Interval Deep Learning for Uncertainty Quantification in Safety Applications

TL;DR

This paper introduces Deep Interval Neural Networks (DINN), a novel deep learning approach that quantifies both input and parameter uncertainty using interval analysis, enhancing reliability in safety-critical applications.

Contribution

The work presents a new end-to-end DNN training method with interval analysis to quantify epistemic input and parameter uncertainty, addressing limitations of existing approaches.

Findings

DINN provides accurate bounded estimates with uncertain input data.

Experiments on air pollution data demonstrate DINN's effectiveness.

DINN outperforms traditional models in uncertainty quantification.

Abstract

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.