classification - Loss function for class imbalanced binary classifier in Tensor flow

Question

I am trying to apply deep learning for a binary classification problem with high class imbalance between target classes (500k, 31K). I want to write a custom loss function which should be like: minimize(100-((predicted_smallerclass)/(total_smallerclass))*100)

Appreciate any pointers on how I can build this logic.

Answer 1

You can add class weights to the loss function, by multiplying logits. Regular cross entropy loss is this:

loss(x, class) = -log(exp(x[class]) / (sum_j exp(x[j])))
               = -x[class] + log(sum_j exp(x[j]))

in weighted case:

loss(x, class) = weights[class] * -x[class] + log(sum_j exp(weights[class] * x[j]))

So by multiplying logits, you are re-scaling predictions of each class by its class weight.

For example:

ratio = 31.0 / (500.0 + 31.0)
class_weight = tf.constant([ratio, 1.0 - ratio])
logits = ... # shape [batch_size, 2]
weighted_logits = tf.mul(logits, class_weight) # shape [batch_size, 2]
xent = tf.nn.softmax_cross_entropy_with_logits(
  weighted_logits, labels, name="xent_raw")

There is a standard losses function now that supports weights per batch:

tf.losses.sparse_softmax_cross_entropy(labels=label, logits=logits, weights=weights)

Where weights should be transformed from class weights to a weight per example (with shape [batch_size]). See documentation here.