English: Bias-variance decomposition in the case of mean squared loss. The green dots are samples of test label at a fixed test feature . Their variance around the mean is the irreducible error . The red dots are test label predictions as the training set is randomly sampled. Their variance around the mean is the variance . The difference between the red dash and the green dash is the bias . The bias-variance decomposition is then visually clear: the mean squared error between the red dots and the green dots is the sum of the three components.
Matplotlib code
import numpy as np
import matplotlib.pyplot as plt
# Set random seed for reproducibility
np.random.seed(42)
# Create figure and axis
fig, ax = plt.subplots(figsize=(10, 6))
# Remove y-axis and x-ticks
ax.yaxis.set_visible(False)
ax.set_xticks([])
# Set x_0
x_0 = 0
xmin, xmax = -np.pi /3 , np.pi/3
x = np.linspace(xmin, xmax, 1000)
# Plot curves
for _ in range(200):
epsilon = np.random.normal(0, 0.1)
y = 1 + (1 + epsilon) * np.cos(x) + epsilon
ax.plot(x, y, color='blue', alpha=0.1)
n_points = 500
x_jitter = np.random.normal(x_0, 0.01, n_points)
y_values = 1 + (1 + np.random.normal(0, 0.1, n_points)) * np.cos(x_0) + np.random.normal(0, 0.2, n_points)
ax.scatter(x_jitter, y_values, color='red', alpha=0.5, s=1, label=r"$f(x
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