# CreINNs: Credal-Set Interval Neural Networks for Uncertainty Estimation in Classification Tasks

arXiv: https://arxiv.org/abs/2401.05043 · HTML: https://mlsanity.com/paper/2401.05043/

## Key facts

- Cited by 26 papers in the map (data through 14 Oct 2026).
- Builds on 30 of its 76 references that are in the map.
- First posted on arXiv 10 Jan 2024.

## Builds on (most cited first, 30 of 30)

- [Deep Residual Learning for Image Recognition](https://mlsanity.com/paper/1512.03385/) (2015)
- [Batch Normalization: Accelerating Deep Network Training by Reducing Internal Covariate Shift](https://mlsanity.com/paper/1502.03167/) (2015)
- [Dropout as a Bayesian Approximation: Representing Model Uncertainty in Deep Learning](https://mlsanity.com/paper/1506.02142/) (2015)
- [Simple and Scalable Predictive Uncertainty Estimation using Deep Ensembles](https://mlsanity.com/paper/1612.01474/) (2016)
- [What Uncertainties Do We Need in Bayesian Deep Learning for Computer Vision?](https://mlsanity.com/paper/1703.04977/) (2017)
- [Can You Trust Your Model's Uncertainty? Evaluating Predictive Uncertainty Under Dataset Shift](https://mlsanity.com/paper/1906.02530/) (2019)
- [Aleatoric and Epistemic Uncertainty in Machine Learning: An Introduction to Concepts and Methods](https://mlsanity.com/paper/1910.09457/) (2019)
- [A Review of Uncertainty Quantification in Deep Learning: Techniques, Applications and Challenges](https://mlsanity.com/paper/2011.06225/) (2020)
- [A Survey of Uncertainty in Deep Neural Networks](https://mlsanity.com/paper/2107.03342/) (2021)
- [Simple and Principled Uncertainty Estimation with Deterministic Deep Learning via Distance Awareness](https://mlsanity.com/paper/2006.10108/) (2020)
- [Hands-on Bayesian Neural Networks -- a Tutorial for Deep Learning Users](https://mlsanity.com/paper/2007.06823/) (2020)
- [Variational Dropout Sparsifies Deep Neural Networks](https://mlsanity.com/paper/1701.05369/) (2017)
- [Fairness without Demographics through Adversarially Reweighted Learning](https://mlsanity.com/paper/2006.13114/) (2020)
- [Evaluating Scalable Bayesian Deep Learning Methods for Robust Computer Vision](https://mlsanity.com/paper/1906.01620/) (2019)
- [Flipout: Efficient Pseudo-Independent Weight Perturbations on Mini-Batches](https://mlsanity.com/paper/1803.04386/) (2018)
- [High-Quality Prediction Intervals for Deep Learning: A Distribution-Free, Ensembled Approach](https://mlsanity.com/paper/1802.07167/) (2018)
- [Shifts: A Dataset of Real Distributional Shift Across Multiple Large-Scale Tasks](https://mlsanity.com/paper/2107.07455/) (2021)
- [Bayesian Deep Ensembles via the Neural Tangent Kernel](https://mlsanity.com/paper/2007.05864/) (2020)
- [Large Scale Structure of Neural Network Loss Landscapes](https://mlsanity.com/paper/1906.04724/) (2019)
- [Deep Ensembles Work, But Are They Necessary?](https://mlsanity.com/paper/2202.06985/) (2022)
- [Benchmarking Bayesian Deep Learning on Diabetic Retinopathy Detection Tasks](https://mlsanity.com/paper/2211.12717/) (2022)
- [Credal Bayesian Deep Learning](https://mlsanity.com/paper/2302.09656/) (2023)
- [Tractable Function-Space Variational Inference in Bayesian Neural Networks](https://mlsanity.com/paper/2312.17199/) (2023)
- [Is the Volume of a Credal Set a Good Measure for Epistemic Uncertainty?](https://mlsanity.com/paper/2306.09586/) (2023)
- [Fast Predictive Uncertainty for Classification with Bayesian Deep Networks](https://mlsanity.com/paper/2003.01227/) (2020)
- [The Two Dimensions of Worst-case Training and the Integrated Effect for Out-of-domain Generalization](https://mlsanity.com/paper/2204.04384/) (2022)
- [Ensemble-based Uncertainty Quantification: Bayesian versus Credal Inference](https://mlsanity.com/paper/2107.10384/) (2021)
- [Epistemic Deep Learning](https://mlsanity.com/paper/2206.07609/) (2022)
- [Prediction Intervals: Split Normal Mixture from Quality-Driven Deep Ensembles](https://mlsanity.com/paper/2007.09670/) (2020)
- [Conformal Credal Self-Supervised Learning](https://mlsanity.com/paper/2205.15239/) (2022)

## Built on by (most cited first, 26 of 26)

- [Credal Learning Theory](https://mlsanity.com/paper/2402.00957/) (2024)
- [Credal Wrapper of Model Averaging for Uncertainty Estimation in Classification](https://mlsanity.com/paper/2405.15047/) (2024)
- [Integral Imprecise Probability Metrics](https://mlsanity.com/paper/2505.16156/) (2025)
- [Scoring Rules and Calibration for Imprecise Probabilities](https://mlsanity.com/paper/2410.23001/) (2024)
- [A Unified Evaluation Framework for Epistemic Predictions](https://mlsanity.com/paper/2501.16912/) (2025)
- [Epistemic Artificial Intelligence is Essential for Machine Learning Models to Truly 'Know When They Do Not Know'](https://mlsanity.com/paper/2505.04950/) (2025)
- [A calibration test for evaluating set-based epistemic uncertainty representations](https://mlsanity.com/paper/2502.16299/) (2025)
- [Random-Set Large Language Models](https://mlsanity.com/paper/2504.18085/) (2025)
- [Learning Credal Ensembles via Distributionally Robust Optimization](https://mlsanity.com/paper/2602.08470/) (2026)
- [Generalising realisability in statistical learning theory under epistemic uncertainty](https://mlsanity.com/paper/2402.14759/) (2024)
- [Epistemic Wrapping for Uncertainty Quantification](https://mlsanity.com/paper/2505.02277/) (2025)
- [Beyond Prediction-Set Size: Quantifying Conformal Uncertainty through Credal Geometry](https://mlsanity.com/paper/2602.01667/) (2026)
- [Direct Interval Propagation Methods using Neural-Network Surrogates for Uncertainty Quantification in Physical Systems Surrogate Model](https://mlsanity.com/paper/2603.21308/) (2026)
- [Random-Set Graph Neural Networks](https://mlsanity.com/paper/2605.11987/) (2026)
- [Credal Graph Neural Networks](https://mlsanity.com/paper/2512.02722/) (2025)
- [Quantification of Credal Uncertainty: A Distance-Based Approach](https://mlsanity.com/paper/2603.27270/) (2026)
- [Credal Large Language Models for Semantic Commitment under Uncertainty](https://mlsanity.com/paper/2608.23244/) (2026)
- [When Do Credal Sets Stabilize? Fixed-Point Theorems for Credal Set Updates](https://mlsanity.com/paper/2510.04769/) (2025)
- [Set-based v.s. Distribution-based Representations of Epistemic Uncertainty: A Comparative Study](https://mlsanity.com/paper/2602.22747/) (2026)
- [Efficient Credal Prediction through Decalibration](https://mlsanity.com/paper/2603.08495/) (2026)
- [A neurosymbolic Approach with Epistemic Deep Learning for Hierarchical Image Classification](https://mlsanity.com/paper/2605.16383/) (2026)
- [A formal definition and meta-model for a machine theory of mind](https://mlsanity.com/paper/2606.03471/) (2026)
- [Generalisation of Total Uncertainty in AI: A Theoretical Study](https://mlsanity.com/paper/2408.00946/) (2024)
- [SSP-RACL: Classification of Noisy Fundus Images with Self-Supervised Pretraining and Robust Adaptive Credal Loss](https://mlsanity.com/paper/2409.18147/) (2024)
- [XU-RS: Explaining Credal Width in Random-Set Language Models](https://mlsanity.com/paper/2609.37594/) (2026)
- [Understanding as No-Arbitrage: Bounded Dutch Books as a Definition and Training Objective for Language Models](https://mlsanity.com/paper/2609.39341/) (2026)

## Abstract (arXiv)

Effective uncertainty estimation is becoming increasingly attractive for enhancing the reliability of neural networks. This work presents a novel approach, termed Credal-Set Interval Neural Networks (CreINNs), for classification. CreINNs retain the fundamental structure of traditional Interval Neural Networks, capturing weight uncertainty through deterministic intervals. CreINNs are designed to predict an upper and a lower probability bound for each class, rather than a single probability value. The probability intervals can define a credal set, facilitating estimating different types of uncertainties associated with predictions. Experiments on standard multiclass and binary classification tasks demonstrate that the proposed CreINNs can achieve superior or comparable quality of uncertainty estimation compared to variational Bayesian Neural Networks (BNNs) and Deep Ensembles. Furthermore, CreINNs significantly reduce the computational complexity of variational BNNs during inference. Moreover, the effective uncertainty quantification of CreINNs is also verified when the input data are intervals.