Web: http://arxiv.org/abs/2209.10093

Sept. 22, 2022, 1:13 a.m. | Zhaoqiang Liu, Jun Han

stat.ML updates on arXiv.org arxiv.org

In this paper, we propose projected gradient descent (PGD) algorithms for
signal estimation from noisy nonlinear measurements. We assume that the unknown
$p$-dimensional signal lies near the range of an $L$-Lipschitz continuous
generative model with bounded $k$-dimensional inputs. In particular, we
consider two cases when the nonlinear link function is either unknown or known.
For unknown nonlinearity, similarly to \cite{liu2020generalized}, we make the
assumption of sub-Gaussian observations and propose a linear least-squares
estimator. We show that when there is no …

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