mpc

empulse.metrics.mpc(y_true, y_score, *, accept_rate=0.3, clv=200, incentive_cost=10, contact_cost=1, check_input=True)

Maximum Profit Measure for Customer Churn (MPC).

MPC presumes a situation where identified churners are contacted and offered an incentive to remain customers. Only a fraction of churners accepts the incentive offer. For detailed information, consult the paper [1].

See also

mpc_score : to only return the MPC score.

empc : for a stochastic version of this metric.

Parameters:

y_true1D array-like, shape=(n_samples,)

Binary target values (‘churn’: 1, ‘no churn’: 0).

y_score1D array-like, shape=(n_samples,)

Target scores, can either be probability estimates or non-thresholded decision values.

accept_ratefloat, default=0.3

Probability of a customer accepting the retention offer (0 < accept_rate < 1).

clvfloat or 1D array-like, shape=(n_samples), default=200

If float: average customer lifetime value of retained customers (clv > incentive_cost). If array: customer lifetime value of each customer when retained (mean(clv) > incentive_cost).

Note

Passing a CLV array is equivalent to passing a float with the average CLV of that array.

incentive_costfloat, default=10

Cost of incentive offered to a customer (incentive_cost > 0).

contact_costfloat, default=1

Cost of contacting a customer (contact_cost > 0).

check_inputbool, default=True

Perform input validation. Turning off improves performance, useful when using this metric as a loss function.

Returns:

empcfloat

Maximum Profit Measure for Customer Churn

thresholdfloat

Fraction of the customer base that should be targeted to maximize profit

Notes

The MPC is defined as [1]:

\[CLV (\gamma (1 - \delta) - \phi) \pi_0 F_0(T) - CLV (\delta + \phi) \pi_1 F_1(T)\]

The MPC requires that the churn class is encoded as 0, and it is NOT interchangeable (see [3] p37). However, this implementation assumes the standard notation (‘churn’: 1, ‘no churn’: 0).

An equivalent R implementation is available in [2].

References

[1] (1,2)

Verbraken, T., Verbeke, W. and 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. Available Online: http://ieeexplore.ieee.org/iel5/69/6486492/06165289.pdf?arnumber=6165289

[2]

Bravo, C. and Vanden Broucke, S. and Verbraken, T. (2019). EMP: Expected Maximum Profit Classification Performance Measure. R package version 2.0.5. Available Online: http://cran.r-project.org/web/packages/EMP/index.html

[3]

Verbraken, T. (2013). Business-Oriented Data Analytics: Theory and Case Studies. Ph.D. dissertation, Dept. LIRIS, KU Leuven, Leuven, Belgium, 2013.

Examples

>>> from empulse.metrics import mpc
>>>
>>> y_true = [0, 1, 0, 1, 0, 1, 0, 1]
>>> y_score = [0.1, 0.2, 0.3, 0.4, 0.5, 0.7, 0.8, 0.9]
>>> mpc(y_true, y_score)
(23.874999999999996, 0.875)