Nous recevrons Pedro Rodrigues le Jeudi 25 Février à 10h

Title : Leveraging Global Parameters for Flow-based Neural Posterior Estimation
Presenter : Pedro L. C. Rodrigues (post-doctorant équipe Parietal, INRIA-Saclay)

Inferring the parameters of a stochastic model based on experimental observations is central to the scientific method. A particularly challenging setting is when the model is strongly indeterminate, i.e., when distinct sets of parameters yield identical observations. This arises in many practical situations, such as when inferring the distance and power of a radio source (is the source close and weak or far and strong?) or when estimating the amplifier gain and underlying brain activity of an electrophysiological experiment. In this work, we present a method for cracking such indeterminacy by exploiting additional information conveyed by an auxiliary set of observations sharing global parameters. Our method extends recent developments in simulation-based inference (SBI) based on normalizing flows to Bayesian hierarchical models. We validate quantitatively our proposal on a motivating example amenable to analytical solutions and then apply it to invert a well known non-linear model from computational neuroscience.

Le Lundi 8 Février à 10h30 nous accueillerons Julien Fageot post-doctorant à McGill University qui nous parlera de reconstruction parcimonieuse dans le domaine continu.

Title: TV- based methods for sparse reconstruction in continuous-domain

Abstract: We consider the problem of reconstructing an unknown function from some finitely many and possibly corrupted linear measurements. This is achieved by considering an optimization task using a sparsity-promoting regularization. More precisely, we consider the total-variation norm on Radon measures – which is the infinite-dimensional counterpart of the classic L1 norm used for sparse reconstruction in sparse statistical learning and compressed sensing – and a regularization operator that controls the smoothness of the reconstruction. The goal of this presentation is to discuss some theoretical and computational aspects of this infinite-dimensional optimization problem (form of the solutions, connection with spline theory, uniqueness issues, algorithmic strategies) and to illustrate the potential of the method for continuous-domain signal reconstruction.

This Thursday 14 Jan at 4.pm we will welcome Mathurin Massias post-doctoral researcher at University of Genova who will present his works on structured inverse problem:

Title: Fast resolution resolution of structured inverse problems: extrapolation and iterative regularization

Abstract: Overparametrization is common in linear inverse problems, which poses the question of stability and uniqueness of the solution. A remedy is to select a specific solution by minimizing a bias functional over all interpolating solutions. This functional is frequently neither smooth nor convex (e.g. L1, L2/L1, nuclear norm, TV). In the first part of the talk, we study fast solvers for the so called Tikhonov approach, where the bilevel optimization problem is relaxed into “datafit + regularization” (e.g., the Lasso). We show that, for separable problems arising in ML, coordinate descent algorithms can be accelerated by Anderson extrapolation, which surpasses full gradient methods and inertial acceleration.
The Tikhonov approach can be costly, as it requires to calibrate the regularization strength over a grid of values, and thus to solve many optimization problems. In the second part of the talk, we present results on iterative regularization: a single optimization problem is solved, and the number of iterations acts as the regularizer. We derive novel results on the early stopped iterates, in the case where the bias is convex but not strongly convex.

The presentation is based on:

– https://arxiv.org/abs/2011.10065 Anderson acceleration of coordinate descent
– https://arxiv.org/abs/2006.09859 Iterative regularization for convex regularizers
– https://arxiv.org/abs/1907.05830 Dual extrapolation for sparse generalized linear models

(joint works with Alexandre Gramfort, Joseph Salmon, Samuel Vaiter, Quentin Bertrand, Cesare Molinari, Lorenzo Roscasco and Silvia Villa)

Friday 11th February, 2018 at 11am.  – LIP Meeting room M7 (3rd floor)

Our next seminar will be given by Marion Foare, who will present on “Recent advances on solving the Mumford-Shah model for discrete images
”

Abstract-“Essential image processing and analysis tasks, such as image segmentation, simplification and denoising, can be conducted in a unified way by minimizing the Mumford-Shah functional. Although seductive, this minimization is in practice difficult because it requires to jointly define a sharp set of contours and a smooth version of the initial image. For this reason, various relaxations of the original formulations have been proposed, together with optimisation methods. In this talk, we propose several discrete approximations of the Mumford-Shah and their numerical resolution for image processing tasks. We compare the results with state-of-the-art convex relaxations of the Mumford–Shah functional, and show that the proposed methods lead to competitive denoising, restoration and segmentation results.“

Friday, October 26th, 2018 at 11am.  – LIP Meeting room M7

Esteban Bautista  will present on “Anomalous diffusion for graph-based data classification”.

The talk will be a one time-merging of the PhD seminar and the DL Journal club of the DANTE team.