Approximate Message Passing for HIgh-dimensional data analysis
Axe & tâche scientifique DigiCosme : DataSence –
Coordinateurs :Bertrand THIRION – Lenka Zdeborová – Lenka ZDEBOROVA.
Nom & Prénom du Candidat : Andre Manoel
Adresse mail :andremanoel à gmail.com
Institutions : Inria, CEA Institut de physique theorique
Laboratoire gestionnaire :
Adossé à l’action DigiCosme :GT PASADENA
Durée & Dates de la mission : 1 an – 01/12/2017 — 30/11/2018
In many fields of physics or life sciences, improving the resolution of observations (signal, images,spectra) is a major endeavor, as it is a pre-requisite toward more accurate information. Data acquisition devices benefit thus of hardware improvement to increase the resolution of the observed phenomena, leading to ever larger datasets. From a statistical perspective, these datasets have a high dimensionality and the signals show some prominent structures that require adequate modeling. While the dimensionality has increased, the number of samples available is sometimes limited, due to physical or financial limits. This becomes a problem when these data are processed with estimators that have a large sample complexity, such as many multivariate estimators(classifiers, regression models, covariance estimators, structure learning). In that case it is very useful to rely on structured priors, so that the resulting models reflect the state of knowledge on the phenomena of interest. Wellchosen priors improve the accuracy of the models and decrease the sample complexity of the estimators. The study of the human brain activity through functional Magnetic Resonance Imaging belongs among these
problems. The number of features per image reaches 105 to 106 —thanks to the rise of high-field MRI acquisitions that cross the mm scale— yet the number of observations is limited by the duration of scanning sessions and the number of subjects that can be included in studies. The key challenge addressed here is to set up a novel generation of efficient techniques to enforce structured priors on high-resolution MRI datasets to improve statistical analysis.
We propose to join forces between the three groups to design a new generation of inverse problem solvers that can take into account the complex structure of brain images and provide guarantees in the low-sample regime where they are used. To this end, we will first adapt AMP tools to the neuroimaging setting, using standard sparsity priors (a.k.a. l0 norm, Gauss-Bernoulli etc.) on the estimated model.
We will then consider more complex structured priors, that control the variation of the learned image patterns in space This is related to the well known analysis sparsity framework : the signals of interest should have a sparse representation in a well-chosen signal basis.
Productions Scientifiques :