Absolute

Absolute loss, also known as the mean absolute error or L1 loss.

Mathematically, it is defined as

\[L = |p_i - y_i|\]

It's gradient w.r.t. to \(p_i\) is

\[\frac{\partial L}{\partial p_i} = sgn(p_i - y_i)\]

Examples

>>> from river import optim

>>> loss = optim.losses.Absolute()
>>> loss(-42, 42)
84
>>> loss.gradient(1, 2)
1
>>> loss.gradient(2, 1)
-1

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).