6.3.8. Cell2Cell Customer Churn

6.3.8.1. Summary

Customer data of the US wireless operator Cell2Cell, released for the churn modelling tournament of the Teradata Center for Customer Relationship Management at Duke University. It is the “Duke” data that runs through the profit-driven churn literature [1] [2] [3]. Each row is a subscriber, described by usage, call quality, handset, household and retention-contact variables, with a label indicating whether they churned.

The Duke center no longer distributes the data, so Empulse downloads the cell2celltrain.csv file from a public GitHub mirror, pinned to a fixed commit. The 156 customers without a MonthlyRevenue are dropped.

Classes	2
Churners	14641
Non-churners	36250
Samples	50891
Features	56

6.3.8.2. Using the Dataset

The dataset is fetched through fetch_cell2cell. It is downloaded on first use and cached under ~/empulse_data (override with $EMPULSE_DATA_HOME or the data_home argument), so later calls work offline.

It returns a Dataset object with the following attributes:

• data: the feature matrix

• target: the target vector

• cost_matrix: a CostMatrix with default values pre-filled

• instance_costs: a dict of per-instance cost drivers ('monthly_revenue')

• feature_names: the feature names

• target_names: the target names

• DESCR: the full description of the dataset

import pandas as pd
from empulse.datasets import fetch_cell2cell

dataset = fetch_cell2cell(backend=pd)
X, y = dataset.data, dataset.target

The backend argument selects the dataframe library used for data and target. Pass the module itself — backend=pd for pandas or backend=pl for polars.

A few numeric features have missing values, and the categorical features need encoding. Pass the cost matrix to the model as a Metric loss, and hand it the monthly revenue at fit time:

from empulse.metrics import Metric, Cost
from empulse.models import CSLogitClassifier
from sklearn.compose import ColumnTransformer
from sklearn.impute import SimpleImputer
from sklearn.pipeline import Pipeline, make_pipeline
from sklearn.preprocessing import StandardScaler, TargetEncoder

numeric = X.select_dtypes(include=['number']).columns
categorical = X.select_dtypes(exclude=['number']).columns

pipeline = Pipeline([
    ('preprocessor', ColumnTransformer([
        ('num', make_pipeline(SimpleImputer(strategy='median'), StandardScaler()), numeric),
        ('cat', make_pipeline(
            SimpleImputer(strategy='constant', fill_value='missing'),
            TargetEncoder(),
        ), categorical),
    ])),
    ('model', CSLogitClassifier(loss=Metric(dataset.cost_matrix, Cost()))),
])
pipeline.fit(X, y, model__monthly_revenue=dataset.instance_costs['monthly_revenue'])

6.3.8.3. Cost Matrix

The cost matrix is the churn retention matrix of Verbraken et al. [4], the framing every paper above uses for this data. Contacting a customer costs a fixed amount \(f\), whether or not they accept. A contacted churner accepts the retention offer with probability \(\gamma\), in which case their value is retained minus the incentive, a fraction \(d\) of that value. A churner who is not contacted simply leaves, which costs the campaign nothing.

	Actual churner \(y_i = 1\)	Actual non-churner \(y_i = 0\)
Predicted churner \(\hat{y}_i = 1\)	tp_benefit \(= \gamma (CLV_i - d \cdot CLV_i - f) - (1-\gamma) f\)	fp_cost \(= d \cdot CLV_i + f\)
Predicted non-churner \(\hat{y}_i = 0\)	fn_cost \(= 0\)	tn_benefit \(= 0\)

The papers use a single average lifetime value of 200 for every customer [1]. This version of the data records each customer’s monthly revenue, so Empulse makes the lifetime value instance-dependent by counting \(m\) months of it:

\[CLV_i = m \cdot \max(MonthlyRevenue_i, 0)\]

The 3 customers with a negative revenue (net credits) get a lifetime value of 0: a customer who costs money has nothing to retain.

The symbolic parameters carry these defaults, and can be overridden by passing their alias:

Alias	Default	Meaning
clv_months (\(m\))	12	Months of revenue counted as lifetime value
accept_rate (\(\gamma\))	0.3	Probability a contacted churner accepts the offer, the mean of the Beta(6, 14) distribution used by the expected maximum profit measure
incentive_fraction (\(d\))	0.05	Retention incentive as a fraction of CLV, as an incentive of 10 on a CLV of 200 in Verbeke et al. [1]
contact_cost (\(f\))	1	Cost of contacting a customer, as an absolute amount

y_score = pipeline.predict_proba(X)[:, 1]

cost = Metric(dataset.cost_matrix, Cost())
default_cost = cost(y, y_score, **dataset.instance_costs)
longer_lifetime = cost(y, y_score, clv_months=24, **dataset.instance_costs)

6.3.8.4. Data Description

The mirror does not document the variables individually; they fall into these groups.

Features	Description
monthly_revenue, monthly_minutes, total_recurring_charge, director_assisted_calls, overage_minutes, roaming_calls, perc_change_minutes, perc_change_revenues	Revenue and usage, and their recent percentage change. monthly_revenue is also the cost driver.
dropped_calls, blocked_calls, unanswered_calls, customer_care_calls, threeway_calls, received_calls, outbound_calls, inbound_calls, peak_calls_in_out, off_peak_calls_in_out, dropped_blocked_calls, call_forwarding_calls, call_waiting_calls	Call volumes and call quality
months_in_service, unique_subs, active_subs, service_area	Account tenure, number of subscriptions and service area
handsets, handset_models, current_equipment_days, handset_refurbished, handset_web_capable, handset_price	Handset history and the current handset
age_hh1, age_hh2, children_in_hh, income_group, homeownership, marital_status, occupation, prizm_code, truck_owner, rv_owner, owns_motorcycle, owns_computer, has_credit_card, buys_via_mail_order, responds_to_mail_offers, opt_out_mailings, non_us_travel, new_cellphone_user, not_new_cellphone_user	Household demographics and lifestyle
credit_rating, adjustments_to_credit_rating	Credit rating and adjustments to it
retention_calls, retention_offers_accepted, made_call_to_retention_team, referrals_made_by_subscriber	Contacts with the retention team, and referrals
churn (target)	Whether the customer churned (1 = yes, 0 = no)

6.3.8.5. References

[1] (1,2,3)

Verbeke, W., Dejaeger, K., Martens, D., Hur, J., & Baesens, B. (2012). New insights into churn prediction in the telecommunication sector: A profit driven data mining approach. European Journal of Operational Research, 218(1), 211–229.

[2]

Höppner, S., Stripling, E., Baesens, B., vanden Broucke, S., & Verdonck, T. (2020). Profit driven decision trees for churn prediction. European Journal of Operational Research, 284(3), 920–933.

[3]

Maldonado, S., López, J., & Vairetti, C. (2020). Profit-based churn prediction based on Minimax Probability Machines. European Journal of Operational Research, 284(1), 273–284.

[4]

Verbraken, T., Verbeke, W., & Baesens, B. (2013). A novel profit maximizing metric for measuring classification performance of customer churn prediction models. IEEE Transactions on Knowledge and Data Engineering, 25(5), 961–973.