In [1]:

    

%matplotlib inline
import matplotlib.pyplot as plt
import numpy as np
import pandas as pd
import lifelines


    

In [2]:

    

%pylab inline
pylab.rcParams['figure.figsize'] = (14, 9)


    

    




Populating the interactive namespace from numpy and matplotlib

In [3]:

    

from lifetimes.datasets import load_cdnow


    

In [4]:

    

data = load_cdnow(index_col=[0])


    

In [5]:

    

data.head()


    

    
Out[5]:






  

    

      

      
frequency
      
recency
      
T
    
    

      
ID
      

      

      

    
  
  

    

      
1
      
2
      
30.43
      
38.86
    
    

      
2
      
1
      
1.71
      
38.86
    
    

      
3
      
0
      
0.00
      
38.86
    
    

      
4
      
0
      
0.00
      
38.86
    
    

      
5
      
0
      
0.00
      
38.86
    
  

In [6]:

    

from lifetimes import BetaGeoFitter


    

In [7]:

    

bgf = BetaGeoFitter(penalizer_coef=0.0)


    

In [8]:

    

bgf.fit(data['frequency'], data['recency'], data['T'])


    

    
Out[8]:





<lifetimes.BetaGeoFitter: fitted with 2357 subjects, a: 0.79, alpha: 4.41, b: 2.43, r: 0.24>

In [9]:

    

from lifetimes.plotting import plot_frequency_recency_matrix


    

In [10]:

    

plot_frequency_recency_matrix(bgf)


    

    
Out[10]:





<matplotlib.axes._subplots.AxesSubplot at 0x10e334710>






    

In [11]:

    

from lifetimes.plotting import plot_probability_alive_matrix


    

In [12]:

    

plot_probability_alive_matrix(bgf)


    

    
Out[12]:





<matplotlib.axes._subplots.AxesSubplot at 0x10e334828>






    

In [13]:

    

t = 1


    

In [14]:

    

data['predicted_purchases'] = bgf.conditional_expected_number_of_purchases_up_to_time(t, data['frequency'], data['recency'], data['T'])


    

In [15]:

    

data.sort_values(by='predicted_purchases').tail(5)


    

    
Out[15]:






  

    

      

      
frequency
      
recency
      
T
      
predicted_purchases
    
    

      
ID
      

      

      

      

    
  
  

    

      
509
      
18
      
35.14
      
35.86
      
0.424877
    
    

      
841
      
19
      
34.00
      
34.14
      
0.474738
    
    

      
1981
      
17
      
28.43
      
28.86
      
0.486526
    
    

      
157
      
29
      
37.71
      
38.00
      
0.662396
    
    

      
1516
      
26
      
30.86
      
31.00
      
0.710623
    
  

In [16]:

    

from lifetimes.plotting import plot_period_transactions


    

In [17]:

    

plot_period_transactions(bgf)


    

    
Out[17]:





<matplotlib.axes._subplots.AxesSubplot at 0x111bc1a58>






    

In [18]:

    

from lifetimes.datasets import load_transaction_data
from lifetimes.utils import summary_data_from_transaction_data


    

In [19]:

    

transaction_data = load_transaction_data()


    

In [20]:

    

transaction_data.head()


    

    
Out[20]:






  

    

      

      
date
      
id
    
  
  

    

      
0
      
2014-03-08 00:00:00
      
0
    
    

      
1
      
2014-05-21 00:00:00
      
1
    
    

      
2
      
2014-03-14 00:00:00
      
2
    
    

      
3
      
2014-04-09 00:00:00
      
2
    
    

      
4
      
2014-05-21 00:00:00
      
2
    
  

In [21]:

    

summary = summary_data_from_transaction_data(transaction_data, 'id', 'date', observation_period_end='2014-12-31')


    

In [22]:

    

summary.head()


    

    
Out[22]:






  

    

      

      
frequency
      
recency
      
T
    
    

      
id
      

      

      

    
  
  

    

      
0
      
0.0
      
0.0
      
298.0
    
    

      
1
      
0.0
      
0.0
      
224.0
    
    

      
2
      
6.0
      
142.0
      
292.0
    
    

      
3
      
0.0
      
0.0
      
147.0
    
    

      
4
      
2.0
      
9.0
      
183.0
    
  

In [23]:

    

bgf.fit(summary['frequency'], summary['recency'], summary['T'])


    

    
Out[23]:





<lifetimes.BetaGeoFitter: fitted with 5000 subjects, a: 1.83, alpha: 1.17, b: 3.33, r: 0.16>

In [24]:

    

from lifetimes.utils import calibration_and_holdout_data


    

In [25]:

    

summary_cal_holdout = calibration_and_holdout_data(transaction_data, 'id', 'date',
                                        calibration_period_end='2014-09-01',
                                        observation_period_end='2014-12-31' )


    

In [26]:

    

summary_cal_holdout.head()


    

    
Out[26]:






  

    

      

      
frequency_cal
      
recency_cal
      
T_cal
      
frequency_holdout
      
duration_holdout
    
    

      
id
      

      

      

      

      

    
  
  

    

      
0
      
0.0
      
0.0
      
177.0
      
0.0
      
121
    
    

      
1
      
0.0
      
0.0
      
103.0
      
0.0
      
121
    
    

      
2
      
6.0
      
142.0
      
171.0
      
0.0
      
121
    
    

      
3
      
0.0
      
0.0
      
26.0
      
0.0
      
121
    
    

      
4
      
2.0
      
9.0
      
62.0
      
0.0
      
121
    
  

In [27]:

    

from lifetimes.plotting import plot_calibration_purchases_vs_holdout_purchases


    

In [28]:

    

bgf.fit(summary_cal_holdout['frequency_cal'], summary_cal_holdout['recency_cal'], summary_cal_holdout['T_cal'])


    

    




/Users/flavio.clesio/anaconda/lib/python3.5/site-packages/lifetimes/estimation.py:578: RuntimeWarning: invalid value encountered in log
  A_4 = log(a) - log(b + freq - 1) - (r + freq) * log(rec + alpha)






    
Out[28]:





<lifetimes.BetaGeoFitter: fitted with 5000 subjects, a: 1.90, alpha: 1.38, b: 3.52, r: 0.18>

In [29]:

    

plot_calibration_purchases_vs_holdout_purchases(bgf, summary_cal_holdout)


    

    
Out[29]:





<matplotlib.axes._subplots.AxesSubplot at 0x1120a3eb8>






    

In [30]:

    

t = 10 #predict purchases in 10 periods


    

In [31]:

    

individual = summary.iloc[20]


    

In [32]:

    

# The below function is an alias to `bfg.conditional_expected_number_of_purchases_up_to_time`
bgf.predict(t, individual['frequency'], individual['recency'], individual['T'])
# 0.0576511


    

    
Out[32]:





0.058884087242359336

In [33]:

    

from lifetimes.plotting import plot_history_alive


    

In [34]:

    

id = 35
days_since_birth = 200


    

In [35]:

    

sp_trans = transaction_data.ix[transaction_data['id'] == id]


    

In [36]:

    

plot_history_alive(bgf, days_since_birth, sp_trans, 'date')


    

    




/Users/flavio.clesio/anaconda/lib/python3.5/site-packages/lifetimes/plotting.py:203: FutureWarning: how in .resample() is deprecated
the new syntax is .resample(...).sum()
  customer_history = customer_history.resample(freq, how='sum').reset_index()
/Users/flavio.clesio/anaconda/lib/python3.5/site-packages/lifetimes/utils.py:209: FutureWarning: how in .resample() is deprecated
the new syntax is .resample(...).sum()
  purchase_history = customer_history.resample(freq, how='sum').fillna(0)['transactions'].values






    
Out[36]:





<matplotlib.axes._subplots.AxesSubplot at 0x111f1f518>






    

In [37]:

    

from lifetimes.datasets import load_summary_data_with_monetary_value


    

In [38]:

    

summary_with_money_value = load_summary_data_with_monetary_value()


    

In [39]:

    

summary_with_money_value.head()


    

    
Out[39]:






  

    

      

      
frequency
      
recency
      
T
      
monetary_value
    
    

      
customer_id
      

      

      

      

    
  
  

    

      
1
      
2
      
30.43
      
38.86
      
22.35
    
    

      
2
      
1
      
1.71
      
38.86
      
11.77
    
    

      
3
      
0
      
0.00
      
38.86
      
0.00
    
    

      
4
      
0
      
0.00
      
38.86
      
0.00
    
    

      
5
      
0
      
0.00
      
38.86
      
0.00
    
  

In [40]:

    

returning_customers_summary = summary_with_money_value[summary_with_money_value['frequency']>0]


    

In [41]:

    

returning_customers_summary.head()


    

    
Out[41]:






  

    

      

      
frequency
      
recency
      
T
      
monetary_value
    
    

      
customer_id
      

      

      

      

    
  
  

    

      
1
      
2
      
30.43
      
38.86
      
22.35
    
    

      
2
      
1
      
1.71
      
38.86
      
11.77
    
    

      
6
      
7
      
29.43
      
38.86
      
73.74
    
    

      
7
      
1
      
5.00
      
38.86
      
11.77
    
    

      
9
      
2
      
35.71
      
38.86
      
25.55
    
  

In [42]:

    

returning_customers_summary[['monetary_value', 'frequency']].corr()


    

    
Out[42]:






  

    

      

      
monetary_value
      
frequency
    
  
  

    

      
monetary_value
      
1.000000
      
0.113884
    
    

      
frequency
      
0.113884
      
1.000000
    
  

In [43]:

    

from lifetimes import GammaGammaFitter


    

In [44]:

    

ggf = GammaGammaFitter(penalizer_coef = 0)


    

In [45]:

    

ggf.fit(returning_customers_summary['frequency'],
        returning_customers_summary['monetary_value'])


    

    
Out[45]:





<lifetimes.GammaGammaFitter: fitted with 946 subjects, p: 6.25, q: 3.74, v: 15.45>

In [46]:

    

print (ggf)


    

    




<lifetimes.GammaGammaFitter: fitted with 946 subjects, p: 6.25, q: 3.74, v: 15.45>

In [47]:

    

print (ggf.conditional_expected_average_profit(
        summary_with_money_value['frequency'],
        summary_with_money_value['monetary_value']
    ).head())


    

    




customer_id
1    24.658612
2    18.911468
3    35.171004
4    35.171004
5    35.171004
dtype: float64

In [48]:

    

print ("Expected conditional average profit: %s, Average profit: %s" % (
    ggf.conditional_expected_average_profit(
        summary_with_money_value['frequency'],
        summary_with_money_value['monetary_value']
    ).mean(),
    summary_with_money_value[summary_with_money_value['frequency']>0]['monetary_value'].mean()
))


    

    




Expected conditional average profit: 35.252959401290916, Average profit: 35.07855179704026

In [49]:

    

bgf.fit(summary_with_money_value['frequency'], summary_with_money_value['recency'], summary_with_money_value['T'])


    

    
Out[49]:





<lifetimes.BetaGeoFitter: fitted with 2357 subjects, a: 0.79, alpha: 4.41, b: 2.43, r: 0.24>

In [50]:

    

print (ggf.customer_lifetime_value(
    bgf, #the model to use to predict the number of future transactions
    summary_with_money_value['frequency'],
    summary_with_money_value['recency'],
    summary_with_money_value['T'],
    summary_with_money_value['monetary_value'],
    time=12, # months
    discount_rate=0.01 # monthly discount rate ~ 12.7% annually
).head(10))


    

    




customer_id
1      140.096077
2       18.943516
3       38.180469
4       38.180469
5       38.180469
6     1003.864008
7       28.109749
8       38.180469
9      167.418044
10      38.180469
Name: clv, dtype: float64

In [ ]: