How can I implement a weighted cross entropy loss

问题:

I am starting to use tensorflow (coming from Caffe), and I am using the loss sparse_softmax_cross_entropy_with_logits. The function accepts labels like 0,1,...C-1 instead of onehot encodings. Now, I want to use a weighting depending on the class label; I know that this could be done maybe with a matrix multiplication if I use softmax_cross_entropy_with_logits (one hot encoding), Is there any way to do the same with sparse_softmax_cross_entropy_with_logits?

回答1:

import  tensorflow as tf
import numpy as np

np.random.seed(123)
sess = tf.InteractiveSession()

# let's say we have the logits and labels of a batch of size 6 with 5 classes
logits = tf.constant(np.random.randint(0, 10, 30).reshape(6, 5), dtype=tf.float32)
labels = tf.constant(np.random.randint(0, 5, 6), dtype=tf.int32)

# specify some class weightings
class_weights = tf.constant([0.3, 0.1, 0.2, 0.3, 0.1])

# specify the weights for each sample in the batch (without having to compute the onehot label matrix)
weights = tf.gather(class_weights, labels)

# compute the loss
tf.losses.sparse_softmax_cross_entropy(labels, logits, weights).eval()

回答2:

Specifically for binary classification, there is weighted_cross_entropy_with_logits, that computes weighted softmax cross entropy.

sparse_softmax_cross_entropy_with_logits is tailed for a high-efficient non-weighted operation (see SparseSoftmaxXentWithLogitsOp which uses SparseXentEigenImpl under the hood), so it's not "pluggable".

In multi-class case, your option is either switch to one-hot encoding or use tf.losses.sparse_softmax_cross_entropy loss function in a hacky way, as already suggested, where you will have to pass the weights depending on the labels in a current batch.

回答3:

The class weights are multiplied by the logits, so that still works for sparse_softmax_cross_entropy_with_logits. Refer to this solution for "Loss function for class imbalanced binary classifier in Tensor flow."

As a side note, you can pass weights directly into sparse_softmax_cross_entropy

tf.contrib.losses.sparse_softmax_cross_entropy(logits, labels, weight=1.0, scope=None)

This method is for cross-entropy loss using

tf.nn.sparse_softmax_cross_entropy_with_logits.

Weight acts as a coefficient for the loss. If a scalar is provided, then the loss is simply scaled by the given value. If weight is a tensor of size [batch_size], then the loss weights apply to each corresponding sample.