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Last update: February 19, 2014


PPV/NPV Fitness Function

The PPV/NPV fitness function is based on the positive predictive value (PPV) and negative predictive value (NPV).

The PPV/NPV PNi of an individual program i is evaluated by the equation:

where PPVi is the positive predictive value and NPVi is the negative predictive value of the individual program i, and are given by the formulas:

where TPi, TNi, FPi, and FNi represent, respectively, the number of true positives, true negatives, false positives, and false negatives.

True positives (TP), true negatives (TN), false positives (FP), and false negatives (FN), are the four different possible outcomes of a single prediction for a binomial classification task with classes “1” (“yes”) and “0” (“no”). A false positive is when the outcome is incorrectly classified as “yes” (or “positive”), when it is in fact “no” (or “negative”). A false negative is when the outcome is incorrectly classified as negative when it is in fact positive. True positives and true negatives are obviously correct classifications. These four types of classifications are usually shown in a two-way table called the confusion matrix.

The PPV/NPV fitness function can be combined with a cost matrix in order to impose specific constraints on the solutions. In addition, by choosing different rounding thresholds, different fitness functions can be created to explore different solution spaces.

The evolvable rounding thresholds include the ROC threshold, the logistic, class proportions, large margin, average, RMS, interdecile mean, interquartile mean, midrange, midhinge, and trimean threshold. There are also two kinds of fixed thresholds: the rounding threshold of the active model and user defined thresholds.

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