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We propose a new probabilistic method for unsupervised recovery of corrupteddata. Given a large ensemble of degraded samples, our method recovers accurateposteriors of clean values, allowing the exploration of the manifold ofpossible reconstructed data and hence characterising the underlyinguncertainty. In this setting, direct application of classical variationalmethods often gives rise to collapsed densities that do not adequately explorethe solution space. Instead, we derive our novel reduced entropy conditionapproximate inference method that results in rich posteriors. We test our modelin a data recovery task under the common setting of missing values and noise,demonstrating superior performance to existing variational methods forimputation and de-noising with different real data sets. We further show higherclassification accuracy after imputation, proving the advantage of propagatinguncertainty to downstream tasks with our model.

Tomographic Auto-Encoder: Unsupervised Bayesian Recovery of Corrupted Data