Information Gain calculation with Scikit-learn

Question

I am using Scikit-learn for text classification. I want to calculate the Information Gain for each attribute with respect to a class in a (sparse) document-term matrix.

• the Information Gain is defined as H(Class) - H(Class | Attribute), where H is the entropy.
• in weka, this would be calculated with InfoGainAttribute.
• But I haven't found this measure in scikit-learn.

(It was suggested that the formula above for Information Gain is the same measure as mutual information. This matches also the definition in wikipedia. Is it possible to use a specific setting for mutual information in scikit-learn to accomplish this task?)

Gadmann

They are the same Information gain and mutual information: different or equal?, Feature Selection: Information Gain VS Mutual Information, when we're talking about Pointwise Mutual Information not Expected Mutual Information. – Dihedron

@NickMorgan: they are the same when talking about PMI; also it's unhelpful to quote an ephemeral source (table in a third-party paper which has now expired), instead of CV or Wikipedia. – Dihedron

Answer 1

You can use scikit-learn's mutual_info_classif here is an example

from sklearn.datasets import fetch_20newsgroups
from sklearn.feature_selection import mutual_info_classif
from sklearn.feature_extraction.text import CountVectorizer

categories = ['talk.religion.misc',
              'comp.graphics', 'sci.space']
newsgroups_train = fetch_20newsgroups(subset='train',
                                      categories=categories)

X, Y = newsgroups_train.data, newsgroups_train.target
cv = CountVectorizer(max_df=0.95, min_df=2,
                                     max_features=10000,
                                     stop_words='english')
X_vec = cv.fit_transform(X)

res = dict(zip(cv.get_feature_names(),
               mutual_info_classif(X_vec, Y, discrete_features=True)
               ))
print(res)

this will output a dictionary of each attribute, i.e. item in the vocabulary as keys and their information gain as values

here is a sample of the output

{'bible': 0.072327479595571439,
 'christ': 0.057293733680219089,
 'christian': 0.12862867565281702,
 'christians': 0.068511328611810071,
 'file': 0.048056478042481157,
 'god': 0.12252523919766867,
 'gov': 0.053547274485785577,
 'graphics': 0.13044709565039875,
 'jesus': 0.09245436105573257,
 'launch': 0.059882179387444862,
 'moon': 0.064977781072557236,
 'morality': 0.050235104394123153,
 'nasa': 0.11146392824624819,
 'orbit': 0.087254803670582998,
 'people': 0.068118370234354936,
 'prb': 0.049176995204404481,
 'religion': 0.067695617096125316,
 'shuttle': 0.053440976618359261,
 'space': 0.20115901737978983,
 'thanks': 0.060202010019767334}

Equipotential

is this an information gain or mutual info gain? are they same? @Equipotential – Finality

In the above code, if I am keeping 'binary=True' while vectorizing the text, am getting different Mutual Information results. Ideally, mutual information on categorical variables works solely based on the presence or nor right, irrespective of the count? – Inkblot

Is there a way to calculate MI between each feature/term and each category with scikit-larn, e.g. what is MI between "bible" and "'talk.religion.misc'". Chapter from IR book provides some math for that, but I cannot find a way to do that with scikit-learn. – Hallway

Answer 2

Here is my proposition to calculate the information gain using pandas:

from scipy.stats import entropy
import pandas as pd
def information_gain(members, split):
    '''
    Measures the reduction in entropy after the split  
    :param v: Pandas Series of the members
    :param split:
    :return:
    '''
    entropy_before = entropy(members.value_counts(normalize=True))
    split.name = 'split'
    members.name = 'members'
    grouped_distrib = members.groupby(split) \
                        .value_counts(normalize=True) \
                        .reset_index(name='count') \
                        .pivot_table(index='split', columns='members', values='count').fillna(0) 
    entropy_after = entropy(grouped_distrib, axis=1)
    entropy_after *= split.value_counts(sort=False, normalize=True)
    return entropy_before - entropy_after.sum()

members = pd.Series(['yellow','yellow','green','green','blue'])
split = pd.Series([0,0,1,1,0])
print (information_gain(members, split))

Formic

Answer 3

Using pure python:

def ig(class_, feature):
  classes = set(class_)

  Hc = 0
  for c in classes:
    pc = list(class_).count(c)/len(class_)
    Hc += - pc * math.log(pc, 2)
  print('Overall Entropy:', Hc)
  feature_values = set(feature)

  Hc_feature = 0
  for feat in feature_values:

    pf = list(feature).count(feat)/len(feature)
    indices = [i for i in range(len(feature)) if feature[i] == feat]
    clasess_of_feat = [class_[i] for i in indices]
    for c in classes:
        pcf = clasess_of_feat.count(c)/len(clasess_of_feat)
        if pcf != 0:
            temp_H = - pf * pcf * math.log(pcf, 2)
            Hc_feature += temp_H
  ig = Hc - Hc_feature
  return ig    

Gamecock