diff --git a/doc/modules/model_evaluation.rst b/doc/modules/model_evaluation.rst index f4177c61b5025..b125a917ed4d3 100644 --- a/doc/modules/model_evaluation.rst +++ b/doc/modules/model_evaluation.rst @@ -887,11 +887,12 @@ To make this more explicit, consider the following notation: * :math:`y_l` the subset of :math:`y` with label :math:`l` * similarly, :math:`\hat{y}_s` and :math:`\hat{y}_l` are subsets of :math:`\hat{y}` -* :math:`P(y_l, \hat{y}_l) := \frac{\left| y_l \cap \hat{y}_l \right|}{\left|y_l\right|}` -* :math:`R(y_l, \hat{y}_l) := \frac{\left| y_l \cap \hat{y}_l \right|}{\left|\hat{y}_l\right|}` - (Conventions vary on handling :math:`\hat{y}_l = \emptyset`; this implementation uses - :math:`R(y_l, \hat{y}_l):=0`, and similar for :math:`P`.) -* :math:`F_\beta(y_l, \hat{y}_l) := \left(1 + \beta^2\right) \frac{P(y_l, \hat{y}_l) \times R(y_l, \hat{y}_l)}{\beta^2 P(y_l, \hat{y}_l) + R(y_l, \hat{y}_l)}` +* :math:`P(A, B) := \frac{\left| A \cap B \right|}{\left|A\right|}` for some + sets :math:`A` and :math:`B` +* :math:`R(A, B) := \frac{\left| A \cap B \right|}{\left|B\right|}` + (Conventions vary on handling :math:`B = \emptyset`; this implementation uses + :math:`R(A, B):=0`, and similar for :math:`P`.) +* :math:`F_\beta(A, B) := \left(1 + \beta^2\right) \frac{P(A, B) \times R(A, B)}{\beta^2 P(A, B) + R(A, B)}` Then the metrics are defined as: