Flow-based imputation of small data
Keywords: Normalizing flows, imputation, diffeomorphism, out of distribution detection
TL;DR: Likelihood estimation errors resulting from the diffeomorphism constraint in normalizing flows are explicitly quantified, and a tailored mitigation strategy is introduced for low-dimensional scientific applications.
Abstract: Many challenges in the physical sciences can be framed as small data problems, where theoretical progress is hindered by the sparsity, low-dimensionality, and/or limited sample size of available empirical data compared to a physical system’s numerous dynamical degrees of freedom. Developing trustworthy imputation methods for these datasets holds immense scientific importance. Normalizing flows are a promising model choice for imputation due to their ability to explicitly estimate sample likelihoods. However, research has shown that normalizing flows are often unreliable for out-of-distribution (OOD) detection in high-dimensional settings, which undermines their trustworthiness for imputation tasks. In contrast, low-dimensional settings provide opportunities to tractably evaluate and mitigate likelihood estimation errors, revealing strategies to reduce or eliminate specific error modes. We focus on the most stringent assumption in normalizing flows: diffeomorphism between the target and base distributions. This assumption introduces two distinct error modes, which we identify and address through a simple and effective strategy. Our approach significantly enhances the trustworthiness of normalizing flows for imputation in small data problems.
Primary Area: applications to physical sciences (physics, chemistry, biology, etc.)
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Submission Number: 10904
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