Plotting errors for ridge regression v. ordinary least squares as magnitude in noise increases

errors.py

import numpy as np
import matplotlib
matplotlib.use('Agg')  # wizardry to prevent Tkinter error
import matplotlib.pyplot as plt

n = 100
line = lambda x: 2*x + 3 # true line
e = 10
reg = 1e2

es = [i * 40 for i in range(9)]
ols_errors = []
rr_errors = []

plt.figure(figsize=(14,8))
plt.subplots_adjust(wspace=0.2, hspace=0.3)
plt_num = 210
for plt_idx, e in enumerate(es):
  np.random.seed(0)
  # 1. Create n random samples and plot
  xs = list(range(n))  # create xs from 0 to 99
  ys = [line(x) + np.random.random() * e - (e/2.) for x in xs]  # create ys with 0-mean n$

  # 2. Create A and y
  A = np.array([[x, 1] for x in xs])
  y = np.array([[y] for y in ys])
  true_y = np.array([[line(x)] for x in xs])
  
  # 3. Solve for optimal model w and plot predicted ys
  I = np.eye(A.shape[1])
  ols_w = np.linalg.inv(A.T.dot(A)).dot(A.T.dot(y))
  rr_w = np.linalg.inv(A.T.dot(A) + reg * I).dot(A.T.dot(y))
  plt.subplot(3, 3, plt_idx + 1)
  plt.title('%2.fx noise' % e)
  plt.scatter(xs, ys, s=2)
  plt.plot(xs, [line(x) for x in xs], label='true')
  plt.plot(xs, A.dot(ols_w), label='ols')
  #plt.plot(xs, A.dot(rr_w), label='rr')
  plt.savefig('errors_ols_v_ridge_points.png')
  ols_errors.append(np.linalg.norm(A.dot(ols_w) - true_y))
  rr_errors.append(np.linalg.norm(A.dot(rr_w) - true_y))

plt.figure()
plt.plot(es, ols_errors, label='ols')  # plot ols performance
plt.plot(es, rr_errors, label='rr')  # plot ridge regression performance
plt.legend()
plt.savefig('errors_ols_v_ridge.png')