P. Alquier, PAC-Bayesian bounds for randomized empirical risk minimizers, Mathematical Methods of Statistics, vol.17, issue.4, pp.279-304, 2008.
DOI : 10.3103/S1066530708040017
URL : https://hal.archives-ouvertes.fr/hal-00354922

P. Alquier and K. Lounici, PAC-Bayesian bounds for sparse regression estimation with exponential weights, Electronic Journal of Statistics, vol.5, issue.0, pp.127-145, 2011.
DOI : 10.1214/11-EJS601
URL : https://hal.archives-ouvertes.fr/hal-00465801

A. Antoniadis, G. Grégoire, and I. W. Mckeague, Bayesian estimation in single-index models, Statistica Sinica, vol.14, pp.1147-1164, 2004.

J. Audibert, Aggregated estimators and empirical complexity for least square regression. Annales de l'Institut Henri Poincaré: Probability and Statistics, pp.685-736, 2004.

J. Audibert and O. Catoni, Robust linear least squares regression. The Annals of Statistics, in press, 2011.
DOI : 10.1214/11-aos918
URL : https://hal.archives-ouvertes.fr/hal-00522534

R. E. Bellman, Adaptive Control Processes: A Guided Tour, 1961.
DOI : 10.1515/9781400874668

P. J. Bickel, Y. Ritov, and A. B. Tsybakov, Simultaneous analysis of Lasso and Dantzig selector. The Annals of Statistics, pp.1705-1732, 2009.
URL : https://hal.archives-ouvertes.fr/hal-00401585

A. M. Bruckstein, D. L. Donoho, and M. Elad, From Sparse Solutions of Systems of Equations to Sparse Modeling of Signals and Images, SIAM Review, vol.51, issue.1, pp.34-81, 2009.
DOI : 10.1137/060657704

P. Bühlmann and S. Van-de-geer, Statistics for High-Dimensional Data, 2011.
DOI : 10.1007/978-3-642-20192-9

F. Bunea, A. Tsybakov, and M. Wegkamp, Sparsity oracle inequalities for the Lasso, Electronic Journal of Statistics, vol.1, issue.0, pp.169-194, 2007.
DOI : 10.1214/07-EJS008
URL : https://hal.archives-ouvertes.fr/hal-00160646

E. J. Candès and T. Tao, The Dantzig selector: Statistical estimation when p is much larger than n. The Annals of Statistics, pp.2313-2351, 2005.

O. Catoni, Statistical Learning Theory and Stochastic Optimization, 2004.
DOI : 10.1007/b99352
URL : https://hal.archives-ouvertes.fr/hal-00104952

O. Catoni, PAC-Bayesian Supervised Classification: The Thermodynamics of Statistical Learning, Lecture Notes-Monograph Series. IMS, vol.56, 2007.
URL : https://hal.archives-ouvertes.fr/hal-00206119

J. M. Chambers, W. S. Cleveland, B. Kleiner, and P. A. Tukey, Graphical Methods for Data Analysis, 1983.

X. Chen, C. Zou, and R. D. Cook, Coordinate-independent sparse sufficient dimension reduction and variable selection. The Annals of Statistics, pp.3696-3723, 2010.
DOI : 10.1214/10-aos826
URL : http://arxiv.org/abs/1211.3215

A. Cohen, I. Daubechies, R. Devore, G. Kerkyacharian, and D. Picard, Capturing ridge functions in high dimension from point queries. Constructive Approximation, in press, 2011.
DOI : 10.1007/s00365-011-9147-6
URL : https://hal.archives-ouvertes.fr/hal-01432910

P. Cortez, A. Cerdeira, F. Almeida, T. Matos, and J. Reis, Modeling wine preferences by data mining from physicochemical properties, Decision Support Systems, vol.47, issue.4, pp.547-553, 2009.
DOI : 10.1016/j.dss.2009.05.016

A. S. Dalalyan, A. Juditsky, and V. Spokoiny, A new algorithm for estimating the effective dimension-reduction subspace, Journal of Machine Learning Research, vol.9, pp.1647-1678, 2008.
URL : https://hal.archives-ouvertes.fr/hal-00128129

A. S. Dalalyan and A. B. Tsybakov, Aggregation by exponential weighting, sharp PAC-Bayesian bounds and sparsity, Machine Learning, pp.39-61, 2008.
DOI : 10.1007/s10994-008-5051-0
URL : https://hal.archives-ouvertes.fr/hal-00291504

A. S. Dalalyan and A. B. Tsybakov, Sparse regression learning by aggregation and Langevin Monte-Carlo, Journal of Computer and System Sciences, vol.78, issue.5, 2011.
DOI : 10.1016/j.jcss.2011.12.023
URL : https://hal.archives-ouvertes.fr/hal-00362471

M. Delecroix, M. Hristache, and V. Patilea, On semiparametric -estimation in single-index regression, Journal of Statistical Planning and Inference, vol.136, issue.3, pp.730-769, 2006.
DOI : 10.1016/j.jspi.2004.09.006
URL : https://hal.archives-ouvertes.fr/hal-00458962

S. Ga¨?ffasga¨?ffas and G. Lecué, Optimal rates and adaptation in the single-index model using aggregation, Electronic Journal of Statistics, vol.1, issue.0, pp.538-573, 2007.
DOI : 10.1214/07-EJS077

P. J. Green, Reversible jump Markov chain Monte Carlo computation and Bayesian model determination, Biometrika, vol.82, issue.4, pp.711-732, 1995.
DOI : 10.1093/biomet/82.4.711

L. Györfi, M. Kohler, A. Krzy?, and H. Walk, A Distribution-Free Theory of Nonparametric Regression, 2002.
DOI : 10.1007/b97848

W. Härdle, P. Hall, and H. Ichimura, Optimal smoothing in single-index models. The Annals of Statistics, pp.157-178, 1993.

D. Jr, D. L. Harrison, and . Rubinfeld, Hedonic housing prices and the demand for clean air, Journal of Environmental Economics and Management, vol.5, pp.81-102, 1978.

J. L. Horowitz, Semiparametric Methods in Econometrics, 1998.
DOI : 10.1007/978-1-4612-0621-7

H. Ichimura, Semiparametric least squares (SLS) and weighted SLS estimation of single-index models, Journal of Econometrics, vol.58, issue.1-2, pp.71-120, 1993.
DOI : 10.1016/0304-4076(93)90114-K

O. Lopez, Single-index regression models with right-censored responses, Journal of Statistical Planning and Inference, vol.139, issue.3, pp.1082-1097, 2009.
DOI : 10.1016/j.jspi.2008.06.012
URL : https://hal.archives-ouvertes.fr/hal-00261412

J. Marin and C. Robert, Bayesian Core: A Practical Approach to Computational Bayesian Analysis, 2007.

P. Massart, Concentration Inequalities and Model Selection, 2007.

D. A. Mcallester, Some PAC-Bayesian theorems, Proceedings of the eleventh annual conference on Computational learning theory , COLT' 98, pp.230-234, 1998.
DOI : 10.1145/279943.279989

P. Mccullagh and J. A. Nelder, Generalized Linear Models, 1983.

E. A. Nadaraya, On estimating regression. Theory of Probability and its Applications, pp.141-142, 1964.

E. A. Nadaraya, Remarks on nonparametric estimates for density functions and regression curves. Theory of Probability and its Applications, pp.134-137, 1970.
DOI : 10.1137/1115015

J. R. Quinlan, Combining Instance-Based and Model-Based Learning, Proceedings of the Tenth International Conference on Machine Learning, pp.236-243, 1993.
DOI : 10.1016/B978-1-55860-307-3.50037-X
URL : http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.34.6358

R. Development and C. Team, R: A Language and Environment for Statistical Computing. R Foundation for Statistical Computing, 2008.

Y. Seldin, N. Cesa-bianchi, F. Laviolette, P. Auer, J. Shawe-taylor et al., PAC-Bayesian analysis of the exploration-exploitation trade-off, 2011.

J. Shawe-taylor and R. Williamson, A PAC analysis of a Bayes estimator, Proceedings of the Tenth Annual Conference on Computational Learning Theory, pp.2-9, 1997.

C. J. Stone, Optimal global rates of convergence for nonparametric regression . The Annals of Statistics, pp.1040-1053, 1982.

R. Tibshirani, Regression shrinkage and selection via the Lasso, Journal of the Royal Statistical Society, Series B, vol.58, pp.267-288, 1996.

A. B. Tsybakov, Introduction to Nonparametric Estimation, 2009.
DOI : 10.1007/b13794

L. J. Van-'t-veer, H. Dai, M. J. Van-de-vijver, Y. D. He, A. A. Hart et al., Gene expression profiling predicts clinical outcome of breast cancer, Nature, vol.415, issue.6871, pp.530-536, 2002.
DOI : 10.1038/415530a

H. B. Wang, Bayesian estimation and variable selection for single index models, Computational Statistics & Data Analysis, vol.53, issue.7, pp.2617-2627, 2009.
DOI : 10.1016/j.csda.2008.12.010

G. S. Watson, Smooth regression analysis. Sankhy¯ a Series A, pp.359-372, 1964.

I. Yeh, Modeling of strength of high-performance concrete using artificial neural networks, Cement and Concrete Research, vol.28, issue.12, pp.1797-1808, 1998.
DOI : 10.1016/S0008-8846(98)00165-3

I. Yeh, Modeling slump flow of concrete using second-order regressions and artificial neural networks, Cement and Concrete Composites, vol.29, issue.6, pp.474-480, 2007.
DOI : 10.1016/j.cemconcomp.2007.02.001