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# 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.

© 2018 The TensorFlow Authors. All rights reserved.
Licensed under the Creative Commons Attribution License 3.0.
Code samples licensed under the Apache 2.0 License.
https://www.tensorflow.org/api_docs/python/tf/nn/weighted_cross_entropy_with_logits