generate dummy data and apply ridge with varying levels of regularisation. Plots train and test results. This code goes with my blog post: http://snoek.ddns.net/~oliver/mysite/the-bias-variance-tradeoff.html

ridge_bias_variance.py

from sklearn.datasets import make_regression
from sklearn.model_selection import train_test_split
from sklearn.linear_model import Ridge
from sklearn.metrics import mean_squared_error
import numpy as np
import matplotlib.pyplot as plt

# generate data
X, y, w = make_regression(n_samples=1000, n_features=200, coef=True,
                          random_state=1, bias=0, noise=3, tail_strength=0.9, effective_rank=10)

# 60/40 split on train/test data
X_train, X_test, y_train, y_test = train_test_split(
    X, y, test_size=0.4, random_state=1)

# list of alphas
alphas = 10.**np.arange(-4, 3, 0.1)

# loop through alphas, fit model, extract train and test results
scores_test = []
scores_train = []
for a in alphas:
	print(a)
    clf = Ridge(alpha=a, solver='auto')
    clf.fit(X_train, y_train)
    scores_train.append(mean_squared_error(y_train, clf.predict(X_train)))
    scores_test.append(mean_squared_error(y_test, clf.predict(X_test))) 

# plot MSE for train and test sets
fig, ax = plt.subplots(figsize=(15, 7))
ax.set_xscale('log')
ax.plot(alphas, scores_test, 'r', label='test')
ax.plot(alphas, scores_train, 'b', label='train')
ax.set_ylabel('MSE', fontsize=16)
ax.set_xlabel('alpha (regularisation strength)', fontsize=16)
ax.legend(fontsize=18)
plt.ion(); plt.show()