Loss function for class imbalanced binary classifier in Tensor flow

    By multiplying logits, add class weights to the loss function. The cross entropy loss is:

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

    For weighted case:

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

    Hence By class weight you are re-scaling predictions of each class, by multiplying logits.

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")

    It as an standard losses function which supports weights per batch:

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

    The weights are transformed from class weights to a weight per example. Check here.

Here is a solution for the problem:

ratio = 31.0 / (500.0 + 31.0)
class_weight = tf.constant([[ratio, 1.0 - ratio]])
logits = ... # shape [batch_size, 2]
 
weight_per_label = tf.transpose( tf.matmul(labels
                           , tf.transpose(class_weight)) ) #shape [1, batch_size]
# this is the weight for each datapoint, depending on its label
 
xent = tf.mul(weight_per_label
         , tf.nn.softmax_cross_entropy_with_logits(logits, labels, name="xent_raw") #shape [1, batch_size]
loss = tf.reduce_mean(xent) #shape 1

      To determine the Loss function for class imbalanced binary classifier use this tf.nn.weighted_cross_entropy_with_logits()and set pos_weight =1.