Error Bound of Empirical $\ell_2$ Risk Minimization for Noisy Standard and Generalized Phase Retrieval Problems. (arXiv:2205.13827v2 [stat.ML] UPDATED)

In this paper, we study the estimation performance of empirical $\ell_2$ risk
minimization (ERM) in noisy (standard) phase retrieval (NPR) given by $y_k =
|\alpha_k^*x_0|^2+\eta_k$, or noisy generalized phase retrieval (NGPR)
formulated as $y_k = x_0^*A_kx_0 + \eta_k$, where $x_0\in\mathbb{K}^d$ is the
desired signal, $n$ is the sample size, $\eta= (\eta_1,...,\eta_n)^\top$ is the
noise vector. We establish new error bounds under different noise patterns, and
our proofs are valid for both $\mathbb{K}=\mathbb{R}$ and
$\mathbb{K}=\mathbb{C}$. In NPR under arbitrary noise vector …

arxiv error ml retrieval risk standard