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def grid _ search ( xTr , yTr , xVal, yVal, depths ) : Calculates the training and validation loss for trees

def grid_search(xTr, yTr, xVal, yVal, depths):
"""
Calculates the training and validation loss for trees trained on xTr and validated on yTr with a number of depths.
Input:
xTr: nxd training data matrix
yTr: n-dimensional vector of training labels
xVal: mxd validation data matrix
yVal: m-dimensional vector of validation labels
depths: a list of len k of depths
Output:
best_depth, training_losses, validation_losses
best_depth: the depth that yields that lowest validation loss
training_losses: a list of len k. the i-th entry corresponds to the the training loss of the tree of depth=depths[i]
validation_losses: a list of len k. the i-th entry corresponds to the the validation loss of the tree of depth=depths[i]
"""
training_losses =[]
validation_losses =[]
best_depth = None
# Initialize the variable
best_loss = float('inf')
# Loop over all possible depths for the regression tree
for dept in depths:
# Check if the current validation is less than the best validation loss
if validation_loss < best_loss:
best_loss = validation_loss
best_depth = depth
raise NotImplementedError()
return best_depth, training_losses, validation_losses

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