Unsupervised Data Imputation via Variational Inference of Deep Subspaces (1903.03503v1)

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.

• The paper introduces a probabilistic model that leverages nonlinear deep embeddings to improve data imputation over traditional linear methods.
• It employs a variational Bayesian approach with an encoder-decoder CNN to accurately reconstruct missing entries in high-dimensional datasets.
• Benchmarking on MNIST, FASHION-MNIST, and brain MRIs demonstrates the method’s superior performance and practical benefits for medical imaging.

Unsupervised Data Imputation via Variational Inference of Deep Subspaces

The academic paper titled "Unsupervised Data Imputation via Variational Inference of Deep Subspaces" addresses the critical challenge of data imputation, particularly focusing on the unsupervised estimation of missing image data. This research explores a setting where full observations are not available, which is a realistic scenario across various domains, including medical imaging, where acquiring complete datasets can be cost-prohibitive or infeasible.

The paper introduces a robust probabilistic model that conceptualizes sparse high-dimensional imaging data as generated by a non-linear deep embedding. This approach contrasts with traditional linear subspace models which often fail to capture complex relationships inherent in high-dimensional data. The authors propose a variational inference framework that leverages deep convolutional neural networks (CNNs) to estimate the generative process of observed data, addressing missing entries explicitly.

Key Contributions and Methodology

• Probabilistic Modeling: The authors establish a model where high-dimensional data arise from a non-linear subspace, expressed via a deep neural network. This conception allows for richer representation of variations than linear models.
• Variational Inference: The work employs a variational Bayesian approach to approximate posterior distributions, optimizing this via neural networks. An encoder-decoder structure is crafted, wherein the encoder maps observed data to latent space while accounting for missingness, and the decoder reconstructs full data from this latent space estimate.
• Sparsity-aware Networks: The authors introduce network layers specifically designed to accommodate sparse input data. This includes sparsity-aware fully connected and convolutional layers that dynamically adjust operations based on observed data, leveraging observed patterns without imputing unobserved pixels with zero or mean values directly.
• Comparison to Linear Models: The paper provides a theoretical exploration of linear models as special cases of their proposed framework, leading to novel insights into known methods like Principal Component Analysis (PCA) and linear auto-encoders.
• Benchmarking and Evaluation: Through extensive evaluation on public datasets like MNIST, FASHION-MNIST, and medical brain MRIs with simulated missing data, the authors demonstrate the superior performance of their method against baseline models, including traditional linear subspace models, dictionary learning, and Deep Image Priors (DIP).

Results and Implications

The research evidences the capacity of non-linear embeddings to accurately recover missing information, especially in scenarios where data is severely under-sampled. The experimental results underscore the method’s practical applicability in medical imaging, where the reconstruction of missing slice data from MRI scans showed enhanced performance over competing unsupervised techniques.

The novel architectural components such as sparsity-aware layers not only facilitate remarkable imputation quality but also represent a meaningful advancement for constructing networks capable of accommodating environments with incomplete data.

Future Directions

The work opens several avenues for future research. Enhancements could include exploring the adaptability of such models to other types of high-dimensional data, or integrating these methods into real-time imaging systems with strict temporal constraints. Moreover, with the rise of hybrid approach in AI, combining supervised fine-tuning with this unsupervised framework might further enhance data recovery accuracies.

Overall, the paper makes a significant contribution to the fields of data imputation and unsupervised machine learning by offering a framework equipped to handle the complexities of sparse high-dimensional imaging, particularly in the context of medical data where the implications of accurate imputation can drive substantial downstream benefits in diagnostics and treatment planning.