ArbitraryDiscretiser

The ArbitraryDiscretiser() divides continuous numerical variables into contiguous intervals are arbitrarily entered by the user.

The user needs to enter a dictionary with variable names as keys, and a list of the limits of the intervals as values. For example {'var1': [0, 10, 100, 1000], 'var2': [5, 10, 15, 20]}.

Note

For this demonstration, we use the Ames House Prices dataset produced by Professor Dean De Cock:

Dean De Cock (2011) Ames, Iowa: Alternative to the Boston Housing Data as an End of Semester Regression Project, Journal of Statistics Education, Vol.19, No. 3

http://jse.amstat.org/v19n3/decock.pdf

https://www.tandfonline.com/doi/abs/10.1080/10691898.2011.11889627

The version of the dataset used in this notebook can be obtained from Kaggle

In [1]:
import pandas as pd
import numpy as np
import matplotlib.pyplot as plt

from sklearn.model_selection import train_test_split

from feature_engine.discretisation import ArbitraryDiscretiser
plt.rcParams["figure.figsize"] = [15,5]
In [2]:
data = pd.read_csv('housing.csv')
data.head()
Out[2]:
Id MSSubClass MSZoning LotFrontage LotArea Street Alley LotShape LandContour Utilities ... PoolArea PoolQC Fence MiscFeature MiscVal MoSold YrSold SaleType SaleCondition SalePrice
0 1 60 RL 65.0 8450 Pave NaN Reg Lvl AllPub ... 0 NaN NaN NaN 0 2 2008 WD Normal 208500
1 2 20 RL 80.0 9600 Pave NaN Reg Lvl AllPub ... 0 NaN NaN NaN 0 5 2007 WD Normal 181500
2 3 60 RL 68.0 11250 Pave NaN IR1 Lvl AllPub ... 0 NaN NaN NaN 0 9 2008 WD Normal 223500
3 4 70 RL 60.0 9550 Pave NaN IR1 Lvl AllPub ... 0 NaN NaN NaN 0 2 2006 WD Abnorml 140000
4 5 60 RL 84.0 14260 Pave NaN IR1 Lvl AllPub ... 0 NaN NaN NaN 0 12 2008 WD Normal 250000

5 rows × 81 columns

In [3]:
# let's separate into training and testing set
X = data.drop(["Id", "SalePrice"], axis=1)
y = data.SalePrice

X_train, X_test, y_train, y_test = train_test_split(
    X, y, test_size=0.3, random_state=0)

print("X_train :", X_train.shape)
print("X_test :", X_test.shape)
X_train : (1022, 79)
X_test : (438, 79)
In [4]:
# we will discretise two continuous variables

X_train[["LotArea", 'GrLivArea']].hist(bins=50)
plt.show()

The ArbitraryDiscretiser() works only with numerical variables. The discretiser will check if the dictionary entered by the user contains variables present in the training set, and if these variables are cast as numerical, before doing any transformation.

Then it transforms the variables, that is, it sorts the values into the intervals, transform.

In [5]:
'''
Parameters
----------

binning_dict : dict
    The dictionary with the variable : interval limits pairs, provided by the user.
    A valid dictionary looks like this:

     binning_dict = {'var1':[0, 10, 100, 1000], 'var2':[5, 10, 15, 20]}.

return_object : bool, default=False
    Whether the numbers in the discrete variable should be returned as
    numeric or as object. The decision is made by the user based on
    whether they would like to proceed the engineering of the variable as
    if it was numerical or categorical.

return_boundaries: bool, default=False
    whether the output should be the interval boundaries. If True, it returns
    the interval boundaries. If False, it returns integers.
'''

atd = ArbitraryDiscretiser(binning_dict={"LotArea":[-np.inf,4000,8000,12000,16000,20000,np.inf],
                                        "GrLivArea":[-np.inf,500,1000,1500,2000,2500,np.inf]})

atd.fit(X_train)
Out[5]:
ArbitraryDiscretiser(binning_dict={'GrLivArea': [-inf, 500, 1000, 1500, 2000,
                                                 2500, inf],
                                   'LotArea': [-inf, 4000, 8000, 12000, 16000,
                                               20000, inf]},
                     return_boundaries=False, return_object=False)
In [6]:
# binner_dict contains the boundaries of the different bins
atd.binner_dict_
Out[6]:
{'LotArea': [-inf, 4000, 8000, 12000, 16000, 20000, inf],
 'GrLivArea': [-inf, 500, 1000, 1500, 2000, 2500, inf]}
In [7]:
train_t = atd.transform(X_train)
test_t = atd.transform(X_test)
In [8]:
# the below are the bins into which the observations were sorted
print(train_t['GrLivArea'].unique())
print(train_t['LotArea'].unique())
[4 2 1 0 3 5]
[2 0 1 3 5 4]
In [9]:
# here I put side by side the original variable and the transformed variable
tmp = pd.concat([X_train[["LotArea", 'GrLivArea']], train_t[["LotArea", 'GrLivArea']]], axis=1)
tmp.columns = ["LotArea", 'GrLivArea',"LotArea_binned", 'GrLivArea_binned']
tmp.head()
Out[9]:
LotArea GrLivArea LotArea_binned GrLivArea_binned
64 9375 2034 2 4
682 2887 1291 0 2
960 7207 858 1 1
1384 9060 1258 2 2
1100 8400 438 2 0
In [10]:
plt.subplot(1,2,1)
tmp.groupby('GrLivArea_binned')['GrLivArea'].count().plot.bar()
plt.ylabel('Number of houses')
plt.title('Number of observations per bin')
plt.subplot(1,2,2)
tmp.groupby('LotArea_binned')['LotArea'].count().plot.bar()
plt.ylabel('Number of houses')
plt.title('Number of observations per bin')

plt.show()

Now return interval boundaries instead

In [11]:
atd = ArbitraryDiscretiser(binning_dict={"LotArea": [-np.inf, 4000, 8000, 12000, 16000, 20000, np.inf],
                                         "GrLivArea": [-np.inf, 500, 1000, 1500, 2000, 2500, np.inf]},
                           # to return the boundary limits
                           return_boundaries=True)

atd.fit(X_train)
Out[11]:
ArbitraryDiscretiser(binning_dict={'GrLivArea': [-inf, 500, 1000, 1500, 2000,
                                                 2500, inf],
                                   'LotArea': [-inf, 4000, 8000, 12000, 16000,
                                               20000, inf]},
                     return_boundaries=True, return_object=False)
In [12]:
train_t = atd.transform(X_train)
test_t = atd.transform(X_test)
In [13]:
# the numbers are the different bins into which the observations
# were sorted
np.sort(np.ravel(train_t['GrLivArea'].unique()))
Out[13]:
array([Interval(-inf, 500.0, closed='right'),
       Interval(500.0, 1000.0, closed='right'),
       Interval(1000.0, 1500.0, closed='right'),
       Interval(1500.0, 2000.0, closed='right'),
       Interval(2000.0, 2500.0, closed='right'),
       Interval(2500.0, inf, closed='right')], dtype=object)
In [14]:
np.sort(np.ravel(test_t['GrLivArea'].unique()))
Out[14]:
array([Interval(500.0, 1000.0, closed='right'),
       Interval(1000.0, 1500.0, closed='right'),
       Interval(1500.0, 2000.0, closed='right'),
       Interval(2000.0, 2500.0, closed='right'),
       Interval(2500.0, inf, closed='right')], dtype=object)
In [15]:
# bar plot to show the intervals returned by the transformer
test_t.LotArea.value_counts(sort=False).plot.bar(figsize=(6,4))
plt.ylabel('Number of houses')
plt.title('Number of houses per interval')
plt.show()
In [ ]: