Prediction Error Cost-Benefit Matrix

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A Prediction Error Cost-Benefit Matrix is a symmetric matrix that defines the misclassification costs of a classification task.



References

2016

  • (Branco et al., 2016) ⇒ Paula Branco, Luís Torgo, and Rita P. Ribeiro. (2016). “A Survey of Predictive Modeling on Imbalanced Domains.” ACM Computing Surveys (CSUR) 49, no. 2
    • QUOTE: ... In order to perform a modification on a selected algorithm, it is essential to understand why it fails when the distribution is skewed. Also, some of the adaptations assume that a cost/cost-benefit matrix is known for different error types, which is frequently not the case. ...

2015

The technique we'll use is a cost benefit matrix. This is very similar to our confusion matrix:

\begin{bmatrix}TP & FP\\FN & TN\end{bmatrix}

Which to find probabilities turns into this:

\begin{bmatrix}p(TP) & p(FP)\\p(FN) & p(TN)\end{bmatrix}

and our cost benefit matrix will be somewhat similar:

\begin{bmatrix}b(TP) & c(FP)\\c(FN) & b(TN)\end{bmatrix}

where:

  • [math]b[/math] represents benefit (the benefits of accurately predicting positives and negatives), while...
  • [math]c[/math] represents cost (the costs of misclassifying positives and negatives).

To simplify we'll associate benefits to be positive value and costs to be negative value:

\begin{bmatrix}v(TP) & -v(FP)\\-v(FN) & v(TN)\end{bmatrix}

... ...