arXiv subjects

Thierry Denoeux

Publications and source records attributed to Thierry Denoeux.

At least 19 recordsLinked to original sources

arXiv2024

Evidential time-to-event prediction with calibrated uncertainty quantification

Time-to-event analysis provides insights into clinical prognosis and treatment recommendations. However, this task is more challenging than standard regression problems due to the presence of censored observations. Additionally, the lack of confidence assessment, model robustness, and prediction calibration raises concerns about the reliability of predictions. To address these challenges, we propose an evidential regression model specifically designed for time-to-event prediction. The proposed model quantifies both epistemic and aleatory uncertainties using Gaussian Random Fuzzy Numbers and belief functions, providing clinicians with uncertainty-aware survival time predictions. The model is trained by minimizing a generalized negative log-likelihood function accounting for data censoring. Experimental evaluations using simulated datasets with different data distributions and censoring conditions, as well as real-world datasets across diverse clinical applications, demonstrate that our model delivers both accurate and reliable performance, outperforming state-of-the-art methods. These results highlight the potential of our approach for enhancing clinical decision-making in survival analysis.

cs.LG↗

arXiv2024

Deep evidential fusion with uncertainty quantification and contextual discounting for multimodal medical image segmentation

Single-modality medical images generally do not contain enough information to reach an accurate and reliable diagnosis. For this reason, physicians generally diagnose diseases based on multimodal medical images such as, e.g., PET/CT. The effective fusion of multimodal information is essential to reach a reliable decision and explain how the decision is made as well. In this paper, we propose a fusion framework for multimodal medical image segmentation based on deep learning and the Dempster-Shafer theory of evidence. In this framework, the reliability of each single modality image when segmenting different objects is taken into account by a contextual discounting operation. The discounted pieces of evidence from each modality are then combined by Dempster's rule to reach a final decision. Experimental results with a PET-CT dataset with lymphomas and a multi-MRI dataset with brain tumors show that our method outperforms the state-of-the-art methods in accuracy and reliability.

eess.IV↗

arXiv2024

An evidential time-to-event prediction model based on Gaussian random fuzzy numbers

We introduce an evidential model for time-to-event prediction with censored data. In this model, uncertainty on event time is quantified by Gaussian random fuzzy numbers, a newly introduced family of random fuzzy subsets of the real line with associated belief functions, generalizing both Gaussian random variables and Gaussian possibility distributions. Our approach makes minimal assumptions about the underlying time-to-event distribution. The model is fit by minimizing a generalized negative log-likelihood function that accounts for both normal and censored data. Comparative experiments on two real-world datasets demonstrate the very good performance of our model as compared to the state-of-the-art.

cs.LG↗

arXiv2024

Reasoning with fuzzy and uncertain evidence using epistemic random fuzzy sets: general framework and practical models

We introduce a general theory of epistemic random fuzzy sets for reasoning with fuzzy or crisp evidence. This framework generalizes both the Dempster-Shafer theory of belief functions, and possibility theory. Independent epistemic random fuzzy sets are combined by the generalized product-intersection rule, which extends both Dempster's rule for combining belief functions, and the product conjunctive combination of possibility distributions. We introduce Gaussian random fuzzy numbers and their multi-dimensional extensions, Gaussian random fuzzy vectors, as practical models for quantifying uncertainty about scalar or vector quantities. Closed-form expressions for the combination, projection and vacuous extension of Gaussian random fuzzy numbers and vectors are derived.

cs.AI↗

arXiv2022

Application of belief functions to medical image segmentation: A review

The investigation of uncertainty is of major importance in risk-critical applications, such as medical image segmentation. Belief function theory, a formal framework for uncertainty analysis and multiple evidence fusion, has made significant contributions to medical image segmentation, especially since the development of deep learning. In this paper, we provide an introduction to the topic of medical image segmentation methods using belief function theory. We classify the methods according to the fusion step and explain how information with uncertainty or imprecision is modeled and fused with belief function theory. In addition, we discuss the challenges and limitations of present belief function-based medical image segmentation and propose orientations for future research. Future research could investigate both belief function theory and deep learning to achieve more promising and reliable segmentation results.

cs.CV↗

arXiv2022

Evidence fusion with contextual discounting for multi-modality medical image segmentation

As information sources are usually imperfect, it is necessary to take into account their reliability in multi-source information fusion tasks. In this paper, we propose a new deep framework allowing us to merge multi-MR image segmentation results using the formalism of Dempster-Shafer theory while taking into account the reliability of different modalities relative to different classes. The framework is composed of an encoder-decoder feature extraction module, an evidential segmentation module that computes a belief function at each voxel for each modality, and a multi-modality evidence fusion module, which assigns a vector of discount rates to each modality evidence and combines the discounted evidence using Dempster's rule. The whole framework is trained by minimizing a new loss function based on a discounted Dice index to increase segmentation accuracy and reliability. The method was evaluated on the BraTs 2021 database of 1251 patients with brain tumors. Quantitative and qualitative results show that our method outperforms the state of the art, and implements an effective new idea for merging multi-information within deep neural networks.

cs.CV↗

arXiv2022

EGMM: an Evidential Version of the Gaussian Mixture Model for Clustering

The Gaussian mixture model (GMM) provides a simple yet principled framework for clustering, with properties suitable for statistical inference. In this paper, we propose a new model-based clustering algorithm, called EGMM (evidential GMM), in the theoretical framework of belief functions to better characterize cluster-membership uncertainty. With a mass function representing the cluster membership of each object, the evidential Gaussian mixture distribution composed of the components over the powerset of the desired clusters is proposed to model the entire dataset. The parameters in EGMM are estimated by a specially designed Expectation-Maximization (EM) algorithm. A validity index allowing automatic determination of the proper number of clusters is also provided. The proposed EGMM is as simple as the classical GMM, but can generate a more informative evidential partition for the considered dataset. The synthetic and real dataset experiments show that the proposed EGMM performs better than other representative clustering algorithms. Besides, its superiority is also demonstrated by an application to multi-modal brain image segmentation.

cs.LG↗

arXiv2022

An Evidential Neural Network Model for Regression Based on Random Fuzzy Numbers

We introduce a distance-based neural network model for regression, in which prediction uncertainty is quantified by a belief function on the real line. The model interprets the distances of the input vector to prototypes as pieces of evidence represented by Gaussian random fuzzy numbers (GRFN's) and combined by the generalized product intersection rule, an operator that extends Dempster's rule to random fuzzy sets. The network output is a GRFN that can be summarized by three numbers characterizing the most plausible predicted value, variability around this value, and epistemic uncertainty. Experiments with real datasets demonstrate the very good performance of the method as compared to state-of-the-art evidential and statistical learning algorithms. \keywords{Evidence theory, Dempster-Shafer theory, belief functions, machine learning, random fuzzy sets.

cs.LG↗

arXiv2022

Lymphoma segmentation from 3D PET-CT images using a deep evidential network

An automatic evidential segmentation method based on Dempster-Shafer theory and deep learning is proposed to segment lymphomas from three-dimensional Positron Emission Tomography (PET) and Computed Tomography (CT) images. The architecture is composed of a deep feature-extraction module and an evidential layer. The feature extraction module uses an encoder-decoder framework to extract semantic feature vectors from 3D inputs. The evidential layer then uses prototypes in the feature space to compute a belief function at each voxel quantifying the uncertainty about the presence or absence of a lymphoma at this location. Two evidential layers are compared, based on different ways of using distances to prototypes for computing mass functions. The whole model is trained end-to-end by minimizing the Dice loss function. The proposed combination of deep feature extraction and evidential segmentation is shown to outperform the baseline UNet model as well as three other state-of-the-art models on a dataset of 173 patients.

cs.CV↗

arXiv2022

Clustering acoustic emission data streams with sequentially appearing clusters using mixture models

The interpretation of unlabeled acoustic emission (AE) data classically relies on general-purpose clustering methods. While several external criteria have been used in the past to select the hyperparameters of those algorithms, few studies have paid attention to the development of dedicated objective functions in clustering methods able to cope with the specificities of AE data. We investigate how to explicitly represent clusters onsets in mixture models in general, and in Gaussian Mixture Models (GMM) in particular. By modifying the internal criterion of such models, we propose the first clustering method able to provide, through parameters estimated by an expectation-maximization procedure, information about when clusters occur (onsets), how they grow (kinetics) and their level of activation through time. This new objective function accommodates continuous timestamps of AE signals and, thus, their order of occurrence. The method, called GMMSEQ, is experimentally validated to characterize the loosening phenomenon in bolted structure under vibrations. A comparison with three standard clustering methods on raw streaming data from five experimental campaigns shows that GMMSEQ not only provides useful qualitative information about the timeline of clusters, but also shows better performance in terms of cluster characterization. In view of developing an open acoustic emission initiative and according to the FAIR principles, the datasets and the codes are made available to reproduce the research of this paper.

stat.ML↗

arXiv2021

Fusion of evidential CNN classifiers for image classification

We propose an information-fusion approach based on belief functions to combine convolutional neural networks. In this approach, several pre-trained DS-based CNN architectures extract features from input images and convert them into mass functions on different frames of discernment. A fusion module then aggregates these mass functions using Dempster's rule. An end-to-end learning procedure allows us to fine-tune the overall architecture using a learning set with soft labels, which further improves the classification performance. The effectiveness of this approach is demonstrated experimentally using three benchmark databases.

cs.CV↗

arXiv2021

Deep PET/CT fusion with Dempster-Shafer theory for lymphoma segmentation

Lymphoma detection and segmentation from whole-body Positron Emission Tomography/Computed Tomography (PET/CT) volumes are crucial for surgical indication and radiotherapy. Designing automatic segmentation methods capable of effectively exploiting the information from PET and CT as well as resolving their uncertainty remain a challenge. In this paper, we propose an lymphoma segmentation model using an UNet with an evidential PET/CT fusion layer. Single-modality volumes are trained separately to get initial segmentation maps and an evidential fusion layer is proposed to fuse the two pieces of evidence using Dempster-Shafer theory (DST). Moreover, a multi-task loss function is proposed: in addition to the use of the Dice loss for PET and CT segmentation, a loss function based on the concordance between the two segmentation is added to constrain the final segmentation. We evaluate our proposal on a database of polycentric PET/CT volumes of patients treated for lymphoma, delineated by the experts. Our method get accurate segmentation results with Dice score of 0.726, without any user interaction. Quantitative results show that our method is superior to the state-of-the-art methods.

eess.IV↗

arXiv2021

NN-EVCLUS: Neural Network-based Evidential Clustering

Evidential clustering is an approach to clustering based on the use of Dempster-Shafer mass functions to represent cluster-membership uncertainty. In this paper, we introduce a neural-network based evidential clustering algorithm, called NN-EVCLUS, which learns a mapping from attribute vectors to mass functions, in such a way that more similar inputs are mapped to output mass functions with a lower degree of conflict. The neural network can be paired with a one-class support vector machine to make it robust to outliers and allow for novelty detection. The network is trained to minimize the discrepancy between dissimilarities and degrees of conflict for all or some object pairs. Additional terms can be added to the loss function to account for pairwise constraints or labeled data, which can also be used to adapt the metric. Comparative experiments show the superiority of N-EVCLUS over state-of-the-art evidential clustering algorithms for a range of unsupervised and constrained clustering tasks involving both attribute and dissimilarity data.

cs.LG↗

arXiv2021

Evidential segmentation of 3D PET/CT images

PET and CT are two modalities widely used in medical image analysis. Accurately detecting and segmenting lymphomas from these two imaging modalities are critical tasks for cancer staging and radiotherapy planning. However, this task is still challenging due to the complexity of PET/CT images, and the computation cost to process 3D data. In this paper, a segmentation method based on belief functions is proposed to segment lymphomas in 3D PET/CT images. The architecture is composed of a feature extraction module and an evidential segmentation (ES) module. The ES module outputs not only segmentation results (binary maps indicating the presence or absence of lymphoma in each voxel) but also uncertainty maps quantifying the classification uncertainty. The whole model is optimized by minimizing Dice and uncertainty loss functions to increase segmentation accuracy. The method was evaluated on a database of 173 patients with diffuse large b-cell lymphoma. Quantitative and qualitative results show that our method outperforms the state-of-the-art methods.

eess.IV↗

arXiv2021

Belief function-based semi-supervised learning for brain tumor segmentation

Precise segmentation of a lesion area is important for optimizing its treatment. Deep learning makes it possible to detect and segment a lesion field using annotated data. However, obtaining precisely annotated data is very challenging in the medical domain. Moreover, labeling uncertainty and imprecision make segmentation results unreliable. In this paper, we address the uncertain boundary problem by a new evidential neural network with an information fusion strategy, and the scarcity of annotated data by semi-supervised learning. Experimental results show that our proposal has better performance than state-of-the-art methods.

cs.CV↗

arXiv2021

Covid-19 classification with deep neural network and belief functions

Computed tomography (CT) image provides useful information for radiologists to diagnose Covid-19. However, visual analysis of CT scans is time-consuming. Thus, it is necessary to develop algorithms for automatic Covid-19 detection from CT images. In this paper, we propose a belief function-based convolutional neural network with semi-supervised training to detect Covid-19 cases. Our method first extracts deep features, maps them into belief degree maps and makes the final classification decision. Our results are more reliable and explainable than those of traditional deep learning-based classification models. Experimental results show that our approach is able to achieve a good performance with an accuracy of 0.81, an F1 of 0.812 and an AUC of 0.875.

eess.IV↗

arXiv2020

Belief functions induced by random fuzzy sets: A general framework for representing uncertain and fuzzy evidence

We revisit Zadeh's notion of "evidence of the second kind" and show that it provides the foundation for a general theory of epistemic random fuzzy sets, which generalizes both the Dempster-Shafer theory of belief functions and possibility theory. In this perspective, Dempster-Shafer theory deals with belief functions generated by random sets, while possibility theory deals with belief functions induced by fuzzy sets. The more general theory allows us to represent and combine evidence that is both uncertain and fuzzy. We demonstrate the application of this formalism to statistical inference, and show that it makes it possible to reconcile the possibilistic interpretation of likelihood with Bayesian inference.

cs.AI↗

arXiv2020

An Interval-Valued Utility Theory for Decision Making with Dempster-Shafer Belief Functions

The main goal of this paper is to describe an axiomatic utility theory for Dempster-Shafer belief function lotteries. The axiomatic framework used is analogous to von Neumann-Morgenstern's utility theory for probabilistic lotteries as described by Luce and Raiffa. Unlike the probabilistic case, our axiomatic framework leads to interval-valued utilities, and therefore, to a partial (incomplete) preference order on the set of all belief function lotteries. If the belief function reference lotteries we use are Bayesian belief functions, then our representation theorem coincides with Jaffray's representation theorem for his linear utility theory for belief functions. We illustrate our representation theorem using some examples discussed in the literature, and we propose a simple model for assessing utilities based on an interval-valued pessimism index representing a decision-maker's attitude to ambiguity and indeterminacy. Finally, we compare our decision theory with those proposed by Jaffray, Smets, Dubois et al., Giang and Shenoy, and Shafer.

cs.AI↗