  Most practical data science problems encounter missing data. A wide variety
of solutions exist, each with strengths and weaknesses that depend upon the
missingness-generating process. Here we develop a theoretical framework for
training and inference using only observed variables enabling modeling of
incomplete datasets without imputation. Using an information and
measure-theoretic argument we construct models with latent space
representations that regularize against the potential bias introduced by
missing data. The theoretical properties of this approach are demonstrated
empirically using a synthetic dataset. The performance of this approach is
tested on 11 benchmarking datasets with missingness and 18 datasets corrupted
across three missingness patterns with comparison against a state-of-the-art
model and industry-standard imputation. We show that our proposed method
overcomes the weaknesses of imputation methods and outperforms the current
state-of-the-art.
