The Generalized Lasso with Nonlinear Observations and Generative Priors

In this paper, we study the problem of signal estimation from noisy non-linear measurements when the unknown n -dimensional signal is in the range of an L -Lipschitz continuous generative model with bounded k -dimensional inputs. We make the assumption of sub-Gaussian measurements, which is satisfied by a wide range of measurement models, such as linear, logistic, 1-bit, and other quantized models. In addition, we consider the impact of adversarial corruptions on these measurements. Our analysis is based on a generalized Lasso approach (Plan and Vershynin, 2016). We first provide a non-uniform recovery guarantee, which states that under i.i.d.