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Update cross_validation.rst.
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mbaudin47 committed Jun 29, 2023
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6 changes: 3 additions & 3 deletions python/doc/theory/meta_modeling/cross_validation.rst
Original file line number Diff line number Diff line change
Expand Up @@ -403,15 +403,15 @@ We substitute the previous equation in the definition of the K-Fold MSE and get:

.. math::
\widehat{\operatorname{MSE}}_{KFold}
\widehat{\operatorname{MSE}}_{KFold}
& = \frac{1}{k n_\ell} \sum_{\ell = 1}^k \sum_{j \in \mathcal{S}_\ell}
\left[y^{(j)} - \hat{g}^{(-j)} \left(\boldsymbol{x}^{(j)}\right)\right]^2.
This implies:

.. math::
\widehat{\operatorname{MSE}}_{KFold}
\widehat{\operatorname{MSE}}_{KFold}
& = \frac{1}{n} \sum_{\ell = 1}^k \sum_{j \in \mathcal{S}_\ell}
\frac{n}{k n_\ell} \left[y^{(j)} - \hat{g}^{(-j)} \left(\boldsymbol{x}^{(j)}\right)\right]^2.
Expand All @@ -427,7 +427,7 @@ for :math:`j = 1, ..., n`. Hence:

.. math::
\widehat{\operatorname{MSE}}_{KFold}
\widehat{\operatorname{MSE}}_{KFold}
& = \frac{1}{n} \sum_{\ell = 1}^k \sum_{j \in \mathcal{S}_\ell} \left(\Delta^{(j)}\right)^2 \\
& = \frac{1}{n} \sum_{j = 1}^n \left(\Delta^{(j)}\right)^2
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