# Logistic Regression, Neural Networks and Dempster-Shafer Theory: a New Perspective

arXiv: https://arxiv.org/abs/1807.01846 · HTML: https://mlsanity.com/paper/1807.01846/

## Key facts

- Cited by 11 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 5 Jul 2018.

## Built on by (most cited first, 11 of 11)

- [An evidential classifier based on Dempster-Shafer theory and deep learning](https://mlsanity.com/paper/2103.13549/) (2021)
- [Lymphoma segmentation from 3D PET-CT images using a deep evidential network](https://mlsanity.com/paper/2201.13078/) (2022)
- [Evidential fully convolutional network for semantic segmentation](https://mlsanity.com/paper/2103.13544/) (2021)
- [Evidential Softmax for Sparse Multimodal Distributions in Deep Generative Models](https://mlsanity.com/paper/2110.14182/) (2021)
- [Application of belief functions to medical image segmentation: A review](https://mlsanity.com/paper/2205.01733/) (2022)
- [Fusion of neural networks, for LIDAR-based evidential road mapping](https://mlsanity.com/paper/2102.03326/) (2021)
- [BF-QC: Belief Functions on Quantum Circuits](https://mlsanity.com/paper/2107.03930/) (2021)
- [A neurosymbolic Approach with Epistemic Deep Learning for Hierarchical Image Classification](https://mlsanity.com/paper/2605.16383/) (2026)
- [Feature Fusion for Improved Classification: Combining Dempster-Shafer Theory and Multiple CNN Architectures](https://mlsanity.com/paper/2405.20230/) (2024)
- [A Sugeno Integral View of Binarized Neural Network Inference](https://mlsanity.com/paper/2604.17967/) (2026)
- [Evidential Rule Learning for Interpretable Classification with Abstention](https://mlsanity.com/paper/2608.05859/) (2026)

## Abstract (arXiv)

We revisit logistic regression and its nonlinear extensions, including multilayer feedforward neural networks, by showing that these classifiers can be viewed as converting input or higher-level features into Dempster-Shafer mass functions and aggregating them by Dempster's rule of combination. The probabilistic outputs of these classifiers are the normalized plausibilities corresponding to the underlying combined mass function. This mass function is more informative than the output probability distribution. In particular, it makes it possible to distinguish between lack of evidence (when none of the features provides discriminant information) from conflicting evidence (when different features support different classes). This expressivity of mass functions allows us to gain insight into the role played by each input feature in logistic regression, and to interpret hidden unit outputs in multilayer neural networks. It also makes it possible to use alternative decision rules, such as interval dominance, which select a set of classes when the available evidence does not unambiguously point to a single class, thus trading reduced error rate for higher imprecision.