Optimal transport of the joint distribution between data sources

loss_crossentropy(Y, F)

Cross entropy is typically used as a loss in multi-class classification, in which case the labels y are given in a one-hot format. dims specifies the dimension (or the dimensions) containing the class probabilities. The prediction ŷ is usually probabilities but in our case it is also one hot encoded vector.

modality_cost(loss, weight)

• loss: matrix of size len(weight) * len(levels)
• weight: vector of weights

Returns the scalar product <loss[level,],weight>