max_profit_score

empulse.metrics.max_profit_score

Maximum Profit Measure (MP).

A generic Metric built from the MaxProfit strategy on a plain cost matrix, accepting class- or instance-dependent tp_cost, tn_cost, fp_cost, and fn_cost parameters (all costs; a benefit is a negative cost).

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.

Methods

__call__(y_true, y_score, *, tp_cost=0.0, tn_cost=0.0, fp_cost=0.0, fn_cost=0.0)

Compute the maximum profit that can be achieved by a classifier at its optimal decision threshold.

optimal_threshold(y_true, y_score, *, tp_cost=0.0, tn_cost=0.0, fp_cost=0.0, fn_cost=0.0)

Compute the classification threshold that maximizes the profit.

optimal_rate(y_true, y_score, *, tp_cost=0.0, tn_cost=0.0, fp_cost=0.0, fn_cost=0.0)

Compute the predicted positive rate at which the maximum profit is achieved.

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.

Examples

Reimplement MPC:

from empulse.metrics import max_profit_score

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_cost = -(clv * (gamma * (1 - (d / clv)) - (f / clv)))
fp_cost = d + f

max_profit_score(y_true, y_score, tp_cost=tp_cost, fp_cost=fp_cost)