tf.nn.weighted_cross_entropy_with_logits(
targets,
logits,
pos_weight,
name=None
)
Defined in tensorflow/python/ops/nn_impl.py
.
Computes a weighted cross entropy.
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:
targets * -log(sigmoid(logits)) +
(1 - targets) * -log(1 - sigmoid(logits))
A value pos_weights > 1
decreases the false negative count, hence increasing
the recall.
Conversely setting pos_weights < 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 targets term
in the loss expression:
targets * -log(sigmoid(logits)) * pos_weight +
(1 - targets) * -log(1 - sigmoid(logits))
For brevity, let x = logits
, z = targets
, 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 targets
must have the same type and shape.
Args:
targets
: ATensor
of the same type and shape aslogits
.logits
: ATensor
of typefloat32
orfloat64
.pos_weight
: A coefficient to use on the positive examples.name
: A name for the operation (optional).
Returns:
A Tensor
of the same shape as logits
with the componentwise
weighted logistic losses.
Raises:
ValueError
: Iflogits
andtargets
do not have the same shape.