

In [63]:

    
# Inspired from the Data Science for business, on Introduction to predictive modeling example
# dataset from https://archive.ics.uci.edu/ml/datasets/Mushroom



In [64]:

    
# necessary imports
from matplotlib import pyplot as plt
import pandas as pd
import numpy as np
%load_ext autoreload
%autoreload 2
import sys
sys.path.append("../lib_math")
import information as info
import scatter_boxplot as sbp
%matplotlib inline
import seaborn as sns
from scipy.stats.stats import pearsonr
from scipy import stats









    



The autoreload extension is already loaded. To reload it, use:
  %reload_ext autoreload

data input

""" class: edible=e, poisonous=p cap-shape: bell=b, conical=c, convex=x, flat=f, knobbed=k, sunken=s cap-surface: fibrous=f, grooves=g, scaly=y, smooth=s cap-color: brown=n ,buff=b, cinnamon=c, gray=g, green=r, pink=p, purple=u, red=e, white=w, yellow=y bruises?: bruises=t, no=f odor: almond=a, anise=l, creosote=c, fishy=y, foul=f, musty=m, none=n, pungent=p, spicy=s gill-attachment: attached=a, descending=d, free=f, notched=n gill-spacing: close=c, crowded=w, distant=d gill-size: broad=b, narrow=n gill-color: black=k, brown=n, buff=b, chocolate=h, gray=g, green=r, orange=o, pink=p, purple=u, red=e, white=w, yellow=y stalk-shape: enlarging=e, tapering=t stalk-root: bulbous=b, club=c, cup=u, equal=e, rhizomorphs=z, rooted=r, missing=? stalk-surface-above-ring: fibrous=f, scaly=y, silky=k, smooth=s stalk-surface-below-ring: fibrous=f, scaly=y, silky=k, smooth=s stalk-color-above-ring: brown=n, buff=b, cinnamon=c, gray=g, orange=o, pink=p, red=e, white=w, yellow=y stalk-color-below-ring: brown=n, buff=b, cinnamon=c, gray=g, orange=o, pink=p, red=e, white=w, yellow=y veil-type: partial=p, universal=u veil-color: brown=n, orange=o, white=w, yellow=y ring-number: none=n, one=o, two=t ring-type: cobwebby=c, evanescent=e, flaring=f, large=l, none=n, pendant=p, sheathing=s, zone=z spore-print-color: black=k, brown=n, buff=b, chocolate=h, green=r, orange=o, purple=u, white=w, yellow=y population: abundant=a, clustered=c, numerous=n, scattered=s, several=v, solitary=y habitat: grasses=g, leaves=l, meadows=m, paths=p, urban=u, waste=w, woods=d """



In [65]:

    
#https://archive.ics.uci.edu/ml/datasets/Mushroom
df = pd.read_csv('../small_data_samples/agaricus-lepiota.data')
print len(df)



In [66]:

    
df.head(3)









    Out[66]:






  
    
      
      p
      x
      s
      n
      t
      p.1
      f
      c
      n.1
      k
      ...
      s.2
      w
      w.1
      p.2
      w.2
      o
      p.3
      k.1
      s.3
      u
    
  
  
    
      0
       e
       x
       s
       y
       t
       a
       f
       c
       b
       k
      ...
       s
       w
       w
       p
       w
       o
       p
       n
       n
       g
    
    
      1
       e
       b
       s
       w
       t
       l
       f
       c
       b
       n
      ...
       s
       w
       w
       p
       w
       o
       p
       n
       n
       m
    
    
      2
       p
       x
       y
       w
       t
       p
       f
       c
       n
       n
      ...
       s
       w
       w
       p
       w
       o
       p
       k
       s
       u
    
  

3 rows × 23 columns

Ranking of attributes



In [67]:

    
# Here we deal with a Classification Task, target variable "p" is categorial
# and the attributes are also categorial
# => we can use the infromation gain



In [69]:

    
# Calculate the global entropy:
print 'global entropy is :', info.entropy(df, "p")
# If the two classes were perfectly balanced in the dataset it would have an entropy of 1. 
# since entropy ~ 1 we should not be far from this, but lets see exactly how far we are:
print 'total edible: ',  len(df[df.p=='e'])
print 'total poisonous : ',  len(df[df.p=='p'])









    



global entropy is : Asdf
0.999061269148
total edible:  4208
total poisonous :  3915



In [75]:

    
# Lets see the information gain for the GILL-COLOR
info.information_gain(df, "k", "p")









    Out[75]:





0.4172294080316872



In [76]:

    
# Lets see the information gain for the SPORE-PRINT-COLOR
info.information_gain(df, "k.1", "p")









    Out[76]:





0.4810119039604144



In [77]:

    
# Lets see the information gain for the SPORE-PRINT-COLOR
info.information_gain(df, "p.1", "p")









    Out[77]:





0.9060569015595047



In [ ]:

    
# => We see that the best information gain, checking these 3 features,  comes from teh odor.
# this is the most informative attribute
# If we were about to build a classification tree, this should be the top node.

	p	x	s	n	t	p.1	f	c	n.1	k	...	s.2	w	w.1	p.2	w.2	o	p.3	k.1	s.3	u
0	e	x	s	y	t	a	f	c	b	k	...	s	w	w	p	w	o	p	n	n	g
1	e	b	s	w	t	l	f	c	b	n	...	s	w	w	p	w	o	p	n	n	m
2	p	x	y	w	t	p	f	c	n	n	...	s	w	w	p	w	o	p	k	s	u

	p	x	s	n	t	p.1	f	c	n.1	k	...	s.2	w	w.1	p.2	w.2	o	p.3	k.1	s.3	u
0	e	x	s	y	t	a	f	c	b	k	...	s	w	w	p	w	o	p	n	n	g
1	e	b	s	w	t	l	f	c	b	n	...	s	w	w	p	w	o	p	n	n	m
2	p	x	y	w	t	p	f	c	n	n	...	s	w	w	p	w	o	p	k	s	u

	p	x	s	n	t	p.1	f	c	n.1	k	...	s.2	w	w.1	p.2	w.2	o	p.3	k.1	s.3	u
0	e	x	s	y	t	a	f	c	b	k	...	s	w	w	p	w	o	p	n	n	g
1	e	b	s	w	t	l	f	c	b	n	...	s	w	w	p	w	o	p	n	n	m
2	p	x	y	w	t	p	f	c	n	n	...	s	w	w	p	w	o	p	k	s	u