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Implements the Weighted Kappa loss function.

Weighted Kappa loss was introduced in the Weighted kappa loss function for multi-class classification of ordinal data in deep learning. Weighted Kappa is widely used in Ordinal Classification Problems. The loss value lies in [-inf, log 2], where log 2 means the random prediction.


kappa_loss = WeightedKappaLoss(num_classes=4)
y_true = tf.constant([[0, 0, 1, 0], [0, 1, 0, 0],
                      [1, 0, 0, 0], [0, 0, 0, 1]])
y_pred = tf.constant([[0.1, 0.2, 0.6, 0.1], [0.1, 0.5, 0.3, 0.1],
                      [0.8, 0.05, 0.05, 0.1], [0.01, 0.09, 0.1, 0.8]])
loss = kappa_loss(y_true, y_pred)
print('Loss: ', loss.numpy())  # Loss: -1.1611923

Usage with tf.keras API:

# outputs should be softmax results
# if you want to weight the samples, just multiply the outputs
# by the sample weight.
model = tf.keras.Model(inputs, outputs)
model.compile('sgd', loss=tfa.losses.WeightedKappa(num_classes=4))

num_classes Number of unique classes in your dataset.
weightage (Optional) Weighting to be considered for calculating kappa statistics. A valid value is one of ['linear', 'quadratic']. Defaults to quadratic since it's mostly used.
name (Optional) String name of the metric instance.
epsilon (Optional) increment to avoid log zero, so the loss will be log(1 - k + epsilon), where k belongs to [-1, 1], usually you can use the default value which is 1e-6.
dtype (Optional) Data type of the metric result. Defaults to tf.float32.

ValueError If the value passed for weightage is invalid i.e. not any one of ['linear', 'quadratic']



Instantiates a Loss from its config (output of get_config()).

config Output of get_config().

A Loss instance.


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Returns the config dictionary for a Loss instance.


Invokes the Loss instance.

y_true Ground truth values. shape = [batch_size, d0, .. dN], except sparse loss functions such as sparse categorical crossentropy where shape = [batch_size, d0, .. dN-1]
y_pred The predicted values. shape = [batch_size, d0, .. dN]
sample_weight Optional sample_weight acts as a coefficient for the loss. If a scalar is provided, then the loss is simply scaled by the given value. If sample_weight is a tensor of size [batch_size], then the total loss for each sample of the batch is rescaled by the corresponding element in the sample_weight vector. If the shape of sample_weight is [batch_size, d0, .. dN-1] (or can be broadcasted to this shape), then each loss element of y_pred is scaled by the corresponding value of sample_weight. (Note ondN-1: all loss functions reduce by 1 dimension, usually axis=-1.)

Weighted loss float Tensor. If reduction is NONE, this has shape [batch_size, d0, .. dN-1]; otherwise, it is scalar. (Note dN-1 because all loss functions reduce by 1 dimension, usually axis=-1.)

ValueError If the shape of sample_weight is invalid.