Description 
PhD position in Deep Neural Networks with Dempster Shafer Theory (Fully funded) 
Place: LGI2A, Université d’Artois, Béthune, France 
Starting date: October 2023 
Candidate before May 2023 
Duration : 3 years 
Website: [ 
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Subject 
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. 

To apply, please send the following documents grouped in one pdf file: your CV, 
your grades for the current and past years, a motivation letter, and at most 
two recommendations (optional) to sebastien.ra...@univ-artois.fr , 
frederic.pic...@univ-artois.fr and david.merc...@univ-artois.fr 

References 
[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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