tf.nn.weighted_cross_entropy_with_logits

tf.nn.weighted_cross_entropy_with_logits(
    targets,
    logits,
    pos_weight,
    name=None
)

Defined in tensorflow/python/ops/nn_impl.py.

See the guide: Neural Network > Classification

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: A Tensor of the same type and shape as logits.
• logits: A Tensor of type float32 or float64.
• 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: If logits and targets do not have the same shape.