# Interval Deep Learning for Uncertainty Quantification in Safety Applications

arXiv: https://arxiv.org/abs/2105.06438 · HTML: https://mlsanity.com/paper/2105.06438/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- Builds on 11 of its 57 references that are in the map.
- First posted on arXiv 13 May 2021.

## Builds on (most cited first, 11 of 11)

- [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)
- [What Uncertainties Do We Need in Bayesian Deep Learning for Computer Vision?](https://mlsanity.com/paper/1703.04977/) (2017)
- [Deep Recurrent Q-Learning for Partially Observable MDPs](https://mlsanity.com/paper/1507.06527/) (2015)
- [Probabilistic Backpropagation for Scalable Learning of Bayesian Neural Networks](https://mlsanity.com/paper/1502.05336/) (2015)
- [Deep Hidden Physics Models: Deep Learning of Nonlinear Partial Differential Equations](https://mlsanity.com/paper/1801.06637/) (2018)
- [Algorithms for Verifying Deep Neural Networks](https://mlsanity.com/paper/1903.06758/) (2019)
- [Formal Security Analysis of Neural Networks using Symbolic Intervals](https://mlsanity.com/paper/1804.10829/) (2018)
- [Bayesian Recurrent Neural Network Models for Forecasting and Quantifying Uncertainty in Spatial-Temporal Data](https://mlsanity.com/paper/1711.00636/) (2017)
- [Cumulo: A Dataset for Learning Cloud Classes](https://mlsanity.com/paper/1911.04227/) (2019)
- [Optimizing Taxi Carpool Policies via Reinforcement Learning and Spatio-Temporal Mining](https://mlsanity.com/paper/1811.04345/) (2018)

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

- [Spelunking the Deep: Guaranteed Queries on General Neural Implicit Surfaces via Range Analysis](https://mlsanity.com/paper/2202.02444/) (2022)
- [Uncertainty Quantification in Machine Learning for Biosignal Applications -- A Review](https://mlsanity.com/paper/2312.09454/) (2023)

## Abstract (arXiv)

Deep neural networks (DNNs) are becoming more prevalent in important safety-critical applications, where reliability in the prediction is paramount. Despite their exceptional prediction capabilities, current DNNs do not have an implicit mechanism to quantify and propagate significant input data uncertainty -- which is common in safety-critical applications. In many cases, this uncertainty is epistemic and can arise from multiple sources, such as lack of knowledge about the data generating process, imprecision, ignorance, and poor understanding of physics phenomena. Recent approaches have focused on quantifying parameter uncertainty, but approaches to end-to-end training of DNNs with epistemic input data uncertainty are more limited and largely problem-specific. In this work, we present a DNN optimized with gradient-based methods capable to quantify input and parameter uncertainty by means of interval analysis, which we call Deep Interval Neural Network (DINN). We perform experiments on an air pollution dataset with sensor uncertainty and show that the DINN can produce accurate bounded estimates from uncertain input data.