# What is a good loss function in multiclass multilabel classification where only one of the possible labels is observed?

I am training an ANN in multiclass multilabel scenario, where only one of the possible labels is observed at a time, let me illustrate on an example:

I have a state X and the ground truth label Y for this state is for example [0, 1, 0, 1, 1, 0, 0]. However I can only see a label Z, which contains only one of the ones in the ground truth label Y. So to get a complete information, I need 3 different pairs {X,Z}:

{X, [0, 1, 0, 0, 0, 0, 0]}

{X, [0, 0, 0, 1, 0, 0, 0]}

{X, [0, 0, 0, 0, 1, 0, 0]}


Could you suggest a good loss function to use to train this network? I have tried binary crossentropy, categorical crossentropy and mean square error but none of them seemed to work very well.

edit: I forgot to specify that after the network is trained I would like to observe the whole ground truth vector Y and not just one of the possibilities Z.

• Is it possible to pre-process your data so that all of the samples with the same $X$ are grouped together? Do all samples have the same number of labels, or can different samples have different numbers of labels(One has A, B and another has C, D, E)? – Sycorax Jul 4 '18 at 13:11