I'm trying to replicate the results of the paper in the link
https://nlp.stanford.edu/IR-book/html/htmledition/naive-bayes-text-classification-1.html
This link explains how Multinomial Naive Bayes works for text classification.
I've tried to reproduce the example using scikit learn.
from sklearn.feature_extraction.text import CountVectorizer
from sklearn.model_selection import train_test_split
import pandas as pd
import numpy as np
import matplotlib.pyplot as plt
from sklearn.metrics import accuracy_score
from sklearn.feature_extraction.text import TfidfVectorizer
from sklearn import preprocessing, decomposition, model_selection, metrics, pipeline
from sklearn.model_selection import GridSearchCV, cross_val_score, KFold
from sklearn.metrics import accuracy_score
from sklearn.metrics import make_scorer
from sklearn.naive_bayes import MultinomialNB
#TRAINING SET
dftrain = pd.DataFrame(data=np.array([["Chinese Beijing Chinese", "Chinese Chinese Shanghai", "Chinese Macao", "Tokyo Japan Chinese"],
["yes", "yes", "yes", "no"]]))
dftrain = dftrain.T
dftrain.columns = ['text', 'label']
#TEST SET
dftest = pd.DataFrame(data=np.array([["Chinese Chinese Chinese Tokyo Japan"]]))
dftest.columns = ['text']
count_vectorizer = CountVectorizer(min_df=0, token_pattern=r"\b\w+\b", stop_words = None)
count_train = count_vectorizer.fit_transform(dftrain['text'])
count_test = count_vectorizer.transform(dftest['text'])
clf = MultinomialNB()
clf.fit(count_train, df['label'])
clf.predict(count_test)
The output is correctly printed as:
array(['yes'],
dtype='<U3')
Just like how its mentioned in the paper! The paper predicts it as YES because
P(yes | test set) = 0.0003 > P(no | test set) = 0.0001
I want to be able to see those two probabilities!
When I type:
clf.predict_proba(count_test)
I get
array([[ 0.31024139, 0.68975861]])
I think what this means is:
P(test belongs to label 'no') = 0.31024139
and P(test belongs to label 'yes') = 0.68975861
Therefore, scikit-learn predicts the text as belonging to the label yes, but
My question is: Why are the probabilities different? P(yes | test set) = 0.0003 > P(no | test set) = 0.0001, I don't see the numbers 0.0003 and 0.0001 but instead see 0.31024139 and 0.68975861
Am I missing something here? Does this have something to do with class_prior parameter?
I did read the documentation!
http://scikit-learn.org/stable/modules/naive_bayes.html#multinomial-naive-bayes
Apparently, the parameter is estimated by a smoothed version of maximum likelihood, i.e. relative frequency counting.
What I'm wondering is, is there anyway, I can replicated and see the results as the one in the research paper?
This is more to do with the meaning of the probability predict_proba produces. the number .0003 and .0001 are not normalised i.e. they don't sum to one. if you normalise these values you'll get the same result
see the snippet below:
clf.predict_proba(count_test)
Out[63]: array([[ 0.31024139, 0.68975861]])
In [64]: p = (3/4)*((3/7)**3)*(1/14)*(1/14)
In [65]: p
Out[65]: 0.00030121377997263036
In [66]: p0 = (1/4)*((2/9)**3)*(2/9)*(2/9)
In [67]: p0
Out[67]: 0.00013548070246744223
#normalised values
In [68]: p/(p0+p)
Out[68]: 0.6897586117634674
In [69]: p0/(p0+p)
Out[69]: 0.3102413882365326