The ATLAS workshop
The ATLAS - Khronos workshop on Statistical Tools for Data-Mining
Dates: 23-24 May 2016
Location: Auditorium of Batiment IMAG, RdC, Campus de St Martin d'Hères, Grenoble, France
Registration is closed!
Submission of an abstract for a short talk/poster at the email address : firstname.lastname@example.org. Deadline : May 2, 2016
Notification of acceptance : May 9, 2016
Description: The ATLAS conference is an interdisciplinary workshop on mathematical and algorithmimcal approaches for high dimensional problems in data sciences. This year’s event is particularly dedicated to signal processing and applications in different fields as medical imaging, neurosciences, astrophysics.... with a particular emphasis on the use of innovative optimization methods. The workshop’s program will feature plenary talks given by experts in the field, as well as short talk.
- Massil Achab (Ecole Polytechnique) : "SGD with Variance Reduction beyond Empirical Risk Minimization"
- Abstract: We introduce a doubly stochastic proximal gradient algorithm for optimizing a finite average of smooth convex functions, whose gradients depend on numerically expensive expectations. Our main motivation is the acceleration of the optimization of the regularized Cox partial-likelihood (the core model used in survival analysis), but our algorithm can be used in different settings as well. The proposed algorithm is doubly stochastic in the sense that gradient steps are done using stochastic gradient descent (SGD) with variance reduction, where the inner expectations are approximated by a Monte-Carlo Markov-Chain (MCMC) algorithm. We derive conditions on the MCMC number of iterations guaranteeing convergence, and obtain a linear rate of convergence under strong convexity and a sublinear rate without this assumption. We illustrate the fact that our algorithm improves the state-of the-art solver for regularized Cox partial-likelihood on several datasets from survival analysis
- Stéphanie Allassonnière (Ecole Polytechnique) : "Mixed-effect model for the spatiotemporal analysis of longitudinal manifold-valued data"
- Abstract: In this work, we propose a generic hierarchical spatiotemporal model for longitudinal manifold-valued data, which consist in repeated measurements over time for a group of individuals. This model allows us to estimate a
- group-average trajectory of progression, considered as a geodesic of a given Riemannian manifold. Individual trajectories of progression are obtained as random variations, which consist in parallel shifting and time reparametrization, of ::the average trajectory. These spatiotemporal transformations allow us to characterize changes in the direction and in the pace at which trajectories are followed. We propose to estimate the parameters of the model using a stochastic ::version of the expectation-maximization (EM) algorithm, the Monte Carlo Markov Chain Stochastic Approximation EM (MCMC SAEM) algorithm.
- This generic spatiotemporal model is used to analyze the temporal progression of a family of biomarkers. This progression model estimates a normative scenario of the progressive impairments of several cognitive functions, considered here ::as biomarkers, during the course of Alzheimer’s disease. The estimated average trajectory provides a normative scenario of disease progression. Random effects provide unique insights into the variations in the ordering and timing of the ::succession of cognitive impairments across different individuals.
- Pascal Bianchi (CNRS and Telecom ParisTech) : "Some stochastic approximation methods for large scale convex optimization"
- Abstract: In the first part of the talk, I will present a stochastic version of the celebrated proximal point algorithm and some variants. The proximal point algorithm searches for a zero of a monotone operator A. Here, we assume that A ::is unknown but revealed online through realizations of a random monotone operator whose expectation coincides with A. As an application, I will consider the fused lasso problem over large graphs. In the second part, I will discuss the ::application of random coordinate descent to primal-dual algorithms and its application to distributed optimization
- Laure Blanc-Féraud (CNRS and Université de Nice Sophia Antipolis): "Exact smooth approximation of L2-L0 penalized criterion"
- Irène Gannaz (INSA de Lyon): "Estimation of the fractal connectivity"
- Abstract:A challenge in imaging neuroscience is to characterize the brain organization. One way to estimate the functional connectivity consists in estimating correlations of measurements of neuronal activity. The aim of the present work is to take into account the long range dependence properties of the recordings. Long-run connectivity can statistically be defined as the spectral correlations between long memory processes over a range of low frequency scales. We first introduce a semi-parametric multivariate model, defining the long-run connectivity for a large class of multivariate time series. We propose an estimation of the long-dependence parameters and of the long-run connectivity, based on the Whittle approximation and on a wavelet representation of the time series. Finally we present an application to the estimation of a human brain functional network based on MEG data sets
- Rémi Gribonval (INRIA and Rennes University) : "Compressive Learning: Projections, Learning, and Sparsity for Efficient Data Processing"
- Abstract:The talk will discuss generalizations of sparse recovery guarantees and compressive sensing to the context of machine learning. Assuming some low-dimensional model on the probability distribution of the data, we will see that in certain scenarios it is indeed possible to (randomly) compress a large data- collection into a reduced representation, of size driven by the complexity of the learning task, while preserving the essential information necessary to process it. Two case studies will be given: compressive clustering, and compressive Gaussian Mixture Model estimation, with an illustration on large-scale model-based speaker verification.
- Fred Koriche (Université du Littoral) : "Online Learning of Probabilistic Graphical Models"
- Abstract : Probabilistic graphical models (including Bayesian networks and Markov networks) are a widely accepted framework for representing, in a compact and intelligible way, high dimensional probability distributions. One of the most ::important problems in this setting is to extract from a series of outcomes the structure and the parameters of a graphical model that explains, as best as possible, the distribution of observed outcomes. In this talk, we shall focus on ::the “online” version of this learning problem, where outcomes are supplied one-by-one. Online learning is particularly suitable for large-scale domains and streamline applications. We shall present several theoretical and experimental ::results for online learning with different classes of graphical models. The online learning algorithms rely on both convex relaxation techniques and constraint optimization methods which exploit the polytope structure of the target model class.
- Hongzhou Lin (INRIA and Grenoble University): "A Universal Catalyst for First-Order Optimization"
- Abstract : We introduce a generic scheme for accelerating first-order optimization methods in the sense of Nesterov, which builds upon a new analysis of the accelerated proximal point algorithm. Our approach consists of minimizing a convex objective by approximately solving a sequence of well-chosen auxiliary problems, leading to faster convergence. This strategy applies to a large class of algorithms, including gradient descent, block coordinate descent, SAG, SAGA, SDCA, SVRG, Finito/MISO, and their proximal variants. For all of these methods, we provide acceleration and explicit support for non-strongly convex objectives. In addition to theoretical speed-up, we also show that acceleration is useful in practice, especially for ill-conditioned problems where we measure significant improvements. Joint work with Julien Mairal and Zaid Harchaoui.
- Djalel-E. Meskaldji : "Comparing groups of networks and graphical models"
- Abstract: Relation between different variables could be represented by a network or a graphical model. This representation is used in a variety of application fields and different adaptive methods have been developed to answer different questions related to statistical inference for such type of data. Here, we consider the problem of local and global testing of dependent multiple hypotheses where dependency is represented by complex networks. By combining complex graph theory tools and statistical testing, we propose different kinds of tests that assess data structure deviance from null models or between groups of networks. We also show how to exploit data structure and prior information of dependency to derive hierarchical multiple testing procedures for the local testing case, without relying on strong assumptions. At the top level, we decompose the networks or the graphical models into subnetworks using data driven techniques. For each subnetwork, we compute a summary statistic that is associated with a subnetwork p-value. The subnetwork scores or equivalently the subnetwork p-values are transformed, in an optimal way, to p-value weights for the lower levels of the hierarchy. The weights are chosen to guarantee the control of any desired error rate. We show by means of spatial and network simulated data, the gain that could be obtained when considering dependency with our method. As an application, our method is applied on groups of human brain networks derived from neuroimaging data
- Kevin Polisano (Universite de Grenoble) : "Convex Super Resolution Detection of Lines in Images" (Joint work with L. Condat, M. Clausel and V. Perrier)
- Abstract:Recovering structures in images from lowpass and noisy measurements is a challenging issue of image processing. In this lecture, I will present a new convex formulation for the problem of recovering lines in degraded images. This optimization problem is formed by the combination of a data fidelity term and a norm-based regularizer which favors some notion of complexity. By choosing the atomic norm as penalty, we enforce the solution to be expressed in terms of atoms, lying continuously on a infinite dictionary, namely the set of line parameters. This parsimonious model enables the reconstruction of the lines from lowpass measurements, even in presence of a large amount of noise or blur. We solve the optimization problem by means of a recent primal-dual algorithm. Furthermore, a Prony method performed on rows and columns of the restored image, leads to a spectral estimation of line parameters, with subpixel accuracy. This approach is able to provides a lines estimation procedure with infinite precision, where the Hough and the Radon transform fail, due to their discrete nature. Our work is part of the super-resolution methods, which achieve this goal of recovering fine scale information lost in the data, beyond the Rayleigh or Nyquist resolution limit of the acquisition system. This kind of techniques have been intensively exploited to reconstruct 1D sparse signals like spikes, but not yet for 2D elongated structures like filaments, neurons and veins, which motivates the present work.
- Maite Termenon (Université de Grenoble) : "Reliability of graph analysis of rs-fMRI using test-retest dataset from the Human Connectome Project " (Joint work with A. Jaillard, C. Delon-Martin and S. Achard)
- Abstract: The exploration of brain networks with rs-fMRI combined with graph theoretical approaches has become popular, with the perspective of finding network graph metrics as biomarkers in the context of clinical studies. A preliminary requirement for such findings is to assess the reliability of the graph based connectivity metrics. In previous test-retest (TRT) studies (Braun et al., 2012; Cao et al., 2014; Liang et al., 2012; Wang et al., 2011; Schwarz and McGonigle, 2011; Guo et al., 2012), this reliability has been explored using intraclass correlation coefficient (ICC) with heterogeneous results, and always with small sample size. Here, we report the influence of sample size and scan duration on the reliability of the graph based connectivity metrics. Our findings showed that graph metric reliability computed at both global and regional level depends, at optimal cost, on two key parameters, the sample size and the number of time points or scan duration. In order to obtain reliable results in small sample size studies, we use a trade-off between the numbers of subjects and scan duration and to explore reliable regions at regional network level.
- Bertrand Thirion (INRIA and CEA Saclay) : "Identifying structure in human brain activation images"
- Michael Unser (EPFL) : "Splines are universal solutions of linear inverse problems with generalized TV regularization" (Joint work with Julien Fageot and John-Paul Ward)
- Abstract:Ill-posed inverse problems are often constrained by imposing a bound on the total variation of the solution. Here, we consider a generalized version of total-variation regularization that is tied to some differential operator L. We then show that the general form of the solution is a nonuniform L-spline with fewer knots than the number of measurements. For instance, when L is the derivative operator, then the solution is piecewise constant. The powerful aspect of this characterization is that it applies to any linear inverse problem.
- Rémi Agier (INSA de Lyon) : "Recalage massif d'images médicales 3D"
- Abstract : Nous proposons une méthode de recalage sans référence, capable de recaler conjointement plusieurs centaines d'images médicales. En exploitant des points d'intérêt 3D combinés à une optimisation globale, notre algorithme permet de gérer des mises en correspondances partielles, sans a priori sur les données (absence de nécessité d'utiliser une des images comme modèle central), en exploitant toutes les relations inter-volumes. Une expérimentation avec 400 volumes CT-scanner a été menée et montre l'efficacité de notre approche. Une application de détection des yeux et de positionnement de masque a été créée, comme première étape à un processus d'anonymisation, illustrant la diversité des applications possibles de cet algorithme. Enfin nous présentons nos premiers résultats de l'extension de cette approche au recalage non-rigide. Ce travail est une collaboration avec S. Valette, L. Fanton, P. Croisille, et R. Prost de CREATIS. Plus d'information ici : https://www.creatis.insa-lyon.fr/site/fr/hubless.html
- Monday, May 23th 2016
- 9h00-9h40 : Coffee
- 9h40-10h30 : Pascal Bianchi : "Some stochastic approximation methods for large scale convex optimization"
- 10h30-11h00 : Hongzhou Lin : "A Universal Catalyst for First-Order Optimization"
- 11h00-11h30 : Coffee Break
- 11h30-12h20 : Stéphanie Allasonnière : "Mixed-effect model for the spatiotemporal analysis of longitudinal manifold-valued data"
- 12h20-13h40 : Lunch Break
- 13h50-14h40 : Michael Unser : "Splines are universal solutions of linear inverse problems with generalized TV regularization"
- 14h40-15h10 : Rémi Agier : "Recalage massif d'images médicales 3D"
- 15h10-15h40 : Coffee Break
- 15h40-16h10 : Djalel Meskadji: "Comparing groups of networks and graphical models"
- 16h10-17h00 : Bertrand Thirion: "Identifying structure in human brain activation images"
- 17h00-18h30 : Poster session
- Tuesday, May 24th 2016
- 9h00-9h30 : Coffee
- 9h30-10h20 : Rémi Gribonval : "Compressive Learning: Projections, Learning, and Sparsity for Efficient Data Processing"
- 10h20-10h50: Kevin Polisano : "Convex Super Resolution Detection of Lines in Images"
- 10h50-11h10 : Coffee Break
- 11h10-11h40 : Massil Achab : "SGD with Variance Reduction beyond Empirical Risk Minimization"
- 11h40-12h30 : Laure Blanc-Féraud : "Exact smooth approximation of L2-L0 penalized criterion"
- 12h30-13h45 : Lunch Break
- 13h45-14h35 : Fred Koriche : "Online Learning of Probabilistic Graphical Models"
- 14h35-15h05 : Irène Gannaz : "Estimation of the fractal connectivity"
- 15h05-15h35 : Maite Mermenon : "Reliability of graph analysis of rs-fMRI using test-retest dataset from the Human Connectome Project "
- 15h35-16h00 : Coffee Break
- 16h00-17h45 : ERA-Can+ Information Session
Scientific and organizing comittee :
- Sophie Achard (CNRS and Univ. Grenoble Alpes)
- Massih Reza Amini (Univ. Grenoble Alpes)
- Philippe Carré (Université de Poitiers)
- Stéphane Canu (INSA de Rouen)
- Pierre Chainais (Ecole Centrale de Lille)
- Marianne Clausel (Univ. Grenoble Alpes)
- Laurent Condat (CNRS and Univ. Grenoble Alpes)
- Patrick Gallinari (Univ. Pierre et Marie Curie)
- Julien Jacques (Univ. Lyon 2)
- Carole Lartizien (CNRS and INSA de Lyon)
- Guillaume Lecué (CNRS and ENSAE)
- Jérôme Malick (CNRS and Univ. Grenoble Alpes)
- Laurent Navarro (Ecole des Mines de St Etienne)
- Gabriel Peyré (CNRS and Univ. Paris-Dauphine)
- Nathalie Peyrard (INRA Toulouse)