max_profit

empulse.metrics.max_profit(y_true, y_score, *, tp_benefit=0.0, tn_benefit=0.0, fn_cost=0.0, fp_cost=0.0)

Maximum Profit Measure (MP).

See also

max_profit_score : To only return the maximum profit score.

Metric : To create a stochastic version of the maximum profit.

Parameters:

y_true1D array-like, shape=(n_samples,)

Binary target values (‘positive’: 1, ‘negative’: 0).

y_score1D array-like, shape=(n_samples,)

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

tp_benefitfloat, default=0.0

Benefit attributed to true positive predictions.

tn_benefitfloat, default=0.0

Benefit attributed to true negative predictions.

fn_costfloat, default=0.0

Cost attributed to false negative predictions.

fp_costfloat, default=0.0

Cost attributed to false positive predictions.

Returns:

mpfloat

Maximum Profit

thresholdfloat

Threshold at which the maximum profit is achieved

Notes

The MP is defined as [1]:

\[\text{MP} = b_0 \pi_0 F_0(T) + b_1 \pi_1 (1 - F_1(T)) - c_0 \pi_0 (1 - F_0(T)) - c_1 F_1(T)\]

where \(T\) is the threshold at which the maximum profit is achieved.

The MP requires that the positive class is encoded as 0, and negative class as 1. However, this implementation assumes the standard notation (‘positive’: 1, ‘negative’: 0).

References

[1]

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

Examples

Reimplement MPC:

>>> from empulse.metrics import max_profit
>>>
>>> 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]
>>>
>>> clv = 200
>>> d = 10
>>> f = 1
>>> gamma = 0.3
>>> tp_benefit = clv * (gamma * (1 - (d / clv)) - (f / clv))
>>> fp_cost = d + f
>>>
>>> max_profit(y_true, y_score, tp_benefit=tp_benefit, fp_cost=fp_cost)
(23.87..., 0.875)