Living on the edge: phase transitions in convex programs with random data, Information and Inference: A Journal of the IMA (IMAIAI), 2013. ,
DOI : 10.1093/imaiai/iau005
Shape Quantization and Recognition with Randomized Trees, Neural Computation, vol.1, issue.1, pp.1545-1588, 1997. ,
DOI : 10.1016/0031-3203(90)90098-6
URL : http://www.wisdom.weizmann.ac.il/~vision/courses/2003_2/shape.pdf
Regularization of Wavelet Approximations, Journal of the American Statistical Association, vol.96, issue.455, pp.939-967, 2001. ,
DOI : 10.1198/016214501753208942
Consistency of the group lasso and multiple kernel learning, Journal of Machine Learning Research, vol.9, pp.1179-1225, 2008. ,
URL : https://hal.archives-ouvertes.fr/hal-00164735
Adaptive regression and model selection in data mining problems, Thesis (Ph.D.)?Australian National University, 1999. ,
Bregman Monotone Optimization Algorithms, SIAM Journal on Control and Optimization, vol.42, issue.2, pp.596-636, 2003. ,
DOI : 10.1137/S0363012902407120
URL : http://epubs.siam.org/doi/pdf/10.1137/S0363012902407120
Convex analysis and monotone operator theory in Hilbert spaces, 2011. ,
URL : https://hal.archives-ouvertes.fr/hal-01517477
Concentration of quadratic forms under a bernstein moment assumption, 2014. ,
Optimal bounds for aggregation of affine estimators. Working Papers 2015-06, 2015. ,
Prox-regular functions in Hilbert spaces, Journal of Mathematical Analysis and Applications, vol.303, issue.1, pp.1-14, 2005. ,
DOI : 10.1016/j.jmaa.2004.06.003
Analysis of a random forests model, J. Mach. Learn. Res, vol.13, issue.1, pp.1063-1095, 2012. ,
URL : https://hal.archives-ouvertes.fr/hal-00476545
On the layered nearest neighbour estimate, the bagged nearest neighbour estimate and the random forest method in regression and classification, Journal of Multivariate Analysis, vol.101, issue.10, pp.2499-2518, 2010. ,
DOI : 10.1016/j.jmva.2010.06.019
URL : https://hal.archives-ouvertes.fr/hal-00559811
Consistency of random forests and other averaging classifiers, J. Mach. Learn. Res, vol.9, pp.2015-2033, 2008. ,
URL : https://hal.archives-ouvertes.fr/hal-00355368
Simultaneous analysis of Lasso and Dantzig selector, The Annals of Statistics, vol.37, issue.4, pp.1705-1732, 2009. ,
DOI : 10.1214/08-AOS620
URL : https://hal.archives-ouvertes.fr/hal-00401585
SLOPE???Adaptive variable selection via convex optimization, The Annals of Applied Statistics, vol.9, issue.3, pp.1103-1140 ,
DOI : 10.1214/15-AOAS842SUPP
URL : http://europepmc.org/articles/pmc4689150?pdf=render
Concentration Inequalities: A Nonasymptotic Theory of Independence, 2013. ,
DOI : 10.1093/acprof:oso/9780199535255.001.0001
URL : https://hal.archives-ouvertes.fr/hal-00794821
Bagging predictors, Machine Learning, vol.10, issue.2, pp.123-140, 1996. ,
DOI : 10.2307/1403680
Random forests, Machine Learning, vol.45, issue.1, pp.5-32, 2001. ,
DOI : 10.1023/A:1010933404324
Statistics for High-Dimensional Data: Methods, Theory and Applications, 2011. ,
DOI : 10.1007/978-3-642-20192-9
Aggregation for Gaussian regression, The Annals of Statistics, vol.35, issue.4, pp.1674-1697, 2007. ,
DOI : 10.1214/009053606000001587
URL : http://doi.org/10.1214/009053606000001587
singularities, Communications on Pure and Applied Mathematics, vol.9, issue.7, pp.219-266, 2004. ,
DOI : 10.1109/83.847830
Near-ideal model selection by ??? 1 minimization, The Annals of Statistics, vol.37, issue.5A, pp.2145-2177, 2009. ,
DOI : 10.1214/08-AOS653
Simple bounds for low-complexity model reconstruction. Arxiv preprint arXiv, pp.1106-1474, 2011. ,
Robust uncertainty principles: exact signal reconstruction from highly incomplete frequency information, IEEE Transactions on Information Theory, vol.52, issue.2, pp.489-509, 2006. ,
DOI : 10.1109/TIT.2005.862083
Ridgelets: estimating with ridge functions, The Annals of Statistics, vol.31, issue.5, pp.1561-1599, 1999. ,
DOI : 10.1214/aos/1065705119
Compressed sensing with coherent and redundant dictionaries, Applied and Computational Harmonic Analysis, vol.31, issue.1, pp.59-73, 2011. ,
DOI : 10.1016/j.acha.2010.10.002
Robust principal component analysis?, Journal of the ACM, vol.58, issue.3, pp.1-11, 2011. ,
DOI : 10.1145/1970392.1970395
Matrix Completion With Noise, Proceedings of the IEEE, pp.925-936, 2010. ,
DOI : 10.1109/JPROC.2009.2035722
A probabilistic and RIPless theory of compressed sensing. Information Theory, IEEE Transactions on, vol.57, issue.11, pp.7235-7254, 2011. ,
Tight oracle inequalities for low-rank matrix recovery from a minimal number of noisy random measurements. Information Theory, IEEE Transactions on, vol.57, issue.4, pp.2342-2359, 2011. ,
Exact Matrix Completion via Convex Optimization, Foundations of Computational Mathematics, vol.170, issue.1, pp.717-772, 2009. ,
DOI : 10.1017/CBO9780511814068
Stable signal recovery from incomplete and inaccurate measurements, Communications on Pure and Applied Mathematics, vol.7, issue.8, pp.1207-1223, 2006. ,
DOI : 10.1017/CBO9780511804441
PhaseLift: Exact and Stable Signal Recovery from Magnitude Measurements via Convex Programming, Communications on Pure and Applied Mathematics, vol.38, issue.5, pp.1241-1274 ,
DOI : 10.1109/9.554402
Near-optimal signal recovery from random projections: Universal encoding strategies? Information Theory, IEEE Transactions on, vol.52, issue.12, pp.5406-5425, 2006. ,
The power of convex relaxation: Near-optimal matrix completion. Information Theory, IEEE Transactions on, vol.56, issue.5, pp.2053-2080, 2010. ,
A Hamiltonian Monte Carlo Method for Non-Smooth Energy Sampling, IEEE Transactions on Signal Processing, vol.64, issue.21, p.2014 ,
DOI : 10.1109/TSP.2016.2585120
URL : https://hal.archives-ouvertes.fr/hal-01291840
The Convex Geometry of Linear Inverse Problems, Foundations of Computational Mathematics, vol.1, issue.10, pp.805-849, 2012. ,
DOI : 10.1007/978-1-4613-8431-1
Atomic Decomposition by Basis Pursuit, SIAM Journal on Scientific Computing, vol.20, issue.1, pp.33-61, 1999. ,
DOI : 10.1137/S1064827596304010
URL : http://www-stat.stanford.edu/~donoho/Reports/1995/30401.pdf
An efficient proximal-gradient method for general structured sparse learning, 2010. ,
DOI : 10.1214/11-aoas514
URL : http://doi.org/10.1214/11-aoas514
Stein block thresholding for image denoising, Applied and Computational Harmonic Analysis, vol.28, issue.1, pp.67-88, 2010. ,
DOI : 10.1016/j.acha.2009.07.003
URL : https://hal.archives-ouvertes.fr/hal-00323319
Translation-Invariant De-Noising, Wavelets and Statistics, pp.125-150, 1995. ,
DOI : 10.1007/978-1-4612-2544-7_9
URL : http://www-stat.stanford.edu/~donoho/Reports/1995/TIDeNoise.pdf
An introduction to semialgebraic geometry, 2002. ,
Deviation optimal learning using greedy $Q$-aggregation, The Annals of Statistics, vol.40, issue.3, pp.1878-1905, 2012. ,
DOI : 10.1214/12-AOS1025
URL : http://doi.org/10.1214/12-aos1025
Pac-bayesian bounds for the expected error of aggregation by exponential weights, 2009. ,
Aggregation by exponential weighting, sharp PAC-Bayesian bounds and sparsity, Machine Learning, vol.52, issue.1-2, pp.39-61, 2008. ,
DOI : 10.1007/978-3-540-45167-9_23
URL : https://hal.archives-ouvertes.fr/hal-00291504
Theoretical guarantees for approximate sampling from smooth and log-concave densities, Journal of the Royal Statistical Society: Series B (Statistical Methodology), vol.91, issue.3, 2016. ,
DOI : 10.1016/j.spl.2014.04.002
On the Exponentially Weighted Aggregate with the Laplace Prior, 2016. ,
On the prediction performance of the Lasso, Bernoulli, vol.23, issue.1, pp.552-581 ,
DOI : 10.3150/15-BEJ756
Sharp oracle inequalities for aggregation of affine estimators, The Annals of Statistics, vol.40, issue.4, pp.2327-2355, 2012. ,
DOI : 10.1214/12-AOS1038SUPP
URL : https://hal.archives-ouvertes.fr/hal-00587225
Aggregation by Exponential Weighting and Sharp Oracle Inequalities, Proceedings of the 20th Annual Conference on Learning Theory, COLT'07, pp.97-111, 2007. ,
DOI : 10.1007/978-3-540-72927-3_9
URL : https://hal.archives-ouvertes.fr/hal-00160857
Mirror averaging with sparsity priors, Bernoulli, vol.18, issue.3, pp.914-944 ,
DOI : 10.3150/11-BEJ361
URL : https://hal.archives-ouvertes.fr/hal-00461580
Sparse regression learning by aggregation and Langevin Monte-Carlo, Journal of Computer and System Sciences, vol.78, issue.5, pp.1423-1443, 2012. ,
DOI : 10.1016/j.jcss.2011.12.023
URL : https://hal.archives-ouvertes.fr/hal-00773553
Orthogonal Invariance and Identifiability, SIAM Journal on Matrix Analysis and Applications, vol.35, issue.2, 1198. ,
DOI : 10.1137/130916710
URL : http://people.orie.cornell.edu/dd379/spectral_SIAM.pdf
Local Operator Theory, Random Matrices and Banach Spaces, Handbook on the Geometry of Banach spaces, pp.317-366, 2001. ,
DOI : 10.1016/S1874-5849(01)80010-3
Stein Unbiased GrAdient estimator of the Risk (SUGAR) for Multiple Parameter Selection, SIAM Journal on Imaging Sciences, vol.7, issue.4, pp.2448-2487, 2014. ,
DOI : 10.1137/140968045
URL : https://hal.archives-ouvertes.fr/hal-00987295
For most large underdetermined systems of linear equations the minimal ???1-norm solution is also the sparsest solution, Communications on Pure and Applied Mathematics, vol.50, issue.6, pp.797-829, 2006. ,
DOI : 10.1017/CBO9780511662454
Adapting to Unknown Smoothness via Wavelet Shrinkage, Journal of the American Statistical Association, vol.31, issue.432, pp.901200-1224, 1995. ,
DOI : 10.1007/978-3-0346-0416-1
URL : http://www-stat.stanford.edu/~donoho/Reports/1993/ausws.pdf
Counting the Faces of Randomly-Projected Hypercubes and Orthants, with Applications, Discrete & Computational Geometry, vol.42, issue.2, pp.522-541, 2010. ,
DOI : 10.1007/978-1-4613-8431-1
Observed universality of phase transitions in high-dimensional geometry, with implications for modern data analysis and signal processing, Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences, vol.22, issue.27, pp.3674273-4293, 1906. ,
DOI : 10.1073/pnas.0502258102
Ideal spatial adaptation by wavelet shrinkage, Biometrika, vol.81, issue.3, pp.425-455, 1994. ,
DOI : 10.1093/biomet/81.3.425
Wavelet shrinkage: asymptopia, Journal of the Royal Statistical Society, Ser. B, pp.371-394, 1995. ,
Non-asymptotic convergence analysis for the Unadjusted Langevin Algorithm, 2015. ,
URL : https://hal.archives-ouvertes.fr/hal-01176132
Sampling from convex non continuously differentiable functions, when Moreau meets Langevin, 2016. ,
URL : https://hal.archives-ouvertes.fr/hal-01267115
PAC-Bayesian risk bounds for group-analysis sparse regression by exponential weighting, p.1367742, 2016. ,
URL : https://hal.archives-ouvertes.fr/hal-01367742
he number of partitions of a set of n points in k dimensions induced by hyperplanes, Proc. Edinburgh Math. Soc, vol.15, pp.285-289, 1967. ,
Total Variation Projection With First Order Schemes, IEEE Transactions on Image Processing, vol.20, issue.3, pp.657-669, 2011. ,
DOI : 10.1109/TIP.2010.2072512
URL : https://hal.archives-ouvertes.fr/hal-00401251
Stable recovery with analysis decomposable priors, Proc. Sampta'13, pp.113-116, 2013. ,
URL : https://hal.archives-ouvertes.fr/hal-00926727
Variable Selection via Nonconcave Penalized Likelihood and its Oracle Properties, Journal of the American Statistical Association, vol.96, issue.456, 2001. ,
DOI : 10.1198/016214501753382273
URL : http://www.stat.psu.edu/~rli/research/penlike.pdf
Symmetric multivariate and related distributions. Monographs on statistics and applied probability, 1990. ,
DOI : 10.1007/978-1-4899-2937-2
A rank minimization heuristic with application to minimum order system approximation, Proceedings of the 2001 American Control Conference. (Cat. No.01CH37148), pp.4734-4739, 2001. ,
DOI : 10.1109/ACC.2001.945730
Boosting a weak learning algorithm by majority. Information and Computation, pp.256-285, 1995. ,
On Sparse Representations in Arbitrary Redundant Bases, IEEE Transactions on Information Theory, vol.50, issue.6, pp.1341-1344, 2004. ,
DOI : 10.1109/TIT.2004.828141
Waveshrink with firm shrinkage, Statist. Sinica, vol.7, pp.855-874, 1997. ,
Random Forests: elements of theory, variable selection and applications. Theses, 2010. ,
URL : https://hal.archives-ouvertes.fr/tel-00550989
Table of Integrals, Series, and Products, 1965. ,
Linear convergence rates for Tikhonov regularization with positively homogeneous functionals, Inverse Problems, vol.27, issue.7, p.75014, 2011. ,
DOI : 10.1088/0266-5611/27/7/075014
Necessary and sufficient conditions for linear convergence of ???1-regularization, Communications on Pure and Applied Mathematics, vol.52, issue.3, pp.161-182, 2011. ,
DOI : 10.1515/9783110920291
Recovering low-rank matrices from few coefficients in any basis. Information Theory, IEEE Transactions on, vol.57, issue.3, pp.1548-1566, 2011. ,
DOI : 10.1109/tit.2011.2104999
URL : http://arxiv.org/pdf/0910.1879
Strong Convergence of Euler-Type Methods for Nonlinear Stochastic Differential Equations, SIAM Journal on Numerical Analysis, vol.40, issue.3, pp.1041-1063, 2003. ,
DOI : 10.1137/S0036142901389530
Convex Analysis And Minimization Algorithms, volume I and II, 2001. ,
DOI : 10.1007/978-3-662-06409-2
Variable selection in nonparametric additive models, The Annals of Statistics, vol.38, issue.4, pp.2282-2313, 2010. ,
DOI : 10.1214/09-AOS781
Stochastic differential equations and diffusion processes, NH, 1989. ,
Group lasso with overlap and graph lasso, Proceedings of the 26th Annual International Conference on Machine Learning, ICML '09, p.55, 2009. ,
DOI : 10.1145/1553374.1553431
URL : http://www.cs.mcgill.ca/~icml2009/papers/471.pdf
Anti-sparse coding for approximate nearest neighbor search, 2012 IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP), pp.2029-2032, 2012. ,
DOI : 10.1109/ICASSP.2012.6288307
Exponentiated Gradient versus Gradient Descent for Linear Predictors, Information and Computation, vol.132, issue.1, pp.1-63, 1997. ,
DOI : 10.1006/inco.1996.2612
Numerical solution of stochastic differential equations. Stochastic Modelling and Applied Probability, 1995. ,
Oracle inequalities in empirical risk minimization and sparse recovery problems, Lectures from the 38th Probability Summer School held in Saint-Flour, 2008. ,
DOI : 10.1007/978-3-642-22147-7
Nuclear-norm penalization and optimal rates for noisy low-rank matrix completion, The Annals of Statistics, vol.39, issue.5, pp.2302-2329 ,
DOI : 10.1214/11-AOS894
URL : https://hal.archives-ouvertes.fr/hal-00676868
Sparse recovery in large ensembles of kernel machines, 2008. ,
Why the theorem of Scheff?? should be rather called a theorem of Riesz, Periodica Mathematica Hungarica, vol.18, issue.1-2, pp.225-229, 2010. ,
DOI : 10.1007/978-3-7091-2568-7_5
Recursive computation of the invariant distribution of a diffusion, Bernoulli, vol.8, issue.3, pp.367-405, 2002. ,
URL : https://hal.archives-ouvertes.fr/hal-00104799
Simultaneous adaptation to the margin and to complexity in classification, The Annals of Statistics, vol.35, issue.4, pp.1698-1721, 2007. ,
DOI : 10.1214/009053607000000055
The concentration of measure phenomenon Mathematical surveys and monographs Providence (R.I.), 2001. L'ISSN figurant sur le substitut de la page de titre 0076-5376 correspond à la revue Mathematicals surveys, Le titre a changé en 1981 en Mathematicals surveys and monographs et porte le numéro, pp.885-4653 ,
Probability in Banach Spaces: isoperimetry and processes, 1991. ,
DOI : 10.1007/978-3-642-20212-4
Information Theory and Mixing Least-Squares Regressions, IEEE Transactions on Information Theory, vol.52, issue.8, pp.3396-3410, 2006. ,
DOI : 10.1109/TIT.2006.878172
The Weighted Majority Algorithm, Information and Computation, vol.108, issue.2, pp.212-261, 1994. ,
DOI : 10.1006/inco.1994.1009
Convergence rates and source conditions for Tikhonov regularization with sparsity constraints, Journal of Inverse and Ill-Posed Problems, pp.463-478, 2008. ,
DOI : 10.1016/0022-247X(91)90132-J
URL : http://arxiv.org/pdf/0801.1774
Variational and Bayesian models for image denoising : from total variation towards non-local means. Theses, 2008. ,
URL : https://hal.archives-ouvertes.fr/tel-00371438
Oracle inequalities and optimal inference under group sparsity, The Annals of Statistics, vol.39, issue.4, pp.2164-2204, 2011. ,
DOI : 10.1214/11-AOS896
URL : https://hal.archives-ouvertes.fr/hal-00501509
Sampling from non-smooth distribution through Langevin diffusion, p.1492056, 2017. ,
URL : https://hal.archives-ouvertes.fr/hal-01492056
Sharp oracle inequalities for low-complexity priors, 2017. ,
URL : https://hal.archives-ouvertes.fr/hal-01422476
Uncertainty Principles and Vector Quantization, IEEE Transactions on Information Theory, vol.56, issue.7, pp.3491-3501, 2010. ,
DOI : 10.1109/TIT.2010.2048458
URL : http://arxiv.org/pdf/math/0611343
Lectures on change of variables in integral, 2001. ,
Concentration inequalities and model selection Ecole d'Eté de Probabilités de Saint- Flour XXXIII -2003, 2007. ,
The group lasso for logistic regression, Journal of the Royal Statistical Society: Series B (Statistical Methodology), vol.68, issue.1, 2008. ,
DOI : 10.1093/oxfordjournals.pan.a004868
High-dimensional additive modeling, The Annals of Statistics, vol.37, issue.6B, pp.3779-3821, 2009. ,
DOI : 10.1214/09-AOS692
URL : http://doi.org/10.1214/09-aos692
PAC-Bayesian aggregation of linear estimators. ArXiv e-prints, 2014. ,
A Unified Framework for High-Dimensional Analysis of $M$-Estimators with Decomposable Regularizers, Statistical Science, vol.27, issue.4, pp.538-557, 2012. ,
DOI : 10.1214/12-STS400SUPP
Topics in non-parametric statistics, 2000. ,
A new approach to variable selection in least squares problems, IMA Journal of Numerical Analysis, vol.20, issue.3, pp.389-403, 2000. ,
DOI : 10.1093/imanum/20.3.389
Proximal Markov chain Monte Carlo algorithms, Statistics and Computing, vol.1, issue.4, pp.745-760, 2016. ,
DOI : 10.1023/A:1010090512027
URL : http://doi.org/10.1007/s11222-015-9567-4
Adaptive Structured Block Sparsity Via Dyadic Partitioning, In EUSIPCO, 2011. ,
Group sparsity with overlapping partition functions, In EUSIPCO, 2011. ,
Prox-regular functions in variational analysis, 1996. ,
Local differentiability of distance functions, Transactions of the American Mathematical Society, vol.352, issue.11, pp.5231-5249, 2000. ,
DOI : 10.1090/S0002-9947-00-02550-2
Minimax Rates of Estimation for High-Dimensional Linear Regression Over $\ell_q$-Balls, IEEE Transactions on Information Theory, vol.57, issue.10, pp.6976-6994, 2011. ,
DOI : 10.1109/TIT.2011.2165799
Sparse additive models, Journal of the Royal Statistical Society: Series B (Statistical Methodology), vol.101, issue.5, pp.1009-1030, 2009. ,
DOI : 10.1017/CBO9780511802256
Guaranteed Minimum-Rank Solutions of Linear Matrix Equations via Nuclear Norm Minimization, SIAM Review, vol.52, issue.3, pp.471-501, 2010. ,
DOI : 10.1137/070697835
Oracle inequalities, aggregation and adaptation. Theses, 2006. ,
URL : https://hal.archives-ouvertes.fr/tel-00115494
Kullback???Leibler aggregation and misspecified generalized linear models, The Annals of Statistics, vol.40, issue.2, pp.639-665 ,
DOI : 10.1214/11-AOS961SUPP
URL : http://doi.org/10.1214/11-aos961
Linear and convex aggregation of density estimators, Mathematical Methods of Statistics, vol.16, issue.3, pp.260-280, 2007. ,
DOI : 10.3103/S1066530707030052
URL : https://hal.archives-ouvertes.fr/hal-00068216
Exponential Screening and optimal rates of sparse estimation, The Annals of Statistics, vol.39, issue.2, pp.731-771, 2011. ,
DOI : 10.1214/10-AOS854
URL : https://hal.archives-ouvertes.fr/hal-00606059
Sparse Estimation by Exponential Weighting, Statistical Science, vol.27, issue.4, pp.558-575 ,
DOI : 10.1214/12-STS393
URL : http://doi.org/10.1214/12-sts393
Exponential Convergence of Langevin Distributions and Their Discrete Approximations, Bernoulli, vol.2, issue.4, pp.341-363, 1996. ,
DOI : 10.2307/3318418
Convex analysis, 1996. ,
DOI : 10.1515/9781400873173
Variational analysis, 1998. ,
DOI : 10.1007/978-3-642-02431-3
On sparse reconstruction from Fourier and Gaussian measurements, Communications on Pure and Applied Mathematics, vol.52, issue.8, pp.611025-1045, 2008. ,
DOI : 10.1017/CBO9780511662454
Nonlinear total variation based noise removal algorithms, Physica D: Nonlinear Phenomena, vol.60, issue.1-4, pp.259-268, 1992. ,
DOI : 10.1016/0167-2789(92)90242-F
The strength of weak learnability, Mach. Learn, vol.5, issue.2, pp.197-227, 1990. ,
A Useful Convergence Theorem for Probability Distributions, The Annals of Mathematical Statistics, vol.18, issue.3, pp.434-438, 1947. ,
DOI : 10.1214/aoms/1177730390
Variational methods in imaging, 2009. ,
Estimating the Dimension of a Model, The Annals of Statistics, vol.6, issue.2, pp.461-464, 1978. ,
DOI : 10.1214/aos/1176344136
Signal representations with minimum ? ? -norm, 50th Annual Allerton Conference on Communication, Control, and Computing, p.2012 ,
DOI : 10.1109/allerton.2012.6483364
SLOPE is adaptive to unknown sparsity and asymptotically minimax, The Annals of Statistics, vol.44, issue.3, pp.1038-1068, 2015. ,
DOI : 10.1214/15-AOS1397SUPP
URL : http://arxiv.org/pdf/1503.08393
Scaled sparse linear regression, Biometrika, vol.7, issue.39, p.879, 2012. ,
DOI : 10.1214/08-AOS659
The generic chaining. Upper and lower bounds of stochastic processes, 2005. ,
Regression shrinkage and selection via the Lasso, Journal of the Royal Statistical Society. Series B. Methodological, vol.58, issue.1, pp.267-288, 1996. ,
Sparsity and smoothness via the fused lasso, Journal of the Royal Statistical Society: Series B (Statistical Methodology), vol.99, issue.1, pp.91-108, 2005. ,
DOI : 10.1016/S0140-6736(02)07746-2
URL : http://www.stanford.edu/group/SOL/papers/fused-lasso-JRSSB.pdf
Convex Recovery of a Structured Signal from Independent Random Linear Measurements, Sampling Theory, a Renaissance. Birkhäuser, 2014. ,
DOI : 10.1007/978-3-319-19749-4_2
An Introduction to Matrix Concentration Inequalities, Machine Learning, pp.1-230, 2015. ,
DOI : 10.1561/2200000048
URL : http://www.nowpublishers.com/article/DownloadSummary/MAL-048
Optimal Rates of Aggregation, COLT, pp.303-313, 2003. ,
DOI : 10.1007/978-3-540-45167-9_23
URL : https://hal.archives-ouvertes.fr/hal-00104867
Introduction to Nonparametric Estimation, 2008. ,
DOI : 10.1007/b13794
Low Complexity Regularization of Inverse Problems. Theses, 2014. ,
URL : https://hal.archives-ouvertes.fr/hal-01018927
The degrees of freedom of partly smooth regularizers, Annals of the Institute of Statistical Mathematics, vol.31, issue.4, pp.791-832 ,
DOI : 10.1214/009053607000000127
URL : https://hal.archives-ouvertes.fr/hal-00981634
Model selection with low complexity priors, Information and Inference: A Journal of the IMA (IMAIAI), pp.230-287, 2015. ,
DOI : 10.1111/j.1467-9868.2005.00503.x
URL : https://hal.archives-ouvertes.fr/hal-00842603
Low Complexity Regularization of Linear Inverse Problems, Sampling Theory, a Renaissance, Applied and Numerical Harmonic Analysis (ANHA, 2015. ,
DOI : 10.1007/978-3-319-19749-4_3
URL : https://hal.archives-ouvertes.fr/hal-01018927
Model Consistency of Partly Smooth Regularizers, IEEE Transactions on Information Theory, 2017. ,
DOI : 10.1109/TIT.2017.2713822
URL : https://hal.archives-ouvertes.fr/hal-01658847
High-dimensional generalized linear models and the lasso, The Annals of Statistics, vol.36, issue.2, pp.614-645, 2008. ,
DOI : 10.1214/009053607000000929
Weakly decomposable regularization penalties and structured sparsity, Scandinavian Journal of Statistics, vol.41, issue.1, pp.72-86, 2014. ,
DOI : 10.1111/sjos.12032
On the conditions used to prove oracle results for the Lasso, Electronic Journal of Statistics, vol.3, issue.0, pp.1360-1392, 2009. ,
DOI : 10.1214/09-EJS506
The Bernstein???Orlicz norm and deviation inequalities, Probability Theory and Related Fields, vol.248, issue.3, pp.225-250, 2013. ,
DOI : 10.1016/j.jfa.2007.03.019
Estimation in High Dimensions: A Geometric Perspective, Sampling Theory, a Renaissance. Birkhäuser, 2014. ,
DOI : 10.1007/978-3-319-19749-4_1
Minimax risks for sparse regressions: Ultra-high dimensional phenomenons, Electronic Journal of Statistics, vol.6, issue.0, pp.38-90, 2012. ,
DOI : 10.1214/12-EJS666SUPP
URL : https://hal.archives-ouvertes.fr/hal-00508339
AGGREGATING STRATEGIES, Proceedings of the Third Annual Workshop on Computational Learning Theory, COLT '90, pp.371-386, 1990. ,
DOI : 10.1016/B978-1-55860-146-8.50032-1
Adaptive minimax regression estimation over sparse lq-hulls, J. Mach. Learn. Res, vol.15, issue.1, pp.1675-1711, 2014. ,
Consistent group selection in high-dimensional linear regression, Bernoulli, vol.16, issue.4, pp.1369-1384, 2010. ,
DOI : 10.3150/10-BEJ252
Compressed sensing recovery via nonconvex shrinkage penalties . CoRR, abs, 1504. ,
DOI : 10.1088/0266-5611/32/7/075004
URL : http://iopscience.iop.org/article/10.1088/0266-5611/32/7/075004/pdf
Stochastic differential equations and applications, 2007. ,
Aggregating regression procedures to improve performance, Bernoulli, vol.10, issue.1, pp.25-47, 2004. ,
DOI : 10.3150/bj/1077544602
URL : http://doi.org/10.3150/bj/1077544602
Rate minimaxity of the lasso and dantzig selector for the lq loss in lr balls, J. Mach. Learn. Res, vol.11, pp.3519-3540, 2010. ,
Model selection and estimation in regression with grouped variables, Journal of the Royal Statistical Society: Series B (Statistical Methodology), vol.58, issue.1, pp.49-67 ,
DOI : 10.1198/016214502753479356