  Parametric and non-parametric classifiers often have to deal with real-world
data, where corruptions like noise, occlusions, and blur are unavoidable -
posing significant challenges. We present a probabilistic approach to classify
strongly corrupted data and quantify uncertainty, despite the model only having
been trained with uncorrupted data. A semi-supervised autoencoder trained on
uncorrupted data is the underlying architecture. We use the decoding part as a
generative model for realistic data and extend it by convolutions, masking, and
additive Gaussian noise to describe imperfections. This constitutes a
statistical inference task in terms of the optimal latent space activations of
the underlying uncorrupted datum. We solve this problem approximately with
Metric Gaussian Variational Inference (MGVI). The supervision of the
autoencoder's latent space allows us to classify corrupted data directly under
uncertainty with the statistically inferred latent space activations.
Furthermore, we demonstrate that the model uncertainty strongly depends on
whether the classification is correct or wrong, setting a basis for a
statistical "lie detector" of the classification. Independent of that, we show
that the generative model can optimally restore the uncorrupted datum by
decoding the inferred latent space activations.
