Laboratoire de Génie Informatique et d’Automatique de l’Artois

Ph.D. thesis of Serigne Mamadou DIèNE

Developing Deep Neural Networks with Dempster-Shafer Theory

Starting date: 1 October 2023
Funding: 50% Artois University 50% Hauts-de-France region
Keywords: Deep neural networks, Dempster-Shafer Theory, Machine Learning

Deep neural networks (DNNs) refer to predictive models that exploit multiple layers of artificial neurons to compute a prediction [1,4]. In the original version, the layers are sequential and each neuron in a layer is connected with neurons in the previous layer. Many other alternative architectures have been proposed to adapt DNNs to solve specific and complex problems.

On the other hand, a theory called Dempster-Shafer theory of belief functions, or theory of evidence [15], has emerged as a rich and flexible generalization of the Bayesian probability theory, able to deal with imperfect (uncertain, imprecise, …) information. It is notably used in a growing number of applications such as classification (e.g. [2]), clustering (e.g. [3,7]) or information fusion (e.g. [5,13]).

Recent works [6,16,17] have shown the interest of enriching a DNN with an additional distance-based Dempster Shafer layer [2] for predicting belief functions. These belief functions can be of great interest to represent a reality as faithfully as possible, for example to perform a partial classification [8], i.e. decisions in favor of a group of classes.

The main idea of this thesis is to develop such deep evidential networks in more depth by exploiting methods developed at LGI2A allowing one to consider finer knowledge about the quality [12, 14] and the dependence of information [11], or the ignorance in predictions [9,10].

Two applications are envisaged: Image analysis from drones and fish population analysis.


This thesis is co-financed by the Hauts-de-France region and the Artois University.


[1] C. M. Bishop. Pattern recognition and machine learning, 5th Edition. Information science and statistics. Springer, 2007.
[2] T. Denoeux. A neural network classifier based on dempster-shafer theory. IEEE Transactions on Systems, Man, and Cybernetics-Part A: Systems and Humans, 30(2):131–150, 2000.
[3] T. Denœux. Calibrated model-based evidential clustering using bootstrapping. Information Science, 528:17–45, 2020.
[4] I. Goodfellow, Y. Bengio and A. Courville: Deep Learning (Adaptive Computation and Machine Learning), MIT Press, Cambridge (USA), 2016.
[5] L. Huang, T. Denoeux, P. Vera, and S. Ruan. Evidence fusion with contextual discounting for multi-modality medical image segmentation. In International Conference on Medical Image Computing and Computer-Assisted Intervention, pages 401–411. Springer, 2022.
[6] L. Huang, S. Ruan, P. Decazes, and T. Denoeux. Lymphoma segmentation from 3D PET-CT images using a deep evidential network. International Journal of Approximate Reasoning, Volume 149, pages 39-60, 2022.
[7] F. Li, S. Li, and T. Denœux. Combining clusterings in the belief function framework. Array, 6:100018, 2020.
[8] L. Ma and T. Denœux. Partial classification in the belief function framework. Knowledge-Based Systems, 214: article 106742, 2021.
[9] P. Minary, F. Pichon, D. Mercier, E. Lefèvre and B. Droit. Evidential joint calibration of binary SVM classifiers, Soft Computing, pp 4655-4671, Vol. 23, No. 13, 2019.
[10] S. Ramel, F. Pichon and F. Delmotte. A reliable version of choquistic regression based on evidence theory, Knowledge-Based Systems, KBS, pp 106252, Vol. 205, 2020.
[11] F. Pichon. Canonical decomposition of belief functions based on Teugels’ representation of the multivariate Bernoulli distribution. Information Sciences, 428:76-104, 2018.
[12] F. Pichon, D. Dubois, and T. Denœux. Relevance and truthfulness in information correction and fusion. International Journal Approximate Reasoning, 53(2):159–175, 2012.
[13] F. Pichon, D. Dubois, and T. Denoeux. Quality of information sources in information fusion. In Éloi Bossé and Galina L. Rogova, editors, Information Quality in Information Fusion and Decision Making, pages 31–49. Springer, 2019.
[14] F. Pichon, D. Mercier, E. Lefèvre, and F. Delmotte. Proposition and learning of some belief function contextual correction mechanisms. International Journal Approximate Reasoning, 72:4–42, 2016.
[15] G. Shafer. A mathematical theory of evidence, volume 42. Princeton university press, 1976.
[16] Z. Tong, P. Xu, and T. Denoeux. An evidential classifier based on dempster-shafer theory and deep learning. Neurocomputing, 450:275–293, 2021.
[17] Z. Tong, P. Xu, and T. Denœux. Fusion of evidential cnn classifiers for image classification. In International Conference on Belief Functions, pages 168–176. Springer, 2021.

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