Squared¶
Squared loss, also known as the L2 loss.
Mathematically, it is defined as
It's gradient w.r.t. to \(p_i\) is
One thing to note is that this convention is consistent with Vowpal Wabbit and PyTorch, but not with scikit-learn. Indeed, scikit-learn divides the loss by 2, making the 2 disappear in the gradient.
Examples¶
from river import optim
loss = optim.losses.Squared()
loss(-4, 5)
81
loss.gradient(-4, 5)
18
loss.gradient(5, -4)
-18
Methods¶
call
Returns the loss.
Parameters
- y_true
- y_pred
Returns
The loss(es).
gradient
Return the gradient with respect to y_pred.
Parameters
- y_true
- y_pred
Returns
The gradient(s).
mean_func
Mean function.
This is the inverse of the link function. Typically, a loss function takes as input the raw output of a model. In the case of classification, the raw output would be logits. The mean function can be used to convert the raw output into a value that makes sense to the user, such as a probability.
Parameters
- y_pred
Returns
The adjusted prediction(s).