Formulas for woe and iv:

Code to achieve this:

import numpy as np
import pandas as pd
np.random.seed(100)


df = pd.DataFrame({'grade': np.random.choice(list('ABCD'),size=(20)),
                   'pass': np.random.choice([0,1],size=(20))
})

feature,target = 'grade','pass'
df_woe_iv = (pd.crosstab(df[feature],df[target],
                      normalize='columns')
             .assign(woe=lambda dfx: np.log(dfx[1] / dfx[0]))
             .assign(iv=lambda dfx: np.sum(dfx['woe']*
                                           (dfx[1]-dfx[0]))))

df_woe_iv

output

pass     0    1       woe        iv
grade                              
A      0.3  0.3  0.000000  0.690776
B      0.1  0.1  0.000000  0.690776
C      0.2  0.5  0.916291  0.690776
D      0.4  0.1 -1.386294  0.690776

Weight of Evidence (WOE)

The weight of evidence tells the predictive power of an independent variable in relation to the dependent variable. Since it evolved from the credit scoring world, it is generally described as a measure of the separation of good and bad customers. "Bad Customers" refers to the customers who defaulted on a loan. and "Good Customers" refers to the customers who paid back loans.

Many people do not understand the terms goods/bads as they are from a different background than the credit risk. It's good to understand the concept of WOE in terms of events and non-events. It is calculated by taking the natural logarithm (log to base e) of the division of % of non-events and % of events.

Information value

Information value is one of the most useful techniques to select important variables in a predictive model. It helps to rank variables on the basis of their importance. The IV is calculated using the following formula :

Mode detailed explanation at WEIGHT OF EVIDENCE (WOE) AND INFORMATION VALUE (IV) EXPLAINED

Python Implementation

def iv_woe(data, target, bins=10, show_woe=False):
    
    #Empty Dataframe
    newDF,woeDF = pd.DataFrame(), pd.DataFrame()
    
    #Extract Column Names
    cols = data.columns
    
    #Run WOE and IV on all the independent variables
    for ivars in cols[~cols.isin([target])]:
        if (data[ivars].dtype.kind in 'bifc') and (len(np.unique(data[ivars]))>10):
            binned_x = pd.qcut(data[ivars], bins,  duplicates='drop')
            d0 = pd.DataFrame({'x': binned_x, 'y': data[target]})
        else:
            d0 = pd.DataFrame({'x': data[ivars], 'y': data[target]})

        
        # Calculate the number of events in each group (bin)
        d = d0.groupby("x", as_index=False).agg({"y": ["count", "sum"]})
        d.columns = ['Cutoff', 'N', 'Events']
        
        # Calculate % of events in each group.
        d['% of Events'] = np.maximum(d['Events'], 0.5) / d['Events'].sum()

        # Calculate the non events in each group.
        d['Non-Events'] = d['N'] - d['Events']
        # Calculate % of non events in each group.
        d['% of Non-Events'] = np.maximum(d['Non-Events'], 0.5) / d['Non-Events'].sum()

        # Calculate WOE by taking natural log of division of % of non-events and % of events
        d['WoE'] = np.log(d['% of Events']/d['% of Non-Events'])
        d['IV'] = d['WoE'] * (d['% of Events'] - d['% of Non-Events'])
        d.insert(loc=0, column='Variable', value=ivars)
        print("Information value of " + ivars + " is " + str(round(d['IV'].sum(),6)))
        temp =pd.DataFrame({"Variable" : [ivars], "IV" : [d['IV'].sum()]}, columns = ["Variable", "IV"])
        newDF=pd.concat([newDF,temp], axis=0)
        woeDF=pd.concat([woeDF,d], axis=0)

        #Show WOE Table
        if show_woe == True:
            print(d)
    return newDF, woeDF