Story Tag Prediction - Optional Labels
Welcome to our community!

If I understood correctly, you don't trust the labels on your training dataset. 


  The problem is, that the original data wasn't generated but added by users.


That is not properly a problem, actually almost every dataset was created by human labeling. Your problem is that you don't trust the judgement of those users and you think that data might be incomplete.

It is true that this might affect your model's performance. But, you should try either way. Sometimes the model learns to label even better than the training dataset:

Recently I looked the master's dissertation of a friend (Wesley L. Passos,M.Sc. by UFRJ) which used deep learning to detect tires on drone images (for Aedes Aegyptis prevention procedures). The dataset was created by our group my manually annotating images with bounding boxes and while we missed some of the tires that were pretty well hidden the D-CNN model was capable of detecting those hard subjects. 

Note: This dissertation was recently accepted and isn't available online yet. Once it does, I will update this answer with the proper reference.

Since wrangling with data is our everyday job this is a good opportunity for you to put in practice what you have learned:


Clean your data by either removing incomplete samples or filling missing values. This is a common part of our jobs as data scientists.
If you feel that the amount of work is  a bit overwhelming you can try clustering instead or semi-supervised methods to speed up the cleaning process.
Also you can try posting your data online for further contributing.


Curiosity Note:

Crowds are usually more intelligent than individual, so with problem statistical treatment data can actually be better annotated by crowds, using mean answers or by voting. Check for The Wisdom of Crowds (Not the TV Show).