<a id="skfolio-model-selection-optimal-folds-number"></a>

# skfolio.model_selection.optimal_folds_number

<a id="skfolio.model_selection.optimal_folds_number"></a>

### skfolio.model_selection.optimal_folds_number(n_observations, target_train_size, target_n_test_paths, weight_train_size=1, weight_n_test_paths=1)

Find the optimal number of folds (total folds and test folds) for a target
training size and a target number of test paths.

We find `x = n_folds` and `y = n_test_folds` that minimizes the below
cost function of the relative distance from the two targets:

$$
cost(x,y) = w_{f} \times \lvert\frac{f(x,y)-f_{target}}{f_{target}}\rvert + w_{g} \times \lvert\frac{g(x,y)-g_{target}}{g_{target}}\rvert

$$

with $w_{f}$ and $w_{g}$ the weights assigned to the distance
from each target and $f(x,y)$ and $g(x,y)$ the average training size
and the number of test paths as a function of the number of total folds and test
folds.

This is a combinatorial problem with $\frac{T\times(T-3)}{2}$ combinations,
with $T$ the number of observations.

We reduce the search space by using the combinatorial symmetry
${n \choose k}={n \choose n-k}$ and skipping cost computation above 1e5.

* **Parameters:**
  **n_observations** *int*
  : Number of observations.

  **target_train_size** *int*
  : The target number of observation in the training set.

  **target_n_test_paths** *int*
  : The target number of test paths (that can be reconstructed from the train/test
    combinations).

  **weight_train_size** *float, default=1*
  : The weight assigned to the distance from the target train size.
    The default value is 1.

  **weight_n_test_paths** *float, default=1*
  : The weight assigned to the distance from the target number of test paths.
    The default value is 1.
* **Returns:**
  **n_folds** *int*
  : Optimal number of total folds.

  **n_test_folds** *int*
  : Optimal number of test folds.