Calculate error in ensemble
Error rate of the ensemble
Assume you have $n$ classifiers and each has an error $\epsilon$, the combined error of the ensemble is smaller than the error in the individual classifiers.
from scipy.special import comb
import math
def ensemble_error(n_classifier, error):
k_start = int(math.ceil(n_classifier / 2.))
probs = [comb(n_classifier, k) * error**k * (1-error)**(n_classifier - k)
for k in range(k_start, n_classifier + 1)]
return sum(probs)
ensemble_error(11, 0.25)
0.03432750701904297
Ensemble vs base error rates
The base error should be less than 0.5, better than random guessing, in order for the ensemble to perform better.
import numpy as np
error_range = np.arange(0.0, 1.01, 0.01)
ens_errors = [ensemble_error(n_classifier=11, error=error)
for error in error_range]
import matplotlib.pyplot as plt
plt.plot(error_range,
ens_errors,
label='Ensemble error',
linewidth=2)
plt.plot(error_range,
error_range,
linestyle='--',
label='Base error',
linewidth=2)
plt.xlabel('Base error')
plt.ylabel('Base/Ensemble error')
plt.legend(loc='upper left')
plt.grid(alpha=0.5)
#plt.savefig('images/07_03.png', dpi=300)
plt.show()
