empc#

empulse.metrics.empc(y_true, y_score, *, alpha=6, beta=14, clv=200, incentive_cost=10, contact_cost=1, check_input=True)[source]#

Expected Maximum Profit Measure for Customer Churn (EMPC).

EMPC presumes a situation where identified churners are contacted and offered an incentive to remain customers. Only a fraction of churners accepts the incentive offer, this fraction is described by a \(Beta(\alpha, \beta)\) distribution. As opposed to empb, the incentive cost is a fixed value, rather than a fraction of the customer lifetime value. For detailed information, consult the paper [1].

See also

empc_score : to only return the EMPC score.

mpc : for a deterministic version of this metric.

empb : for a similar metric, but with a variable incentive cost.

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.

alphafloat, default=6

Shape parameter of the beta distribution of the probability that a churner accepts the incentive (alpha > 1).

betafloat, default=14

Shape parameter of the beta distribution of the probability that a churner accepts the incentive (beta > 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

Expected Maximum Profit Measure for Customer Churn

thresholdfloat

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

Notes

The EMPC is defined as [1]:

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

The EMPC 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).

Code adapted from [4]. 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 empc
>>>
>>> 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]
>>> empc(y_true, y_score)
(23.875593418348124, 0.8743700763487141)
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