# Hinge¶

Computes the hinge loss.

Mathematically, it is defined as

$L = max(0, 1 - p_i * y_i)$

It's gradient w.r.t. to $$p_i$$ is

$\\frac{\\partial L}{\\partial y_i} = \\left\{ \\begin{array}{ll} \\ 0 & p_iy_i \geqslant 1 \\\\ \\ - y_i & p_iy_i < 1 \\end{array} \\right.$

## Parameters¶

• threshold

Default1.0

Margin threshold. 1 yield the loss used in SVMs, whilst 0 is equivalent to the loss used in the Perceptron algorithm.

## Examples¶

from river import optim

loss = optim.losses.Hinge(threshold=1)
loss(1, .2)

0.8


loss.gradient(1, .2)

-1


## Methods¶

call

Returns the loss.

Parameters

• y_true
• y_pred

Returns

The loss(es).

Return the gradient with respect to y_pred.

Parameters

• y_true
• y_pred

Returns

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