14 citations · 26 across the 12 of their papers we have counts for
14 papers
Distribution of hitting times for dissipative random dynamical systems on , with application to stochastic gradient descent
Stéphane Galatolo, Stéphane Chrétien
Machine Learning and more specifically Deep Learning involves solving large scale nonconvex optimization problems. Several algorithms have been proposed in the literature, that see…
The dual approach to non-negative super-resolution: perturbation analysis and data fidelity
Stéphane Chrétien, Andrew Thompson, Bogdan Toader
We study the problem of super-resolution, where we recover the locations and weights of non-negative point sources from (potentially noisy) samples of their convolution with a Gaus…
Learning with Semi-Definite Programming: new statistical bounds based on fixed point analysis and excess risk curvature
Stéphane Chrétien, Mihai Cucuringu, Guillaume Lecué +1
Many statistical learning problems have recently been shown to be amenable to Semi-Definite Programming (SDP), with community detection and clustering in Gaussian mixture models as…
Boolean learning under noise-perturbations in hardware neural networks
Louis Andreoli, Xavier Porte, Stéphane Chrétien +3
A high efficiency hardware integration of neural networks benefits from realizing nonlinearity, network connectivity and learning fully in a physical substrate. Multiple systems ha…
On the subdifferential of symmetric convex functions of the spectrum for symmetric and orthogonally decomposable tensors
Stéphane Chrétien, Tianwen Wei
The subdifferential of convex functions of the singular spectrum of real matrices has been widely studied in matrix analysis, optimization and automatic control theory. Convex opti…
Small coherence implies the weak Null Space Property
Stéphane Chrétien, Zhen Wai Olivier Ho
In the Compressed Sensing community, it is well known that given a matrix with normalized columns, the Restricted Isometry Property (RIP) imp…
Joint estimation and model order selection for one dimensional ARMA models via convex optimization: a nuclear norm penalization approach
Stéphane Chrétien, Tianwen Wei, Basad Ali Hussain Al-sarray
The problem of estimating ARMA models is computationally interesting due to the nonconcavity of the log-likelihood function. Recent results were based on the convex minimization. J…
Using the LASSO for gene selection in bladder cancer data
Stéphane Chrétien, Christophe Guyeux, Michael Boyer-Guittaut +2
Given a gene expression data array of a list of bladder cancer patients with their tumor states, it may be difficult to determine which genes can operate as disease markers when th…
A Bregman Proximal ADMM for NMF with Outliers: Estimating features with missing values and outliers: a Bregman-proximal point algorithm for robust Non-negative Matrix Factorization with application to gene expression analysis
Stéphane Chrétien, Christophe Guyeux, Bastien Conesa +4
To extract the relevant features in a given dataset is a difficult task, recently resolved in the non-negative data case with the Non-negative Matrix factorization (NMF) method. Th…
Von Neumann's inequality for tensors
Stéphane Chrétien, Tianwen Wei
For two matrices in , the von Neumann inequality says that their scalar product is less than or equal to the scalar product of their singular spectrum. I…
Mixture model for designs in high dimensional regression and the LASSO
Mohamed Ibrahim Assoweh, Emmanuel Caron, Stéphane Chrétien
The LASSO is a recent technique for variable selection in the regression model \bean y & = & Xβ+ z, \eean where and is a centered gaussian i.i.d. noise ve…
On EM algorithms and their proximal generalizations
Stéphane Chrétien, Alfred O. Hero
In this paper, we analyze the celebrated EM algorithm from the point of view of proximal point algorithms. More precisely, we study a new type of generalization of the EM procedure…
Kullback Proximal Algorithms for Maximum Likelihood Estimation
Stéphane Chrétien, Alfred O. Hero
Accelerated algorithms for maximum likelihood image reconstruction are essential for emerging applications such as 3D tomography, dynamic tomographic imaging, and other high dimens…
Invertibility of random submatrices via tail decoupling and a Matrix Chernoff Inequality
Stéphane Chrétien, Sébastien Darses
Let be a matrix with coherence . We present a simplified and improved study of the quasi-isometry property for most submatrices…