Weight of Evidence & Information Value

References

• https://documentation.sas.com/doc/en/vdmmlcdc/8.1/casstat/viyastat_binning_details02.htm

• https://mightypy.readthedocs.io/

• https://www.listendata.com/2015/03/weight-of-evidence-woe-and-information.html

Weight of evidence

• Generally measure of separation

• measure how much evidence supports or undermines the hypothesis

The information value (IV) is a weighted sum of the WOE of the characteristic’s attributes. The weight is the difference between the conditional probability of an attribute for an event and the conditional probability of that attribute for a nonevent.

\begin{align*} \text{Weight of Evidence} &= \ln{(\frac{\text{% of non-event}}{\text{% of event}})} = \ln{\frac{\text{% of y = 0}}{\text{% of y = 1}}}\\ \\ \text{Information Value} &= \sum{(\text{% of non-event} - \text{% of event})} * \text{WOE} \end{align*}

Information Value	Variable Predictiveness
Less than 0.02	Not useful for prediction
0.02 to 0.1	Weak predictive Power
0.1 to 0.3	Medium predictive Power
0.3 to 0.5	Strong predictive Power
>0.5	Suspicious Predictive Power

from sklearn.datasets import load_breast_cancer
from mightypy.stats import WOE_IV
import pandas as pd

import matplotlib.pyplot as plt

dataset = load_breast_cancer(as_frame=True)

df = dataset.frame
df.head(3)

	mean radius	mean texture	mean perimeter	mean area	mean smoothness	mean compactness	mean concavity	mean concave points	mean symmetry	mean fractal dimension	...	worst texture	worst perimeter	worst area	worst smoothness	worst compactness	worst concavity	worst concave points	worst symmetry	worst fractal dimension	target
0	17.99	10.38	122.8	1001.0	0.11840	0.27760	0.3001	0.14710	0.2419	0.07871	...	17.33	184.6	2019.0	0.1622	0.6656	0.7119	0.2654	0.4601	0.11890	0
1	20.57	17.77	132.9	1326.0	0.08474	0.07864	0.0869	0.07017	0.1812	0.05667	...	23.41	158.8	1956.0	0.1238	0.1866	0.2416	0.1860	0.2750	0.08902	0
2	19.69	21.25	130.0	1203.0	0.10960	0.15990	0.1974	0.12790	0.2069	0.05999	...	25.53	152.5	1709.0	0.1444	0.4245	0.4504	0.2430	0.3613	0.08758	0

3 rows × 31 columns

target_map = {0: 'False', 1: 'True'}

df.insert(loc=df.shape[1], column='label', value=df['target'].map(target_map))

woe_iv_obj = WOE_IV(event='True', non_event='False', target_col='label',bucket_col='mean smoothness')

woe, iv = woe_iv_obj.values(df)

woe

label	False	True	adj_event	adj_non_event	%_event_True	%_non_event_False	woe	iv
buckets_mean smoothness
(0.0516, 0.0797]	3	54	54	3	0.151261	0.014151	-2.369222	0.324843
(0.0797, 0.0842]	10	47	47	10	0.131653	0.047170	-1.026413	0.086714
(0.0842, 0.0879]	9	48	48	9	0.134454	0.042453	-1.152827	0.106061
(0.0879, 0.0918]	21	36	36	21	0.100840	0.099057	-0.017847	0.000032
(0.0918, 0.0959]	22	35	35	22	0.098039	0.103774	0.056844	0.000326
(0.0959, 0.0993]	23	33	33	23	0.092437	0.108491	0.160136	0.002571
(0.0993, 0.103]	25	32	32	25	0.089636	0.117925	0.274289	0.007759
(0.103, 0.108]	30	30	30	30	0.084034	0.141509	0.521150	0.029953
(0.108, 0.115]	32	22	22	32	0.061625	0.150943	0.895843	0.080016
(0.115, 0.163]	37	20	20	37	0.056022	0.174528	1.136335	0.134662

iv

0.7729378109850594

fig = woe_iv_obj.plot(figsize=(15,6))
fig.tight_layout();