Saddle-to-Saddle Dynamics in Diagonal Linear Networks

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Sparsest piecewise-linear regression of one-dimensional data

Michaël Unser, Julien René Pierre Fageot, Thomas Jean Debarre, Quentin Alain Denoyelle

We study the problem of one-dimensional regression of data points with total-variation (TV) regularization (in the sense of measures) on the second derivative, which is known to promote piecewise-linear solutions with few knots. While there are efficient a ...

Elsevier2021

Travel Time Prediction for Congested Freeways With a Dynamic Linear Model

Nikolaos Geroliminis, Semin Kwak

Accurate prediction of travel time is an essential feature to support Intelligent Transportation Systems (ITS). The non-linearity of traffic states, however, makes this prediction a challenging task. Here we propose to use dynamic linear models (DLMs) to a ...

IEEE Institute of Electrical and Electronics Engineers2021

TV-based reconstruction of periodic functions

Matthieu Martin Jean-André Simeoni, Julien René Pierre Fageot

We introduce a general framework for the reconstruction of periodic multivariate functions from finitely many and possibly noisy linear measurements. The reconstruction task is formulated as a penalized convex optimization problem, taking the form of a sum ...

IOP PUBLISHING LTD2020

Generalization error in high-dimensional perceptrons: Approaching Bayes error with convex optimization

Florent Gérard Krzakala, Lenka Zdeborová

We consider a commonly studied supervised classification of a synthetic dataset whose labels are generated by feeding a one-layer non-linear neural network with random iid inputs. We study the generalization performances of standard classifiers in the high ...

Curran Associates, Inc.2020

Efficient Greedy Coordinate Descent for Composite Problems

Martin Jaggi, Sebastian Urban Stich, Sai Praneeth Reddy Karimireddy, Anastasiia Koloskova

Coordinate descent with random coordinate selection is the current state of the art for many large scale optimization problems. However, greedy selection of the steepest coordinate on smooth problems can yield convergence rates independent of the dimension ...

2019

Hybrid-Spline Dictionaries for Continuous-Domain Inverse Problems

Michaël Unser, Shayan Aziznejad, Thomas Jean Debarre

We study one-dimensional continuous-domain inverse problems with multiple generalized total-variation regularization, which involves the joint use of several regularization operators. Our starting point is a new representer theorem that states that such in ...

2019

Sparse wars: A survey and comparative study of spherical deconvolution algorithms for diffusion MRI

Jean-Philippe Thiran, Erick Jorge Canales Rodriguez, Gabriel Girard, David Paul Roger Romascano, Jonathan Rafael Patino Lopez, Alessandro Daducci, Muhamed Barakovic, Marco Pizzolato, Gaëtan Olivier D Rensonnet

Spherical deconvolution methods are widely used to estimate the brain's white-matter fiber orientations from diffusion MRI data. In this study, eight spherical deconvolution algorithms were implemented and evaluated. These included two model selection tech ...

2019

Sparse Dictionaries for Continuous-Domain Inverse Problems

Michaël Unser, Shayan Aziznejad, Thomas Jean Debarre

We study 1D continuous-domain inverse problems for multicomponent signals. The prior assumption on these signals is that each component is sparse in a different dictionary specified by a regularization operators. We introduce a hybrid regularization functi ...

2019

Automatic L2 Regularization for Multiple Generalized Additive Models

Yousra El Bachir

Multiple generalized additive models are a class of statistical regression models wherein parameters of probability distributions incorporate information through additive smooth functions of predictors. The functions are represented by basis function expan ...

EPFL2019

B-Spline-Based Exact Discretization of Continuous-Domain Inverse Problems With Generalized TV Regularization

Michaël Unser, Julien René Pierre Fageot, Harshit Gupta, Thomas Jean Debarre

We study continuous-domain linear inverse problems with generalized total-variation (gTV) regularization, expressed in terms of a regularization operator L. It has recently been proved that such inverse problems have sparse spline solutions, with fewer jum ...

IEEE-INST ELECTRICAL ELECTRONICS ENGINEERS INC2019

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