empcs_score

empulse.metrics.empcs_score

Expected Maximum Profit measure for Credit Scoring (EMPCS).

EMPCS presumes a situation where a company is considering whether to grant a loan to a customer. Correctly identifying defaulters results in receiving a return on investment (ROI), while incorrectly identifying non-defaulters as defaulters results in a loss of the loan amount. The degree to which the loan is lost is determined by the probability that the entire loan is lost (default_rate), the probability that the entire loan is paid back (success_rate), and a uniform distribution of partial loan losses (1 - default_rate - success_rate). For detailed information, consult the paper [1].

This is a MixtureMetric of three Metric components (one for each point mass, one for the continuous uniform piece) since sympy.stats cannot express this mixed distribution directly. See mpcs_score for a deterministic version of this metric.

The EMP measure for Credit Scoring is defined as [1]:

\[\int_0^1 \lambda \pi_0 F_0(T) - ROI \pi_1 F_1(T) \cdot h(\lambda) d\lambda\]

The EMP measure for Credit Scoring requires that the default class is encoded as 0, and it is NOT interchangeable. However, this implementation assumes the standard notation (‘default’: 1, ‘no default’: 0).

Methods

__call__(y_true, y_score, *, success_rate=0.55, default_rate=0.1, roi=0.2644)

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

optimal_threshold(y_true, y_score, *, success_rate=0.55, default_rate=0.1, roi=0.2644)

Compute the classification threshold that maximizes the expected profit.

optimal_rate(y_true, y_score, *, success_rate=0.55, default_rate=0.1, roi=0.2644)

Compute the predicted positive rate (fraction of loan applications that should be accepted) at which the maximum expected profit is achieved.

References

[1] (1,2)

Verbraken, T., Bravo, C., Weber, R., & Baesens, B. (2014). Development and application of consumer credit scoring models using profit-based classification measures. European Journal of Operational Research, 238(2), 505-513.

Examples

from empulse.metrics import empcs_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]
empcs_score(y_true, y_score, success_rate=0.55, default_rate=0.1, roi=0.2644)