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

Computes the Huber loss.

The Huber loss is similar to the mean_squared_error() but is less sensitive to outliers in the data. It is defined as

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

where \(a = x - t\) is the difference between the input \(x\) and the target \(t\).

The loss 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).

See: Huber loss - Wikipedia.

  • x (Variable or N-dimensional array) – Input variable. The shape of x should be (\(N\), \(K\), …) if reduce='sum_along_second_axis'.

  • t (Variable or N-dimensional array) – Target variable for regression. The shape of t should be (\(N\), \(K\), …) if reduce='sum_along_second_axis'.

  • 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.

Return type



Example without reduction, in which case the output y will have the same shape as the inputs x and t.

>>> import numpy as np
>>> from chainer import functions as F
>>> x = np.array([[-2.0, 3.0, 0.5], [5.0, 2.0, -0.5]]).astype(np.float32)
>>> x.shape
(2, 3)
>>> t = np.array([[-2.0, 3.0, 0.0], [10.0, 2.0, -0.5]]).astype(np.float32)
>>> t.shape
(2, 3)
>>> y = F.huber_loss(x, t, delta=1.0, reduce='no')
>>> y.shape
(2, 3)
>>> y
variable([[0.   , 0.   , 0.125],
          [4.5  , 0.   , 0.   ]])

Example with reduction along the second axis.

>>> y = F.huber_loss(x, t, delta=1.0, reduce='sum_along_second_axis')
>>> y.shape
>>> y
variable([0.125, 4.5  ])