File:Bias-variance decomposition.png
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Summary
| Description |
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.
Pythonimport 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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| Date | |
| Source | Own work |
| Author | Cosmia Nebula |
![{\displaystyle \mathbb {E} _{y\sim p(\cdot |x)}[y]}](https://wikimedia.org/api/rest_v1/media/math/render/svg/c23faf1477131ac8efa4b9671c13051031db50b3)
![{\displaystyle \mathbb {E} _{D}[f(x|D)]}](https://wikimedia.org/api/rest_v1/media/math/render/svg/d03e366778e4058f3e5c440129a40bfca3090d67)
![{\displaystyle \operatorname {Var} _{D}{\big [}f(x|D){\big ]}}](https://wikimedia.org/api/rest_v1/media/math/render/svg/debf8d2bda6af2b584fe8af5321f8e29830f39d8)
![{\displaystyle \operatorname {Bias} _{D}{\big [}f(x|D){\big ]}}](https://wikimedia.org/api/rest_v1/media/math/render/svg/432e815d6e96765bb20ca9ce8718e36edb71efea)
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| Date/Time | Thumbnail | Dimensions | User | Comment | |
|---|---|---|---|---|---|
| current | 02:47, 16 September 2024 | | 1,000 × 600 (141 KB) | wikimediacommons>Cosmia Nebula | Uploaded while editing "Bias–variance tradeoff" on en.wikipedia.org |
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