  We introduce a data management problem called metadata debt, to identify the
mapping between data concepts and their logical representations. We describe
how this mapping can be learned using semisupervised topic models based on
low-rank matrix factorizations that account for missing and noisy labels,
coupled with sparsity penalties to improve localization and interpretability.
We introduce a gauge transformation approach that allows us to construct
explicit associations between topics and concept labels, and thus assign
meaning to topics. We also show how to use this topic model for semisupervised
learning tasks like extrapolating from known labels, evaluating possible errors
in existing labels, and predicting missing features. We show results from this
topic model in predicting subject tags on over 25,000 datasets from Kaggle.com,
demonstrating the ability to learn semantically meaningful features.
