Séance du 12 juin 2023

Séance organisée par Guillermo Durand et Thanh Mai Pham Ngoc

Lieu : IHP,  salle 314 (Grisvard)

14.00 :  Stéphanie Allassonnière (Université Paris Cité)

Titre :  Data Augmentation in High Dimensional Low Sample Size Setting Using a Geometry-Based Variational Autoencoder

Résumé : In this presentation, we present a new method to perform data augmentation in a reliable way in the High Dimensional Low Sample Size (HDLSS) setting using a geometry-based variational autoencoder (VAE). Our approach combines the proposal of 1) a new VAE model, the latent space of which is modeled as a Riemannian manifold and which combines both Riemannian metric learning and normalizing flows and 2) a new generation scheme which produces more meaningful samples especially in the context of small data sets. The method is tested through a wide experimental study where its robustness to data sets, classifiers and training samples size is stressed. It is also validated on a medical imaging classification task on the challenging ADNI database where a small number of 3D brain magnetic resonance images (MRIs) are considered and augmented using the proposed VAE framework. We show extensions of this view point to the analysis and generation of longitudinal data and multimodal one.

15.00 :  Olivier Bouaziz (Université Paris Cité)

Titre :  Study of the adaptive-ridge algorithm with applications to time to event data

Résumé : The adaptive-ridge (AR) algorithm is an iterative method that was introduced as a penalisation technique designed to ensure variable selection and regularisation. This algorithm depends on two parameters, q (with 0 <= q < 2) and \delta (with \delta>=0). In this talk, we will show that: 

- when 0 < q < 2, delta >= 0, this algorithm solves the minimisation of a (possibly non-convex) l_q penalised contrast

- when q=0, delta>0, this algorithm solves the minimisation of a squared-log penalised contrast which approximates the l_0 penalty when delta is “small”.

Different proofs exist for those results but I will focus on the Majorized-Minimized (MM) approach which can be derived from a simple variational reformulation of the l_q penalty. 

In a second part of this talk I will illustrate the interest of this algorithm on some applications in survival analysis. In particular I will use the AR algorithm in the piecewise constant hazard model where, starting from a large grid, the number and locations of the cuts of the hazard function can be automatically determined with the AR algorithm by penalising on similar adjacent hazard values.

Reference: “A Review on the Adaptive-Ridge Algorithm with several extensions”. R. Abergel, O. Bouaziz, G. Nuel.

https://hal.science/hal-04051929/document

16.00 :  Elisabeth Gassiat (Université Paris Saclay)

Titre : Trouver une sphère cachée dans du bruit inconnu

Résumé :  Je me place dans le modèle de déconvolution, où l’on cherche à identifier la loi d'un signal à partir de données bruitées. Je présenterai tout d’abord un résultat général prouvant que le problème inverse peut être résolu avec des hypothèses très faibles, et notamment sans connaissance a priori (ou basée sur des données auxiliaires) relatives à la loi du bruit. Je montrerai ensuite comment la théorie s’applique aux signaux sphériques.

Basé sur des travaux joints avec L. Léhricy, S. Le Corff et J. Capitao-Miniconi.