File:Traintest.svg
| Uploaded by | Skbkekas |
|---|---|
| Upload date | 2009-05-12T04:33:10Z |
| MIME type | image/svg+xml |
| Dimensions | 720 × 270 px |
| File size | 35.1 KB |
Summary
| Description |
English: Plots showing a training set and a test set from the same statistical population. Two curves are fit to the training set, one of which is an overfit. By plotting these curves with the test data, the overfitting can be seen. |
| Date | |
| Source | Own work |
| Author | Skbkekas |
| Other versions |
[]
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| SVG development |  This plot was created with Matplotlib. |
| Source code | Python codeimport numpy as np
import matplotlib.pyplot as plt
m = 0.2 ## mesh on the abscissa
s = 3 ## standard deviation of errors
def pdesign(X, d):
"""Generate a polynomial design matrix on X of order d."""
V = X[:,np.newaxis]
F = [V**k for k in range(d+1)]
D = np.concatenate(F, axis=1)
return D
def regfit(Y, D):
"""Regress Y on D using least squares."""
U,S,Vt = np.linalg.svd(D,0)
V = np.transpose(Vt)
return np.dot(U, np.dot(np.transpose(U), Y))
X = np.arange(-2, 2, m, dtype=np.float64)
D1 = pdesign(X, 3)
D2 = pdesign(X, 13)
EY = X + X**3
Y1 = EY + np.random.normal(size=len(X))*s
Y2 = EY + np.random.normal(size=len(X))*s
Yhat1 = regfit(Y1, D1)
Yhat2 = regfit(Y1, D2)
plt.clf()
plt.figure(figsize=(8,3))
ax1 = plt.axes([0.06,0.1,0.4,0.8])
plt.title("Training set")
plt.plot(X, Y1, 'o')
plt.hold(True)
plt.plot(X, Yhat1, '-', color='green')
plt.plot(X, Yhat2, '-', color='orange')
ax1.set_ylim(-10, 10)
ax1.set_xticks([-2,-1,0,1,2])
ax2 = plt.axes([0.56,0.1,0.4,0.8])
plt.title("Test set")
plt.plot(X, Y2, 'o')
plt.plot(X, Yhat1, '-', color='green')
plt.plot(X, Yhat2, '-', color='orange')
ax2.set_xticks([-2,-1,0,1,2])
ax2.set_ylim(-10, 10)
plt.savefig("traintest.png")
plt.savefig("traintest.svg")
print ((Yhat1-Y1)**2).mean()
print ((Yhat2-Y1)**2).mean()
print ((Yhat1-Y2)**2).mean()
print ((Yhat2-Y2)**2).mean()
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Licensing
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