Let's implement huber loss. Huber loss is less sensitive to outliers in data than mean squared error.
Below is the formula of huber loss.
Note:
Huber loss is defined as:
error 2/2, if error < delta (ie, if it is a small error)
delta * ( |error| - delta/2), otherwise ( |error| means the absolute value error)
In this exercise, we consider delta=1.
Thus, the huber_fn is defined as:
error 2/2, if error < 1 (ie, if it is a small error).
|error| - 0.5, otherwise
tf.abs(x) returns the positive value(absolute value) of x.
tf.square(x) returns the squared value of x.
tf.where(bool_array, x, y) returns the elements where condition is True in bool_array (multiplexing x and y).
In simpler terms, tf.where will choose an output shape from the shapes of condition, x, and y that all three shapes are broadcastable to.
The condition tensor acts as a mask that chooses whether the corresponding element/row in the output should be taken from x (if the element in the condition is True) or from y (if it is False).
For example, upon executing the following,
tf.where([True, False, False, True], [1,2,3,4], [100,200,300,400])
the output would be : <tf.Tensor: shape=(4,), dtype=int32, numpy=array([ 1, 200, 300, 4], dtype=int32)>
Define the huber_fn, the Huber Loss function, and pass the y_true, y_pred as input arguments to the function. We do this as follows:
Calculate error which is y_true - y_pred
If tf.abs(error) < 1, then is_small_error is True. Else, is_small_error is False.
Define squared_loss as tf.square(error) / 2.
Define linear_loss as tf.abs(error) - 0.5.
Use tf.where and pass is_small_error, squared_loss, linear_loss as input arguments to it, to choose either the squared_loss value or the linear_loss value based on if the is_small_error condition is True or False.
Thus, return the huber loss for each prediction.
So use the following code to do the same:
def huber_fn(y_true, y_pred):
error = y_true - y_pred
is_small_error = tf.abs(error) < 1
squared_loss = tf.square(error) / 2
linear_loss = tf.abs(error) - 0.5
return tf.where(is_small_error, squared_loss, linear_loss)
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