Variables used in formulas

The following common variables are used in formulas of the described metrics:

$\text{[math]}$ is the label value for the i-th object (from the input data for training).
$\text{[math]}$ is the result of applying the model to the i-th object.
$\text{[math]}$ is the predicted success probability $\text{[math]}$
$\text{[math]}$ is the total number of objects.
$\text{[math]}$ is the number of classes.
$\text{[math]}$ is the class of the object for binary classification.

$\text{[math]}$
$\text{[math]}$ is the weight of the i-th object. It is set in the dataset description in columns with the Weight type (if otherwise is not stated) or in the sample_weight parameter of the Python package. The default is 1 for all objects.
$\text{[math]}$ , $\text{[math]}$ , $\text{[math]}$ , $\text{[math]}$ , $\text{[math]}$ are abbreviations for Positive, True Positive, True Negative, False Positive and False Negative.

By default, $\text{[math]}$ , $\text{[math]}$ , $\text{[math]}$ , $\text{[math]}$ , $\text{[math]}$ use weights. For example, $\text{[math]}$
$\text{[math]}$ is the array of pairs specified in the Pairs description or in the pairs parameter of the Python package.
$\text{[math]}$ is the number of pairs for the Pairwise metrics.
$\text{[math]}$ is the value calculated using the resulting model for the winner object for the Pairwise metrics.
$\text{[math]}$ is the value calculated using the resulting model for the loser object for the Pairwise metrics.
$\text{[math]}$ is the weight of the ( $\text{[math]}$ ; $\text{[math]}$ ) pair for the Pairwise metrics.
$\text{[math]}$ is the array of object identifiers from the input dataset with a common GroupId. It is used to calculate theGroupwise metrics.
$\text{[math]}$ is the set of all arrays of identifiers from the input dataset with a common GroupId. It is used to calculate the Groupwise metrics.