13.2. Mean Absolute Error (MAE)

class fhez.nn.loss.mae.MAE

Loss function to node wrapper.

backward(gradient)

Calculate MAE gradient with respect to \(\hat{y}\).

This will take a single gradient value, and return the average gradient with respect to \(\hat{y}\)

\(\dfrac{d}{d\hat{y}}(\text{MAE}) = \begin{cases} +1,\quad \hat{y}>y\\ \ \ \ 0,\quad \hat{y}=y\\-1,\quad \hat{y}<y \end{cases}\)

cost()

Get computational cost of the forward function.

forward(y: numpy.ndarray, y_hat: numpy.ndarray)

Calculate the loss of the output given the ground truth.

This will take multiple values for both \(y\) and \(\hat{y}\), and return a single value that is the mean of their absolute difference.

\(\text{MAE}=\frac{\sum_{i=0}^{N-1} \left\|y-\hat{y}\right\| }{N}\)

update()

Do nothing as there are no parameters to update.

updates()

Do nothing as there are no parameters to update.