#!/usr/bin/env python
# coding: utf-8

# # Exercise 10- CostSensitive Churn
# 
# [paper](http://download.springer.com/static/pdf/125/art%253A10.1186%252Fs40165-015-0014-6.pdf?originUrl=http%3A%2F%2Fdecisionanalyticsjournal.springeropen.com%2Farticle%2F10.1186%2Fs40165-015-0014-6&token2=exp=1462974790~acl=%2Fstatic%2Fpdf%2F125%2Fart%25253A10.1186%25252Fs40165-015-0014-6.pdf*~hmac=05041d990b7e5a5e70d6efc1fbb29c2a380465c6edc84be1feda1b6d49588a1a)
# [slides](http://www.slideshare.net/albahnsen/maximizing-a-churn-campaigns-profitability-with-cost-sensitive-predictive-analytics)
# 
# Customer churn predictive modeling deals with predicting the probability of a customer defecting 
# using historical, behavioral and socio-economical information. This tool is of great benefit to 
# subscription based companies allowing them to maximize the results of retention campaigns. The 
# problem of churn predictive modeling has been widely studied by the data mining and machine learning
# communities. It is usually tackled by using classification algorithms in order to learn the 
# different patterns of both the churners and non-churners. Nevertheless, current state-of-the-art 
# classification algorithms are not well aligned with commercial goals, in the sense that, the models 
# miss to include the real financial costs and benefits during the training and evaluation phases. In 
# the case of churn, evaluating a model based on a traditional measure such as accuracy or predictive 
# power, does not yield to the best results when measured by the actual financial cost, i.e., 
# investment per subscriber on a loyalty campaign and the financial impact of failing to detect a 
# real churner versus wrongly predicting a non-churner as a churner.
# 

# The two main objectives of subscription-based companies are to  acquire new subscribers and 
# retain those they already have, mainly because profits are directly linked with the number of 
# subscribers.  In order to maximize the profit, companies must increase the customer base by 
# incrementing sales  while decreasing the number of churners. Furthermore, it is common knowledge 
# that retaining a  customer is about five times less expensive than acquiring a new one , this creates  pressure to have better and more effective churn campaigns.
# 
# A typical churn campaign consists in identifying from the current customer base which ones are 
# more likely to leave the company, and make an offer in order to avoid that behavior.
# With this in mind the companies use intelligence to create and improve retention and collection
# strategies. In the first case, this usually implies an offer that can be either a discount or a 
# free upgrade during certain span of time. In both cases the company has to 	assume a cost for that 
# offer, therefore, accurate prediction of the churners becomes important. The logic of this flow is 
# shown in the following figure.

# ![fig1](../notebooks/images/ch5_fig1.png)

# The churn campaign process starts with the sales that every month increase the customer 
# base, however, monthly there is a group of customers that decide to leave the company for many 
# reasons. Then the objective of a churn model is to identify those customers before they take the 
# decision of defecting.
# 
# Using a churn model, those customers more likely to leave are predicted as churners and 
# an offer is made in order to retain them. However, it is known that not all customers will accept 
# the offer, in the case when a customer is planning to defect, it is possible that the offer is not 
# good enough to retain him or that the reason for defecting can not be influenced by an offer.
# Using historical information, it is estimated that a customer will accept the offer with 
# probability $\gamma$.
# On the other hand, there is the case in which the churn model misclassified a non-churner as 
# churner, also known as false positives, in that case the customer will always accept the offer that 
# means and additional cost to the company since those misclassified customers do not have the 
# intentions of leaving.
# 
# In the case were the churn model predicts customers as non-churners, there is also the possibility 
# of a misclassification, in this case an actual churner is predicted as non-churner, since 
# these customers do not receive an offer and they will leave the company, these cases are known as 
# false negatives. Lastly, there is the case were the customers are actually non-churners, then 
# there is no need to make a retention offer to these customers since they will continue to be part 
# of the customer base.
# 
# It can be seen that a churn campaign (or churn model) has three main points. First, avoid false 
# positives since there is a financial cost of making an offer where it is not needed. Second, find 
# the right offer to give to those customers identified as churners. And lastly, to decrease 
# the number of false negatives.

# In the following figure, the financial impact of a churn model is shown. 

# ![fig1](../notebooks/images/ch5_fig2.png)

# Note than we take 
# into account the costs and not the profit in each case.
# When a customer is predicted to be a churner, an offer is made with the objective of avoiding 
# the customer defecting. However, if a customer is actually a churner, he may or not accept the 
# offer with a probability $\gamma_i$. If the customer accepts the offer, the financial impact is 
# equal to the cost of the offer ($C_{o_i}$) plus the administrative cost of contacting the 
# customer ($C_a$). On the other hand, if the customer declines the offer, the cost is the 
# expected 	income that the clients would otherwise generate, also called customer lifetime value 
# ($CLV_i$), 	plus $C_a$. Lastly, if the customer is not actually a churner, he will be happy to 
# accept the 	offer and the cost will be $C_{o_i}$ plus $C_a$.
# 	
# In the case that the customer is predicted as non-churner, there are two possible outcomes. 
# Either the customer is not a churner, then the cost is zero, or the customer is a churner and the 
# cost is $CLV_i$. 

# 
# 
# |  	| Actual Positive ($y_i=1$)  	|  Actual Negative 	($y_i=0$)|
# |---	|:-:	|:-:	|
# |   Predicted Positive ($c_i=1$)	|   $C_{TP_i}=\gamma_iC_{o_i}+(1-\gamma_i)(CLV_i+C_a)$	| $C_{FP_i}=C_{o_i}+C_a$ |
# |  Predicted Negative  ($c_i=0$) 	|   $C_{FN_i}=CLV_i$	| $C_{TN_i}=0$	|

# In[1]:


import pandas as pd
import numpy as np


# In[2]:


import zipfile
with zipfile.ZipFile('../datasets/cost_sensitive_classification_churn.csv.zip', 'r') as z:
    f = z.open('cost_sensitive_classification_churn.csv')
    data = pd.read_csv(f, index_col=0)


# In[3]:


data.head()


# In[4]:


data.target.value_counts(normalize=True)


# In[5]:


X =data[['x'+str(i) for i in range(1, 47)]]
y = data.target
cost_mat = data[['C_FP','C_FN','C_TP','C_TN']].values


# In[6]:


from  sklearn.cross_validation import train_test_split
temp = train_test_split(X, y, cost_mat, test_size=0.33, random_state=42)
X_train, X_test, y_train, y_test, cost_mat_train, cost_mat_test = temp


# # Exercice 10.1
# 
# 
# * Train 4 different models to predict target (Churn) using x1-x46 as features
# 1. Logistic Regression
# 2. Ensemble
# 3. Under-sampling LR
# 4. Under-sampling Ensemble

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# # Exercice 10.2
# 
# * Calculate the savings of the different models
# * Compare F1Score and Savings

# In[ ]:





# # Exercice 10.3
# 
# Using the probabilities of each model estimate a BMR classifier
# 
# Compare the savings and F1Score

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# # Exercice 10.4
# 
# Estimate a CostSensitiveDecisionTreeClassifier

# In[ ]: