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Project

Model estimation and selection for multiresolution graphical models.

The main goal of the project is to develop and validate methods to estimate networks at different levels or resolutions. One of the aims is to determine which level is most appropriate to estimate and interpret such network models and this will help researchers in the field to better understand the properties and the characteristics of the appropriate models that should be used to analyze the available data. The techniques I propose are oriented towards the estimation aspect (selecting a graphical object is inherently connected to selecting the nodes between which edges are placed and to the type of edges that one should place between nodes) as well as to a thorough and rigorous study of theoretical properties in a multiresolution framework. The multiresolution aspect relates to having collected data at different levels of coarseness and as such, one is interested in selecting an appropriate level of coarseness. Natural contexts where such situations can occur are, for example, financial applications, image denoising, gene expression data and functional magnetic resonance imaging (fMRI). In the analysis of brain connectivity from fMRI data, a scientist takes a series of measurements on brain regions which range from being very coarse (relatively large in size) to being very fine (relatively small in size). Once new sound methodologies are created, I proceed with proposing extensions with the aim to relax constraining assumptions or towards other classes of models.

Date:1 Oct 2015 →  30 Sep 2018
Keywords:model selection, Model estimation, multiresolution graphical models
Disciplines:Economic development, innovation, technological change and growth