# Unsupervised Data Imputation via Variational Inference of Deep Subspaces

arXiv: https://arxiv.org/abs/1903.03503 · HTML: https://mlsanity.com/paper/1903.03503/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 8 Mar 2019.

## Built on by (most cited first, 2 of 2)

- [FragmGAN: Generative Adversarial Nets for Fragmentary Data Imputation and Prediction](https://mlsanity.com/paper/2203.04692/) (2022)
- [Convolve and Conquer: Data Comparison with Wiener Filters](https://mlsanity.com/paper/2311.06558/) (2023)

## Abstract (arXiv)

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.