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
Default →
1.0Margin 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).
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).