# Uncertainty Estimations by Softplus normalization in Bayesian Convolutional Neural Networks with Variational Inference

arXiv: https://arxiv.org/abs/1806.05978 · HTML: https://mlsanity.com/paper/1806.05978/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 15 Jun 2018.

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

- [Feature Generation and Hypothesis Verification for Reliable Face Anti-Spoofing](https://mlsanity.com/paper/2112.14894/) (2021)
- [Amortized Variational Inference: A Systematic Review](https://mlsanity.com/paper/2209.10888/) (2022)

## Abstract (arXiv)

We introduce a novel uncertainty estimation for classification tasks for Bayesian convolutional neural networks with variational inference. By normalizing the output of a Softplus function in the final layer, we estimate aleatoric and epistemic uncertainty in a coherent manner. The intractable posterior probability distributions over weights are inferred by Bayes by Backprop. Firstly, we demonstrate how this reliable variational inference method can serve as a fundamental construct for various network architectures. On multiple datasets in supervised learning settings (MNIST, CIFAR-10, CIFAR-100), this variational inference method achieves performances equivalent to frequentist inference in identical architectures, while the two desiderata, a measure for uncertainty and regularization are incorporated naturally. Secondly, we examine how our proposed measure for aleatoric and epistemic uncertainties is derived and validate it on the aforementioned datasets.