000, bbox_inches = 'tight', pad_inches = 0)
    fig1.savefig('../../Illustrations/linear-regression-' + fit[count] + '.pdf', format='pdf', dpi=1000, bbox_inches = 'tight', pad_inches = 0)
    fig1.savefig('../../Illustrations/linear-regression-' + fit[count] + '.png', dpi=1000, bbox_inches = 'tight', pad_inches = 0)


plt.show()