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Lifting high-dimensional nonlinear models with Gaussian regressors
[article]
2018
arXiv
pre-print
We study the problem of recovering a structured signal x_0 from high-dimensional data y_i=f(a_i^Tx_0) for some nonlinear (and potentially unknown) link function f, when the regressors a_i are iid Gaussian. Brillinger (1982) showed that ordinary least-squares estimates x_0 up to a constant of proportionality μ_ℓ, which depends on f. Recently, Plan & Vershynin (2015) extended this result to the high-dimensional setting deriving sharp error bounds for the generalized Lasso. Unfortunately, both
arXiv:1712.03638v2
fatcat:62lvexbjyvggtbiyb2laotme7i