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# tf.nn.weighted_cross_entropy_with_logits

Computes a weighted cross entropy. (deprecated arguments)

### Aliases:

• `tf.compat.v1.nn.weighted_cross_entropy_with_logits`
``````tf.nn.weighted_cross_entropy_with_logits(
labels=None,
logits=None,
pos_weight=None,
name=None,
targets=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_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 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. Args: labels: 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). targets: Deprecated alias for labels.

#### 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.