# Why is the “training score” I get from the learning curve of Multinomial Naive Bayes so different from the training score of the Bernoulli version?

I'm comparing the learning curves of Bernoulli and Multinomial Naive Bayes using the 20_newsgroups dataset from scikit-learn for text-classification. I considered both the "training score" and the "cross validation score", but I noticed that while in the Multinomial version the training score is very high at the beginning and decreases and the cross-validation score is very low at the beginning and increases, in the Bernoulli version I have a low training score at the beginning (and then it increases). Is it normal or am I doing something wrong? It sounds a bit strange to me.

Here's the Multinomial plot: This one is the Bernoulli one: Here is some of my Python code (Bernoulli version):

####load dataset####
from sklearn.datasets import fetch_20newsgroups
categories = ['alt.atheism', 'sci.electronics','rec.sport.hockey']
train = fetch_20newsgroups(subset='train', categories=categories, shuffle=True, random_state=42)
y = train.target
test = fetch_20newsgroups(subset='test', categories=categories, shuffle=True, random_state=42)

####bag of words####
from nltk.corpus import stopwords
stopwords = stopwords.words('english')
from sklearn.feature_extraction.text import CountVectorizer
count_vectorizer = CountVectorizer(stop_words=stopwords, binary=True)
matrix_train = count_vectorizer.fit_transform(train.data)

from sklearn.naive_bayes import BernoulliNB
bernoulli = BernoulliNB(alpha = 1.0, fit_prior = True)

####learning curve####
import matplotlib.pyplot as plt
from sklearn.learning_curve import learning_curve
def plot_learning_curve(estimator, title, X, y, ylim, cv, n_jobs=1, train_sizes=np.linspace(.1, 1.0, 8)):
plt.figure()
plt.title(title)
plt.xlabel("Training examples")
plt.ylabel("Score")
train_sizes, train_scores, test_scores = learning_curve( estimator, X, y, cv=cv, n_jobs=n_jobs, train_sizes=train_sizes)
train_scores_mean = np.mean(train_scores, axis=1)
train_scores_std = np.std(train_scores, axis=1)
test_scores_mean = np.mean(test_scores, axis=1)
test_scores_std = np.std(test_scores, axis=1)
plt.grid()
plt.fill_between(train_sizes, train_scores_mean - train_scores_std,
train_scores_mean + train_scores_std, alpha=0.1,
color="r")
plt.fill_between(train_sizes, test_scores_mean - test_scores_std,
test_scores_mean + test_scores_std, alpha=0.1, color="g")
plt.plot(train_sizes, train_scores_mean, 'o-', color="r",
label="Training score")
plt.plot(train_sizes, test_scores_mean, 'o-', color="g",
label="Cross-validation score")

plt.legend(loc="best")
return plt

title = "Learning Curves (Naive Bayes)"
from sklearn import cross_validation
cv = cross_validation.ShuffleSplit(matrix_train.shape, n_iter=100, test_size=0.2, random_state=0)
plot_learning_curve(bernoulli, title, matrix_train, y, ylim=(0.7, 1.01), cv=cv, n_jobs=1)
plt.show()


Why are they so different? The cross validation score is like what I was expecting both in Multinomial and Bernoulli, but the training score should be high at the beginning, right?

• This may be due to the different scaling of the y-axis. If you look at it closely, the decrease in performance in the first plot is very small. This may happen for various reasons, like having some mislabeled examples (e.g. duplicate examples with different labels). The fact that they converge at a different rate indicates that the first classifier is better suited for this problem. – George Jan 22 '16 at 17:37
• I'm pretty sure the Multinomial plot is ok, my problem was with the Bernoulli one. I thought they didn't have to be so different from each other since their differences are transparent to the programmer using scikit-learn, and mainly one has to pay attention to the representation of the document-vector (Bernoulli requires a binarized vector). I don't understand where is the error. Thank you very much for your answer – Trevor Jan 22 '16 at 18:11