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The multi-index model with sparse dimension reduction matrix is a popular approach to circumvent the curse of dimensionality in a high-dimensional regression setting.
A primer on PAC-Bayesian learning
Guedj, B. (2019) · 1901
Earlier work this paper cites.
Sliced inverse regression for dimension reduction
Li, K.-C. (1991) · 1991
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Ten lectures on wavelets
Daubechies, I. (1992) · 1992
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Structure adaptive approach for dimension reduction
Hristache, M., Juditsky, A., Polzehl, J., & Spokoiny, V. (2001) · 2001
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An adaptive estimation of dimension reduction space
Xia, Y., Tong, H., Li, W. K., & Zhu, L.-X. (2002) · 2002
Earlier work this paper cites.
Statistical learning theory and stochastic optimization
Catoni, O. (2004) · 2004
Cited alongside, same era.
On sliced inverse regression with high-dimensional covariates
Zhu, L., Miao, B., & Peng, H. (2006) · 2006
Cited alongside, same era.
PAC-Bayesian supervised classification: The thermodynamics of statistical learning
Catoni, O. (2007) · 2007
Cited alongside, same era.
A constructive approach to the estimation of dimension reduction directions
Xia, Y. (2007) · 2007
Cited alongside, same era.
A new algorithm for estimating the effective dimension-reduction subspace
Dalalyan, A. S., Juditsky, A., & Spokoiny, V. (2008) · 2008
Cited alongside, same era.
A multiple-index model and dimension reduction
Xia, Y. (2008) · 2008
Later among the works it cites.
Sparse single-index model
Alquier, P. & Biau, G. (2013) · 2013
Later among the works it cites.
Mathematical foundations of infinite-dimensional statistical models
Giné, E. & Nickl, R. (2016) · 2016
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User-friendly introduction to PAC-Bayes bounds
Alquier, P. (2021) · 2021
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Estimating multi-index models with response-conditional least squares
Klock, T., Lanteri, A., & Vigogna, S. (2021) · 2021
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