Variables used in formulas

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

    • tit_{i} is the label value for the i-th object (from the input data for training).

    • aia_{i} is the result of applying the model to the i-th object.

    • pip_{i} is the predicted success probability (pi=11+eai)\left(p_{i} = \frac{1}{1 + e^{-a_{i}}}\right)

    • NN is the total number of objects.

    • MM is the number of classes.

    • cic_{i} is the class of the object for binary classification.

      {ci=0,tiborderci=1,ti>border\begin{cases} c_{i} = 0{ , } & t_{i} \leqslant border \\ c_{i} = 1{ , } & t_{i} > border \end{cases}

    • wiw_{i} is the weight of the i-th object. It is set in the dataset description in columns with the Weighttype (if otherwise is not stated) or in the sample_weight parameter of the Python package. The default is 1 for all objects.

    • PP, TPTP, TNTN, FPFP, FNFN are abbreviations for Positive, True Positive, True Negative, False Positive and False Negative.

      By default, PP, TPTP, TNTN, FPFP, FNFN use weights. For example, TP=i=1Nwi[pi>0.5]ciTP = \sum\limits_{i=1}^{N} w_{i} [p_{i} > 0.5] c_{i}

    • PairsPairs is the array of pairs specified in the Pairs description or in the pairs parameter of the Python package.

    • NPairsN_{Pairs} is the number of pairs for the Pairwise metrics.

    • apa_{p} is the value calculated using the resulting model for the winner object for the Pairwise metrics.

    • ana_{n} is the value calculated using the resulting model for the loser object for the Pairwise metrics.

    • wpnw_{pn} is the weight of the (pp; nn) pair for the Pairwise metrics.

    • GroupGroup is the array of object identifiers from the input dataset with a common GroupId. It is used to calculate theGroupwise metrics.

    • GroupsGroups is the set of all arrays of identifiers from the input dataset with a common GroupId. It is used to calculate the Groupwise metrics.