TensorFlow 1 version | View source on GitHub |
Computes a weighted cross entropy.
tf.nn.weighted_cross_entropy_with_logits(
labels, logits, pos_weight, name=None
)
This is like sigmoid_cross_entropy_with_logits()
except that pos_weight
,
allows one to trade off recall and precision by up- or down-weighting the
cost of a positive error relative to a negative error.
The usual cross-entropy cost is defined as:
labels * -log(sigmoid(logits)) +
(1 - labels) * -log(1 - sigmoid(logits))
A value pos_weight > 1
decreases the false negative count, hence increasing
the recall.
Conversely setting pos_weight < 1
decreases the false positive count and
increases the precision.
This can be seen from the fact that pos_weight
is introduced as a
multiplicative coefficient for the positive labels term
in the loss expression:
labels * -log(sigmoid(logits)) * pos_weight +
(1 - labels) * -log(1 - sigmoid(logits))
For brevity, let x = logits
, z = labels
, q = pos_weight
.
The loss is:
qz * -log(sigmoid(x)) + (1 - z) * -log(1 - sigmoid(x))
= qz * -log(1 / (1 + exp(-x))) + (1 - z) * -log(exp(-x) / (1 + exp(-x)))
= qz * log(1 + exp(-x)) + (1 - z) * (-log(exp(-x)) + log(1 + exp(-x)))
= qz * log(1 + exp(-x)) + (1 - z) * (x + log(1 + exp(-x))
= (1 - z) * x + (qz + 1 - z) * log(1 + exp(-x))
= (1 - z) * x + (1 + (q - 1) * z) * log(1 + exp(-x))
Setting l = (1 + (q - 1) * z)
, to ensure stability and avoid overflow,
the implementation uses
(1 - z) * x + l * (log(1 + exp(-abs(x))) + max(-x, 0))
logits
and labels
must have the same type and shape.
labels = tf.constant([1., 0.5, 0.])
logits = tf.constant([1.5, -0.1, -10.])
tf.nn.weighted_cross_entropy_with_logits(
labels=labels, logits=logits, pos_weight=tf.constant(1.5)).numpy()
array([3.0211994e-01, 8.8049585e-01, 4.5776367e-05], dtype=float32)
tf.nn.weighted_cross_entropy_with_logits(
labels=labels, logits=logits, pos_weight=tf.constant(0.5)).numpy()
array([1.00706644e-01, 5.08297503e-01, 4.57763672e-05], dtype=float32)
Args | |
---|---|
labels
|
A Tensor of the same type and shape as logits , with values
between 0 and 1 inclusive.
|
logits
|
A Tensor of type float32 or float64 , any real numbers.
|
pos_weight
|
A coefficient to use on the positive examples, typically a
scalar but otherwise broadcastable to the shape of logits . Its value
should be non-negative.
|
name
|
A name for the operation (optional). |
Returns | |
---|---|
A Tensor of the same shape as logits with the componentwise
weighted logistic losses.
|
Raises | |
---|---|
ValueError
|
If logits and labels do not have the same shape.
|