Dealing with missing data using attention and latent space regularization

Jahan Che Penny-Dimri, Christoph Bergmeir, Julian Smith

Keywords: missing data, missingness, latent space regularization, measure theory

TL;DR: A novel framework for dealing with missing data without imputation by regularizing latent space representations.

Abstract: 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 outperforms common imputation methods and the current state-of-the-art with statistical significance.

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Please Choose The Closest Area That Your Submission Falls Into: Deep Learning and representational learning