tf.contrib.kernel_methods.sparse_multiclass_hinge_loss

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Adds Ops for computing the multiclass hinge loss.

tf.contrib.kernel_methods.sparse_multiclass_hinge_loss(
    labels, logits, weights=1.0, scope=None, loss_collection=tf.GraphKeys.LOSSES,
    reduction=losses.Reduction.SUM_BY_NONZERO_WEIGHTS
)

The implementation is based on the following paper: On the Algorithmic Implementation of Multiclass Kernel-based Vector Machines by Crammer and Singer. link: http://jmlr.csail.mit.edu/papers/volume2/crammer01a/crammer01a.pdf

This is a generalization of standard (binary) hinge loss. For a given instance with correct label c*, the loss is given by:

$$loss = max_{c != c*} logits_c - logits_{c*} + 1.$$

or equivalently

$$loss = max_c { logits_c - logits_{c*} + I_{c != c*} }$$

where \(I_{c != c*} = 1\ \text{if}\ c != c*\) and 0 otherwise.

labels Tensor of shape [batch_size] or [batch_size, 1]. Corresponds to the ground truth. Each entry must be an index in [0, num_classes).
logits Tensor of shape [batch_size, num_classes] corresponding to the unscaled logits. Its dtype should be either float32 or float64.
weights Optional (python) scalar or Tensor. If a non-scalar Tensor, its rank should be either 1 ([batch_size]) or 2 ([batch_size, 1]).
scope The scope for the operations performed in computing the loss.
loss_collection collection to which the loss will be added.
reduction Type of reduction to apply to loss.

Weighted loss float Tensor. If reduction is NONE, this has the same shape as labels; otherwise, it is a scalar.

ValueError If logits, labels or weights have invalid or inconsistent shapes.
ValueError If labels tensor has invalid dtype.