I'm currently working on a project with a bunch of data of devices that can either belong to people, or not. The ultimate goal is to estimate a number of people detected. Sadly, it is impossible to get labels for which device should be classified as human and which shouldn't. So a basic binary classification network will not be trainable.
I do however have for each moment in time a number of people, that can be correlated to the number of human-devices that should be detected (it is not the exact sum of devices that should be detected because we won't be able to detect all).
So... I though of this weird construct, where I have a binary classification neural network (green box in the picture) copied n times along itself, and then have its outputs propagate to an outer network which will perform a regression using both the outputs of the classifiers and some other variables (pink) that will determine the scaling (for example, if only 50% of the humans are detectable using the devices, then the scaling will have to be 2. But this is a non-linear function so it'll also be determined by the NN).
The green neural networks should all share the same weights, because they will perform identical work.
Another possibility would be to use the pink scaling variables from the outer (red) NN, to the green-NN's, and then let it result in a non-binary value, but more like a scaled value. So in the same example as above, a 1 would return 2.
Would this be possible in theory? Has it been done before? What would be the best approach for this?
I already had a talk with my adviser about this, but he was very skeptical about it.