Quantitative estimates of the convergence of the empirical covariance matrix in log-concave ensembles, J. AMS, vol.23, issue.2, pp.535-561, 2010. ,
URL : https://hal.archives-ouvertes.fr/hal-00793769
Restricted isometry property of matrices with independent columns and neighborly polytopes by random sampling, Constr. Approx, vol.34, pp.61-88, 2011. ,
URL : https://hal.archives-ouvertes.fr/hal-00793771
Random polytopes, convex bodies, and approximation, Stochastic geometry, vol.1892, pp.77-118, 2007. ,
Learnability and the VapnikChervonenkis dimension, J. ACM, vol.36, pp.929-965, 1989. ,
Convex measures on locally convex spaces, Ark. Mat, vol.12, issue.1, pp.239-252, 1974. ,
A Bennett concentration inequality and its application to suprema of empirical processes, C. R. Math, vol.334, issue.6, pp.495-500, 2002. ,
Geometry of isotropic convex bodies, 2014. ,
Robustness to unknown error in sparse regularization, IEEE Trans. Inform. Theory, vol.64, issue.10, pp.6638-6661, 2018. ,
Interactions between compressed sensing random matrices and high dimensional geometry, of Panoramas et Synthèses, vol.37 ,
, , 2012.
Asymptotic shape of a random polytope in a convex body, J. Funct. Anal, vol.257, issue.9, pp.2820-2839, 2009. ,
From dependence to independence. Randomly stopped processes, U-statistics and processes, martingales and beyond, 2012. ,
Instance-optimality in probability with an 1 -minimization decoder, Appl. Comput. Harmon. Anal, vol.27, issue.3, pp.275-288, 2009. ,
On the gap between restricted isometry properties and sparse recovery conditions, IEEE Trans. Inform. Theory, vol.64, issue.8, pp.5478-5487, 2018. ,
Compressed sensing, IEEE Trans. Inform. Theory, vol.52, issue.4, pp.1289-1306, 2006. ,
URL : https://hal.archives-ouvertes.fr/inria-00369486
Stability and robustness of 1 -minimizations with Weibull matrices and redundant dictionaries, Linear Algebra Appl, vol.441, pp.4-21, 2014. ,
A Mathematical Introduction to Compressive Sensing. Applied and Numerical Harmonic Analysis, 2013. ,
Random spaces generated by vertices of the cube, Discrete Comput. Geom, vol.28, issue.2, pp.255-273, 2002. ,
Extremal properties of orthogonal parallelepipeds and their applications to the geometry of Banach spaces, Sb. Math, vol.64, issue.1, p.85, 1989. ,
Random polytopes obtained by matrices with heavy tailed entries, Commun. Contemp. Math, 2019. ,
Concentration inequalities and geometry of convex bodies, Analytical and probabilistic methods in the geometry of convex bodies, vol.2, pp.9-86, 2014. ,
Sphere packing numbers for subsets of the Boolean n-cube with bounded VapnikChervonenkis dimension, J. Combinat. Theory, Ser. A, vol.69, pp.217-232, 1995. ,
A quotient property for matrices with heavy-tailed entries and its application to noise-blind compressed sensing, 2018. ,
Suprema of chaos processes and the restricted isometry property, Comm. Pure Appl. Math, vol.67, issue.11, pp.1877-1904, 2014. ,
Random series and stochastic integrals: single and multiple. Probability and its Applications, 1992. ,
Probability in Banach spaces, Classics in Mathematics, 2011. ,
Smallest singular value of random matrices and geometry of random polytopes, Adv. Math, vol.195, issue.2, pp.491-523, 2005. ,
URL : https://hal.archives-ouvertes.fr/hal-00693800
Blaschke-Santaló inequalities, J. Diff. Geom, vol.45, pp.1-16, 1997. ,
A few notes on statistical learning theory, Advanced Lectures on Machine Learning, vol.2600, pp.1-40, 2003. ,
Learning without concentration, J. ACM, vol.62, issue.3, 2015. ,
, On the geometry of random polytopes, 2019.
URL : https://hal.archives-ouvertes.fr/hal-02276997
Sparse recovery under weak moment assumptions, J. Eur. Math. Soc, vol.19, issue.3, pp.881-904, 2017. ,
Characterizations of affinely-rotation-invariant log-concave measures by section-centroid location, Geometric aspects of functional analysis, vol.1469, pp.145-152, 1991. ,
Foundations of Machine Learning, 2012. ,
The distribution of Rademacher sums, Proc. Amer. Math. Soc, vol.109, issue.2, pp.517-522, 1990. ,
Concentration of mass on convex bodies, Geom. Funct. Anal, vol.16, issue.5, pp.1021-1049, 2006. ,
URL : https://hal.archives-ouvertes.fr/hal-00693783
The convex floating body, Math. Scand, vol.66, issue.2, pp.275-290, 1990. ,
Sharper bounds for Gaussian and empirical processes, Ann. Prob, vol.22, issue.1, pp.28-76, 1994. ,
New concentration inequalities in product spaces, Invent. Math, vol.126, issue.3, pp.505-563, 1996. ,
On the uniform convergence of relative frequencies of events to their probabilities, Theor. Probab. Appl, vol.16, pp.264-280, 1971. ,
Stability and instance optimality for Gaussian measurements in compressed sensing, Found. Comput. Math, vol.10, issue.1, pp.1-13, 2010. ,