This paper focuses on a theoretical performance analysis of subspace-based algorithms for the localization of spatially correlated rectilinear sources embedded in circular complex elliptically symmetric (C-CES) distributed noise model and also when the observations are non-circular CES (NC-CES) distributed with dependent scatter matrices on the dir...
There are two major routes to address the ubiquitous family of inverse problems appearing in signal and image processing, such as denoising or deblurring. A first route relies on Bayesian modeling, where prior probabilities are used to embody models of both the distribution of the unknown variables and their statistical dependence with respect to t...
This paper aims at presenting a simulative analysis of the main properties of a new R-estimator of shape matrices in Complex Elliptically Symmetric (CES) distributed observations. First proposed by Hallin, Oja and Paindaveine for the real-valued case and then extended to the complex field in our recent work, this R-estimator has the remarkable prop...
Geometry, calculus and in particular integrals, are too often seen by young students as technical tools with no link to the reality. This fact generates into the students a loss of interest with a consequent removal of motivation in the study of such topics and more widely in pursuing scientific curricula. With this note we put to the fore a simple...
Principal Component Analysis (PCA) is a popular method for dimension reduction and has attracted an unfailing interest for decades. Recently, kernel PCA has emerged as an extension of PCA but, despite its use in practice, a sound theoretical understanding of kernel PCA is missing. In this paper, we contribute lower and upper bounds on the efficienc...
Fast Incremental Expectation Maximization was introduced to design Expectation-Maximization (EM) for the large scale learning framework involving finite-sum and possibly non-convex optimization. In this paper, we first recast this iterative algorithm and other incremental EM type algorithms in the Stochastic Approximation within EM framework. Then,...
International audience
We propose a theoretical framework for the problem of learning a real-valued function which meets fairness requirements. This framework is built upon the notion of $\alpha$-relative (fairness) improvement of the regression function which we introduce using the theory of optimal transport. Setting $\alpha = 0$ corresponds to the regression problem u...
We study the problem of learning a real-valued function that satisfies the Demographic Parity constraint. It demands the distribution of the predicted output to be independent of the sensitive attribute. We consider the case that the sensitive attribute is available for prediction. We establish a connection between fair regression and optimal trans...
We study the problem of learning an optimal regression function subject to a fairness constraint. It requires that, conditionally on the sensitive feature, the distribution of the function output remains the same. This constraint naturally extends the notion of demographic parity, often used in classification, to the regression setting. We tackle t...
