Unsupervised Data Imputation via Variational Inference of Deep Subspaces

TL;DR

This paper presents a novel unsupervised deep learning approach for imputing missing data in high-dimensional images, especially medical images, using variational inference of deep non-linear subspaces, outperforming traditional linear methods.

Contribution

Introduces a probabilistic model with deep non-linear embeddings and sparsity-aware networks for unsupervised image data imputation, extending beyond linear subspace models.

Findings

Effective imputation demonstrated on public imaging datasets.

Outperforms traditional linear subspace methods.

Enables imputation in complex real-world medical imaging scenarios.

Abstract

A wide range of systems exhibit high dimensional incomplete data. Accurate estimation of the missing data is often desired, and is crucial for many downstream analyses. Many state-of-the-art recovery methods involve supervised learning using datasets containing full observations. In contrast, we focus on unsupervised estimation of missing image data, where no full observations are available - a common situation in practice. Unsupervised imputation methods for images often employ a simple linear subspace to capture correlations between data dimensions, omitting more complex relationships. In this work, we introduce a general probabilistic model that describes sparse high dimensional imaging data as being generated by a deep non-linear embedding. We derive a learning algorithm using a variational approximation based on convolutional neural networks and discuss its relationship to linear imputation models, the variational auto encoder, and deep image priors. We introduce sparsity-aware network building blocks that explicitly model observed and missing data. We analyze proposed sparsity-aware network building blocks, evaluate our method on public domain imaging datasets, and conclude by showing that our method enables imputation in an important real-world problem involving medical images. The code is freely available as part of the \verb|neuron| library at http://github.com/adalca/neuron.