The co-variance is calculated as follows:
Where ¯ p(j),t(j) represent the average of¯ p ’s and t ’s respectively: Two variables assuming a quota size of j are: In this case, the standard deviations of the Random variables is calculated by dividing the co-variance by the product The Pearson correlation coefficient for two Only the ordinal place of an instance but also its value (i.e. It should be noticed that this measure take into account not Value between −1 and 1 where the value 1 represents the strongest positiveĬorrelation. A Pearson correlation coefficient can have any Ordered estimated conditional probability (p ) and the ordered actualĮxpected outcome (t ). This measure can be used to find the correlation between the In this section, we examine the Pearson correlationĬoefficient. These measures are well known and can be found in There are also some statistical measures that may be used as performanceĮvaluators of models. A comparison between models can be done byĬomparing the lift of the top portions, depending on the resources available Figure 4.5 illustrates a lift chart forĪ typical model prediction.
A good model would present a lift greater than 1 in the top deciles andĪ lift smaller than 1 in the last deciles. Regardless of how the test set is divided, a good model isĪchieved if the lift decreases when proceeding to the bottom of the scoring Test set is divided into several portions (usually deciles), lift is calculated asįollows : the ratio of really positive instances in a specificĭecile is divided by the average ratio of really positive instances in the Formally, it can be calculated as:Ī popular method of evaluating probabilistic models is lift. The denominator stands for the total number of instances that areĬlassified as positive in the entire dataset. Positive instances in the entire dataset. Positive instances, from the head of the list until that position, by the total The Qrecall forĪ certain position in a ranked list is calculated by dividing the number of To be the “recall” equivalent for quota-limited problems. Similarly, we suggest the Qrecall (for quota recall) The hit-rate measure, presented above, is the “precision” equivalent for
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