arXiv subjects

Franck Vermet

Publications and source records attributed to Franck Vermet.

At least 19 recordsLinked to original sources

arXiv2026

Bayesian spatial modelling framework for assessing residential flood risk in property insurance

Spatial heterogeneity in insurance risk modelling is often represented using coarse areal structures, which can obscure fine-scale patterns critical for accurate risk assessment. This study introduces a point-referenced Bayesian framework to model claim occurrence and severity at the policyholder level, avoiding reliance on predefined geographic aggregation. Drawing on a large French insurance portfolio combined with high-resolution environmental variables, rainfall records, and institutional hazard maps, we compare a benchmark GLM with several discrete Bayesian specifications, including independent random effects, intrinsic conditional autoregressive (iCAR) and Besag-York-Mollie (BYM) models, and a continuously indexed Gaussian random field constructed using the stochastic partial differential equation (SPDE) approach. Inference is performed using Integrated Nested Laplace Approximation (INLA), enabling efficient estimation of latent spatial fields and non-linear covariate effects. Our results show that accounting for spatial dependence substantially improves occurrence modelling, while gains in severity prediction are more limited. The SPDE formulation further outperforms areal models by capturing sub-municipal risk gradients and reducing artefacts induced by arbitrary geographic partitioning. By conditioning on detailed building-level attributes, we isolate the contribution of latent spatial effects, refine the interpretation of observed covariates, and improve the allocation of risk premiums across the portfolio. In addition to enhanced predictive performance, the framework provides coherent uncertainty quantification and supports tail-risk assessment. To our knowledge, this is the first application of point-referenced SPDE models to flood insurance, offering a scalable statistical alternative for pricing and managing risks with strong spatial structure.

stat.AP↗

arXiv2026

Few-class Fidelity: Evaluating Explanations of Real-conditions CNN classifiers with Optimized Perturbations

The wide use of Convolutional Neural Networks (CNN) in numerous domains and real-world classification applications is justified by their high precision and automation speed, helping users concentrate on higher-expertise tasks. To better understand the models and avoid bias during deployment, eXplainable Artificial Intelligence (XAI) techniques can be used after training. But as the list of XAI solutions expand, comparisons between them diverge, and consensus over their evaluation cannot be reached. This paper proposes a variation of Fidelity-based XAI metrics, with a focus on real-conditions applications, where the number of classes is often low. The approach generates in-distribution, uncertainty-provoking perturbations, to ensure proper measurement of the XAI methods faithfulness. As demonstration of the evaluation framework usefulness, it is compared with human-centric object localization and segmentation metrics. Once applied to both medical and natural imaging applications, it highlights the intricate correlation between domain, data curation, and XAI solution choices in order to validate training of a new CNN model.

cs.CV↗

arXiv2026

On associative neural networks for sparse patterns with huge capacities

Generalized Hopfield models with higher-order or exponential interaction terms are known to have substantially larger storage capacities than the classical quadratic model. On the other hand, associative memories for sparse patterns, such as the Willshaw and Amari models, already outperform the classical Hopfield model in the sparse regime. In this paper we combine these two mechanisms. We introduce higher-order versions of sparse associative memory models and study their storage capacities. For fixed interaction order $n$, we obtain storage capacities of polynomial order in the system size. When the interaction order is allowed to grow logarithmically with the number of neurons, this yields super-polynomial capacities. We also discuss an analogue in the Gripon--Berrou architecture which was formulated for non-sparse messages (see \cite{griponc}). Our results show that the capacity increase caused by higher-order interactions persists in the sparse setting, although the precise storage scale depends on the underlying architecture.

math.PR↗

arXiv2026

Contributions of geolocated weather and building related data for insurance assessment of flood risks

Floods rank among the costliest natural hazards, causing over USD 100 billion in insured losses between 2013 and 2023. In France, persistent deficits in the natural catastrophe scheme highlight the need for accurate, building-scale flood risk assessment. Insurers typically rely on frequency-severity models supported by hazard maps and regional climate indicators. However, previous studies show that such large-scale variables explain only a limited share of the variability in individual flood losses. This study evaluates the marginal contribution of multiple georeferenced data layers to modeling flood claim occurrence and severity in a large French home insurance portfolio. Starting from a baseline model based on standard underwriting information, we sequentially introduce climate-expert variables, extreme rainfall indicators, and fine-scale geolocated building and environmental attributes. The analysis focuses on a practical setting in which insurers cannot deploy full hydrological or hydraulic catastrophe models because of budgetary, licensing, or operational constraints. Results show that rainfall-based indicators, particularly a newly constructed metric capturing intense local precipitation, substantially improve claim modeling performance. Building and environmental variables further enhance occurrence prediction. Overall, the findings demonstrate how high-resolution geolocated data improve exposure and vulnerability assessment, complement official flood maps, and provide insurers with an operational framework for refining flood risk evaluation and pricing.

stat.AP↗

arXiv2025

DocPolarBERT: A Pre-trained Model for Document Understanding with Relative Polar Coordinate Encoding of Layout Structures

We introduce DocPolarBERT, a layout-aware BERT model for document understanding that eliminates the need for absolute 2D positional embeddings. We extend self-attention to take into account text block positions in relative polar coordinate system rather than the Cartesian one. Despite being pre-trained on a dataset more than six times smaller than the widely used IIT-CDIP corpus, DocPolarBERT achieves state-of-the-art results. These results demonstrate that a carefully designed attention mechanism can compensate for reduced pre-training data, offering an efficient and effective alternative for document understanding.

cs.CL↗

arXiv2025

Material Decomposition in Photon-Counting Computed Tomography with Diffusion Models: Comparative Study and Hybridization with Variational Regularizers

Photon-counting computed tomography (PCCT) has emerged as a promising imaging technique, enabling spectral imaging and material decomposition (MD). However, images typically suffer from a low signal-to-noise ratio (SNR) due to constraints such as low photon counts and sparse-view settings which provoke artifacts. To prevent this, variational methods minimize a data-fit function coupled with handcrafted regularizers that mimic a prior by enforcing image properties such as gradient sparsity. In the last few years, diffusion models (DMs) have become predominant in the field of generative models and have been used as a learned prior for image reconstruction. This work investigates the use of DMs as regularizers for MD tasks in PCCT, specifically using diffusion posterior sampling (DPS) guidance. Three DPS-based approaches -- image-domain two-step DPS (im-TDPS), projection-domain two-step DPS (proj-TDPS), and one-step DPS (ODPS) -- are evaluated. The first two methods achieve MD in two steps by performing reconstruction and MD separately. The last method, ODPS, samples the material images directly from the measurement data. The results indicate that ODPS achieves superior performance compared to im-TDPS and proj-TDPS, providing sharper, noise-free and crosstalk-free images. Furthermore, we introduce a novel hybrid method for scenarios involving materials absent from the training dataset which combines DM priors with standard variational handcrafted regularizers for the materials unknown to the DM. This hybrid method demonstrates improved MD quality compared to a standard variational method and does not require additional training of the DM neural network (NN).

physics.med-ph↗

arXiv2025

FlowKac: An Efficient Neural Fokker-Planck solver using Temporal Normalizing Flows and the Feynman-Kac Formula

Solving the Fokker-Planck equation for high-dimensional complex dynamical systems remains a pivotal yet challenging task due to the intractability of analytical solutions and the limitations of traditional numerical methods. In this work, we present FlowKac, a novel approach that reformulates the Fokker-Planck equation using the Feynman-Kac formula, allowing to query the solution at a given point via the expected values of stochastic paths. A key innovation of FlowKac lies in its adaptive stochastic sampling scheme which significantly reduces the computational complexity while maintaining high accuracy. This sampling technique, coupled with a time-indexed normalizing flow, designed for capturing time-evolving probability densities, enables robust sampling of collocation points, resulting in a flexible and mesh-free solver. This formulation mitigates the curse of dimensionality and enhances computational efficiency and accuracy, which is particularly crucial for applications that inherently require dimensions beyond the conventional three. We validate the robustness and scalability of our method through various experiments on a range of stochastic differential equations, demonstrating significant improvements over existing techniques.

cs.LG↗

arXiv2024

Training LayoutLM from Scratch for Efficient Named-Entity Recognition in the Insurance Domain

Generic pre-trained neural networks may struggle to produce good results in specialized domains like finance and insurance. This is due to a domain mismatch between training data and downstream tasks, as in-domain data are often scarce due to privacy constraints. In this work, we compare different pre-training strategies for LayoutLM. We show that using domain-relevant documents improves results on a named-entity recognition (NER) problem using a novel dataset of anonymized insurance-related financial documents called Payslips. Moreover, we show that we can achieve competitive results using a smaller and faster model.

cs.CL↗

arXiv2024

Oops, I Sampled it Again: Reinterpreting Confidence Intervals in Few-Shot Learning

The predominant method for computing confidence intervals (CI) in few-shot learning (FSL) is based on sampling the tasks with replacement, i.e.\ allowing the same samples to appear in multiple tasks. This makes the CI misleading in that it takes into account the randomness of the sampler but not the data itself. To quantify the extent of this problem, we conduct a comparative analysis between CIs computed with and without replacement. These reveal a notable underestimation by the predominant method. This observation calls for a reevaluation of how we interpret confidence intervals and the resulting conclusions in FSL comparative studies. Our research demonstrates that the use of paired tests can partially address this issue. Additionally, we explore methods to further reduce the (size of the) CI by strategically sampling tasks of a specific size. We also introduce a new optimized benchmark, which can be accessed at https://github.com/RafLaf/FSL-benchmark-again

cs.LG↗

arXiv2024

Spectral CT Two-step and One-step Material Decomposition using Diffusion Posterior Sampling

This paper proposes a novel approach to spectral computed tomography (CT) material decomposition that uses the recent advances in generative diffusion models (DMs) for inverse problems. Spectral CT and more particularly photon-counting CT (PCCT) can perform transmission measurements at different energy levels which can be used for material decomposition. It is an ill-posed inverse problem and therefore requires regularization. DMs are a class of generative model that can be used to solve inverse problems via diffusion posterior sampling (DPS). In this paper we adapt DPS for material decomposition in a PCCT setting. We propose two approaches, namely Two-step Diffusion Posterior Sampling (TDPS) and One-step Diffusion Posterior Sampling (ODPS). Early results from an experiment with simulated low-dose PCCT suggest that DPSs have the potential to outperform state-of-the-art model-based iterative reconstruction (MBIR). Moreover, our results indicate that TDPS produces material images with better peak signal-to-noise ratio (PSNR) than images produced with ODPS with similar structural similarity (SSIM).

physics.med-ph↗

arXiv2024

Diffusion Posterior Sampling for Synergistic Reconstruction in Spectral Computed Tomography

Using recent advances in generative artificial intelligence (AI) brought by diffusion models, this paper introduces a new synergistic method for spectral computed tomography (CT) reconstruction. Diffusion models define a neural network to approximate the gradient of the log-density of the training data, which is then used to generate new images similar to the training ones. Following the inverse problem paradigm, we propose to adapt this generative process to synergistically reconstruct multiple images at different energy bins from multiple measurements. The experiments suggest that using multiple energy bins simultaneously improves the reconstruction by inverse diffusion and outperforms state-of-the-art synergistic reconstruction techniques.

physics.med-ph↗

arXiv2023

Time-changed normalizing flows for accurate SDE modeling

The generative paradigm has become increasingly important in machine learning and deep learning models. Among popular generative models are normalizing flows, which enable exact likelihood estimation by transforming a base distribution through diffeomorphic transformations. Extending the normalizing flow framework to handle time-indexed flows gave dynamic normalizing flows, a powerful tool to model time series, stochastic processes, and neural stochastic differential equations (SDEs). In this work, we propose a novel variant of dynamic normalizing flows, a Time Changed Normalizing Flow (TCNF), based on time deformation of a Brownian motion which constitutes a versatile and extensive family of Gaussian processes. This approach enables us to effectively model some SDEs, that cannot be modeled otherwise, including standard ones such as the well-known Ornstein-Uhlenbeck process, and generalizes prior methodologies, leading to improved results and better inference and prediction capability.

cs.LG↗

arXiv2023

Measuring and Mitigating Biases in Motor Insurance Pricing

The non-life insurance sector operates within a highly competitive and tightly regulated framework, confronting a pivotal juncture in the formulation of pricing strategies. Insurers are compelled to harness a range of statistical methodologies and available data to construct optimal pricing structures that align with the overarching corporate strategy while accommodating the dynamics of market competition. Given the fundamental societal role played by insurance, premium rates are subject to rigorous scrutiny by regulatory authorities. These rates must conform to principles of transparency, explainability, and ethical considerations. Consequently, the act of pricing transcends mere statistical calculations and carries the weight of strategic and societal factors. These multifaceted concerns may drive insurers to establish equitable premiums, taking into account various variables. For instance, regulations mandate the provision of equitable premiums, considering factors such as policyholder gender or mutualist group dynamics in accordance with respective corporate strategies. Age-based premium fairness is also mandated. In certain insurance domains, variables such as the presence of serious illnesses or disabilities are emerging as new dimensions for evaluating fairness. Regardless of the motivating factor prompting an insurer to adopt fairer pricing strategies for a specific variable, the insurer must possess the capability to define, measure, and ultimately mitigate any ethical biases inherent in its pricing practices while upholding standards of consistency and performance. This study seeks to provide a comprehensive set of tools for these endeavors and assess their effectiveness through practical application in the context of automobile insurance.

stat.ML↗

arXiv2023

Uconnect: Synergistic Spectral CT Reconstruction with U-Nets Connecting the Energy bins

Spectral computed tomography (CT) offers the possibility to reconstruct attenuation images at different energy levels, which can be then used for material decomposition. However, traditional methods reconstruct each energy bin individually and are vulnerable to noise. In this paper, we propose a novel synergistic method for spectral CT reconstruction, namely Uconnect. It utilizes trained convolutional neural networks (CNNs) to connect the energy bins to a latent image so that the full binned data is used synergistically. We experiment on two types of low-dose data: simulated and real patient data. Qualitative and quantitative analysis show that our proposed Uconnect outperforms state-of-art model-based iterative reconstruction (MBIR) techniques as well as CNN-based denoising.

physics.med-ph↗

arXiv2022

Geometry-preserving Lie Group Integrators For Differential Equations On The Manifold Of Symmetric Positive Definite Matrices

In many applications, one encounters signals that lie on manifolds rather than a Euclidean space. In particular, covariance matrices are examples of ubiquitous mathematical objects that have a non Euclidean structure. The application of Euclidean methods to integrate differential equations lying on such objects does not respect the geometry of the manifold, which can cause many numerical issues. In this paper, we propose to use Lie group methods to define geometry-preserving numerical integration schemes on the manifold of symmetric positive definite matrices. These can be applied to a number of differential equations on covariance matrices of practical interest. We show that they are more stable and robust than other classical or naive integration schemes on an example.

eess.SP↗

arXiv2022

Evaluation of importance estimators in deep learning classifiers for Computed Tomography

Deep learning has shown superb performance in detecting objects and classifying images, ensuring a great promise for analyzing medical imaging. Translating the success of deep learning to medical imaging, in which doctors need to understand the underlying process, requires the capability to interpret and explain the prediction of neural networks. Interpretability of deep neural networks often relies on estimating the importance of input features (e.g., pixels) with respect to the outcome (e.g., class probability). However, a number of importance estimators (also known as saliency maps) have been developed and it is unclear which ones are more relevant for medical imaging applications. In the present work, we investigated the performance of several importance estimators in explaining the classification of computed tomography (CT) images by a convolutional deep network, using three distinct evaluation metrics. First, the model-centric fidelity measures a decrease in the model accuracy when certain inputs are perturbed. Second, concordance between importance scores and the expert-defined segmentation masks is measured on a pixel level by a receiver operating characteristic (ROC) curves. Third, we measure a region-wise overlap between a XRAI-based map and the segmentation mask by Dice Similarity Coefficients (DSC). Overall, two versions of SmoothGrad topped the fidelity and ROC rankings, whereas both Integrated Gradients and SmoothGrad excelled in DSC evaluation. Interestingly, there was a critical discrepancy between model-centric (fidelity) and human-centric (ROC and DSC) evaluation. Expert expectation and intuition embedded in segmentation maps does not necessarily align with how the model arrived at its prediction. Understanding this difference in interpretability would help harnessing the power of deep learning in medicine.

cs.CV↗

arXiv2022

Model Transparency and Interpretability : Survey and Application to the Insurance Industry

The use of models, even if efficient, must be accompanied by an understanding at all levels of the process that transforms data (upstream and downstream). Thus, needs increase to define the relationships between individual data and the choice that an algorithm could make based on its analysis (e.g. the recommendation of one product or one promotional offer, or an insurance rate representative of the risk). Model users must ensure that models do not discriminate and that it is also possible to explain their results. This paper introduces the importance of model interpretation and tackles the notion of model transparency. Within an insurance context, it specifically illustrates how some tools can be used to enforce the control of actuarial models that can nowadays leverage on machine learning. On a simple example of loss frequency estimation in car insurance, we show the interest of some interpretability methods to adapt explanation to the target audience.

stat.ML↗

arXiv2021

Collaborative Insurance Sustainability and Network Structure

The peer-to-peer (P2P) economy has been growing with the advent of the Internet, with well known brands such as Uber or Airbnb being examples thereof. In the insurance sector the approach is still in its infancy, but some companies have started to explore P2P-based collaborative insurance products (eg. Lemonade in the U.S. or Inspeer in France). The actuarial literature only recently started to consider those risk sharing mechanisms, as in Denuit and Robert (2021) or Feng et al. (2021). In this paper, describe and analyse such a P2P product, with some reciprocal risk sharing contracts. Here, we consider the case where policyholders still have an insurance contract, but the first self-insurance layer, below the deductible, can be shared with friends. We study the impact of the shape of the network (through the distribution of degrees) on the risk reduction. We consider also some optimal setting of the reciprocal commitments, and discuss the introduction of contracts with friends of friends to mitigate some possible drawbacks of having people without enough connections to exchange risks.

q-fin.RM↗