Unsupervised Data Imputation via Variational Inference of Deep Subspaces
This addresses the problem of accurate data imputation for practitioners in fields like medical imaging where full datasets are unavailable, representing an incremental improvement over existing linear subspace methods.
The paper tackles unsupervised imputation of missing image data without full observations by introducing a probabilistic model with deep non-linear embeddings and sparsity-aware neural network blocks, achieving results on public imaging datasets and a real-world medical image problem.
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.