Squared¶

Squared loss, also known as the L2 loss.

Mathematically, it is defined as

L = (p_{i} - y_{i})^{2}

Its gradient w.r.t. to $p_{i}$ is

\frac{\partial L}{\partial p_{i}} = 2 (p_{i} - y_{i})

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)

loss.gradient(-4, 5)

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).