Lifting high-dimensional nonlinear models with Gaussian regressors

11 Dec 2017Christos ThrampoulidisAnkit Singh Rawat

We study the problem of recovering a structured signal $\mathbf{x}_0$ from high-dimensional data $\mathbf{y}_i=f(\mathbf{a}_i^T\mathbf{x}_0)$ for some nonlinear (and potentially unknown) link function $f$, when the regressors $\mathbf{a}_i$ are iid Gaussian. Brillinger (1982) showed that ordinary least-squares estimates $\mathbf{x}_0$ up to a constant of proportionality $\mu_\ell$, which depends on $f$... (read more)

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