Multi-group Binary Choice with Social Interaction and a Random Communication Structure -- a Random Graph Approach

We construct and analyze a random graph model for discrete choice with social interaction and several groups of equal size. We concentrate on the case of two groups of equal sizes and we allow the interaction strength within a group to differ from the interaction strength between the two groups. Given that the resulting graph is sufficiently dense we show that, with probability one, the average decision in each of the two groups is the same as in the fully connected model. In particular, we show that there is a phase transition: If the interaction among a group and between the groups is strong enough the average decision per group will either be positive or negative and the decision of the two groups will be correlated. We also compute the free energy per particle in our model

A Comparative Study of Sparse Associative Memories

We study various models of associative memories with sparse information, i.e. a pattern to be stored is a random string of $0$s and $1$s with about $\log N$ $1$s, only. We compare different synaptic weights, architectures and retrieval mechanisms to shed light on the influence of the various parameters on the storage capacity.Comment: 28 pages, 2 figure

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

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

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.Comment: 4th International Workshop on EXplainable and TRAnsparent AI and Multi-Agent Systems (EXTRAAMAS 2022) - International Conference on Autonomous Agents and Multi-Agent Systems (AAMAS

Étude asymptotique d'un réseau neuronal: le modèle de mémoire associative de Hopfield

The purpose of this thesis is the study of the asymptotic behaviour of the Hopfield model, a model simulating the neural phenomenon of associative memory.L'objet de cette thèse est l'étude asymptotique du modèle de Hopfield dont le but est de simuler le phénomène neuronal de mémoire associative. Après une brève introduction au calcul neuronal et une description générale de la modélisation mathématique de la mémoire associative, nous définissons le modèle étudié dans le cadre d'une dynamique d'évolution déterministe, respectivement séquentielle (modèle de Hopfield) ou parallèle (modèle de Little). Nous étudions alors la stabilité asymptotique de $p$ images originales, au sens presque sûr pour l'espace de probabilité associé aux variables aléatoires modélisant ces images, ainsi que l'attraction de certaines configurations, en une seule étape de la dynamique, si $p$ est de l'ordre $N/\log N$ ($N$ la taille du réseau). La fonction énergie ayant notamment pour minima locaux les images originales et tous les autres points fixes de l'application associée à la dynamique, il est intéressant d'en connaître les fluctuations sur l'espace des configurations. Après avoir rappelé les résultats de Newman, relatifs à l'existence de barrières énergétiques, nous montrons que asymptotiquement et presque sûrement, sous certaines hypothèses sur $p$, les images combinées, combinaisons d'un nombre fine ou de toutes les images combinées, ne peuvent être des minima plus profonds que les images originales elles-mêmes. En ces points, nous calculons la limite presque sûre du hamiltonien normalisé. Au chapitre suivant, nous décrivons la dynamique stochastique de Glauber qui nous conduit à définir les mesures de Gibbs pour la limite thermodynamique de ce systèmes. Nous étudions alors, dans un dernier chapitre, le comportement asymptotique de l'énergie libre: pour toute température, cette variable aléatoire converge presque sûrement vers une constante, si $p/N$ converge vers 0, et vérifie la propriété d'être auto-moyennée, si $p$ est inférieur au proportionnel à $N$. En conclusion, nous terminons en évoquant quelques problèmes ouverts et des extensions possibles du modèle de Hopfield