# Classification and Uncertainty Quantification of Corrupted Data using Semi-Supervised Autoencoders

arXiv: https://arxiv.org/abs/2105.13393 · HTML: https://mlsanity.com/paper/2105.13393/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 14 of its 21 references that are in the map.
- First posted on arXiv 27 May 2021.

## Builds on (most cited first, 14 of 14)

- [Adam: A Method for Stochastic Optimization](https://mlsanity.com/paper/1412.6980/) (2014)
- [Dropout as a Bayesian Approximation: Representing Model Uncertainty in Deep Learning](https://mlsanity.com/paper/1506.02142/) (2015)
- [Fashion-MNIST: a Novel Image Dataset for Benchmarking Machine Learning Algorithms](https://mlsanity.com/paper/1708.07747/) (2017)
- [Auto-Encoding Variational Bayes](https://mlsanity.com/paper/1312.6114/) (2013)
- [A Simple Unified Framework for Detecting Out-of-Distribution Samples and Adversarial Attacks](https://mlsanity.com/paper/1807.03888/) (2018)
- [Evidential Deep Learning to Quantify Classification Uncertainty](https://mlsanity.com/paper/1806.01768/) (2018)
- [Self-Normalizing Neural Networks](https://mlsanity.com/paper/1706.02515/) (2017)
- [Automatic Differentiation Variational Inference](https://mlsanity.com/paper/1603.00788/) (2016)
- [Deep Bayesian Inversion](https://mlsanity.com/paper/1811.05910/) (2018)
- [Uncertainty Quantification with Generative Models](https://mlsanity.com/paper/1910.10046/) (2019)
- [Metric Gaussian Variational Inference](https://mlsanity.com/paper/1901.11033/) (2019)
- [Probabilistic Autoencoder](https://mlsanity.com/paper/2006.05479/) (2020)
- [Conditional Inference in Pre-trained Variational Autoencoders via Cross-coding](https://mlsanity.com/paper/1805.07785/) (2018)
- [Posterior inference unchained with EL_2O](https://mlsanity.com/paper/1901.04454/) (2019)

## Built on by (most cited first, 1 of 1)

- [Failure Prediction at Runtime for Generative Robot Policies](https://mlsanity.com/paper/2510.09459/) (2025)

## Abstract (arXiv)

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.