Magali Champion


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Assistant Professor at I.U.T Paris Descartes (Paris V)



Interests: I am interested in mathematical statistics, from a theoretical and algorithmic point of view, with applications to computational biology.

Keywords: High-dimension, sparse multi-linear models, graphical models, optimization, gene regulatory network inference, multi-omics data integration, cancer research.

Postdoctoral works: PhD works: My PhD works intended to study a theoretical analysis and the use of statistical and optimization methods in the context of gene regulatory networks. Such networks are powerful tools to represent and analyze complex biological systems, and enable the modeling of functional relationships between elements of these systems. The first part of this work was dedicated to the study of statistical learning methods to infer networks from sparse linear regressions, in a high-dimensional setting, and particularly the L2-Boosting algorithm. From a theoretical point of view, some consistency results and support stability results were obtained, assuming conditions on the dimension of the problem.
The second part dealt with the use of L2-Boosting algorithms to learn Sobol indices in a sensitive analysis setting. The estimation of these indices was based on the decomposition of the model with functional ANOVA. The elements of this decomposition were estimated using a procedure of Hierarchical Orthogonalisation of Gram-Schmidt, devoted to build an approximation of the analytical basis, and then a L2-Boosting algorithm, in order to obtain a sparse approximation of the signal. We showed that the obtained estimator is consistant in a noisy setting on the approximation dictionary.
The last part concerned the development of optimization methods to estimate relationships in networks. We showed that the minimization of the log-likelihood could be written as an optimization problem with two components, which consisted in finding the structure of the complete graph (order of variables of the nodes of the graph), and then, in making the graph sparse. We developped GADAG, a combination of a convex program and a tailored genetic algorithm adapted to the particular structure of our problem, to solve it.

Keywords: Statistics, High-dimension, Regression, Sparsity, Optimization.


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