chainer.functions.huber_loss¶

chainer.functions.huber_loss(x, t, delta, reduce='sum_along_second_axis')[source]

Loss function which is less sensitive to outliers in data than MSE.

$a = x - t$

and

$\begin{split}L_{\delta}(a) = \left \{ \begin{array}{cc} \frac{1}{2} a^2 & {\rm if~|a| \leq \delta} \\ \delta (|a| - \frac{1}{2} \delta) & {\rm otherwise,} \end{array} \right.\end{split}$

The output is a variable whose value depends on the value of the option reduce. If it is 'no', it holds the elementwise loss values. If it is 'sum_along_second_axis', loss values are summed up along the second axis (i.e. axis=1).

Parameters: x (Variable or numpy.ndarray or cupy.ndarray) – Input variable. The shape of x should be ($$N$$, $$K$$). t (Variable or numpy.ndarray or cupy.ndarray) – Target variable for regression. The shape of t should be ($$N$$, $$K$$). delta (float) – Constant variable for huber loss function as used in definition. reduce (str) – Reduction option. Its value must be either 'sum_along_second_axis' or 'no'. Otherwise, ValueError is raised. A variable object holding a scalar array of the huber loss $$L_{\delta}$$. If reduce is 'no', the output variable holds array whose shape is same as one of (hence both of) input variables. If it is 'sum_along_second_axis', the shape of the array is same as the input variables, except the second axis is removed. Variable
See:
Huber loss - Wikipedia.

Example

>>> x = np.array([[-2.0, 3.0, 0.5], [5.0, 2.0, -0.5]]).astype('f')
>>> x
array([[-2. ,  3. ,  0.5],
[ 5. ,  2. , -0.5]], dtype=float32)
>>> t = np.array([[-2.0, 3.0, 0.0], [10.0, 2.0, -0.5]]).astype('f')
>>> t
array([[ -2. ,   3. ,   0. ],
[ 10. ,   2. ,  -0.5]], dtype=float32)
>>> y = F.huber_loss(x, t, 1.0)
>>> y.shape
(2,)
>>> y.data
array([ 0.125,  4.5  ], dtype=float32)
>>> y = F.huber_loss(x, t, 1.0, reduce='no')
>>> y.shape
(2, 3)
>>> y.data
array([[ 0.   ,  0.   ,  0.125],
[ 4.5  ,  0.   ,  0.   ]], dtype=float32)