Sébastien Gadat

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We introduce a new model addressing feature selection from a large dictionary of variables that can be computed from a signal or an image. Features are extracted according to an efficiency criterion, on the basis of specified classification or recognition tasks. This is done by estimating a probability distribution P on the complete dictionary, which(More)
Originating in Grenander's pattern theory, the problem of defining appropriate distances between shapes or images and the use of transformation groups to model the variability of natural images is now an active field of research. However, most of the existing results are stated in a deterministic setting while results in a random framework that are(More)
Microarray technology allows for the monitoring of thousands of gene expressions in various biological conditions, but most of these genes are irrelevant for classifying these conditions. Feature selection is consequently needed to help reduce the dimension of the variable space. Starting from the application of the stochastic meta algorithm " Optimal(More)
This paper considers the problem of estimating a mean pattern in the setting of Grenander's pattern theory. Shape variability in a dataset of curves or images is modeled by the random action of elements in a compact Lie group on an infinite dimensional space. In the case of observations contaminated by an additive Gaussian white noise, it is shown that(More)
In this paper, we are interested in a diffusion process based on a gradient descent. The process is non Markov and has a memory term which is built as a weighted average of the drift term all along the past of the trajectory. For this type of diffusion, we study the long time behaviour of the process in terms of the memory. We exhibit some conditions for(More)
J o u r n a l o f P r o b a b i l i t y Electron. Abstract In this paper, we consider a class of diffusions based on a memory gradient descent, i.e. whose drift term is built as the average all along the past of the trajectory of the gradient of a coercive function U. Under some classical assumptions on U , this type of diffusion is ergodic and admits a(More)
This paper deals with the analysis and the visualization of large graphs. Graphs are convenient widespread data structures that are encountered in a growing number of concrete problems: web, information retrieval, social networks, biological interaction networks… The sizes of these graphs become increasingly large as data acquisition and storage are(More)
In this paper we introduce a new class of diffeomorphic smoothers based on general spline smoothing techniques and on the use of some tools that have been recently developed in the context of image warping to compute smooth diffeomor-phisms. This diffeomorphic spline is defined as the solution of an ordinary differential equation governed by an appropriate(More)
The dynamics of the interaction between Cytotoxic T Lymphocytes (CTL) and tumor cells has been addressed in depth, in particular using numerical simulations. However, stochastic mathematical models that take into account the competitive interaction between CTL and tumors undergoing immunoediting, a process of tumor cell escape from immunesurveillance, are(More)