  Generalized Vector Approximate Message Passing (GVAMP) is an efficient
iterative algorithm for approximately minimum-mean-squared-error estimation of
a random vector $\mathbf{x}\sim p_{\mathbf{x}}(\mathbf{x})$ from generalized
linear measurements, i.e., measurements of the form $\mathbf{y}=Q(\mathbf{z})$
where $\mathbf{z}=\mathbf{Ax}$ with known $\mathbf{A}$, and $Q(\cdot)$ is a
noisy, potentially nonlinear, componentwise function. Problems of this form
show up in numerous applications, including robust regression, binary
classification, quantized compressive sensing, and phase retrieval. In some
cases, the prior $p_{\mathbf{x}}$ and/or channel $Q(\cdot)$ depend on unknown
deterministic parameters $\boldsymbol{\theta}$, which prevents a direct
application of GVAMP. In this paper we propose a way to combine expectation
maximization (EM) with GVAMP to jointly estimate $\mathbf{x}$ and
$\boldsymbol{\theta}$. We then demonstrate how EM-GVAMP can solve the phase
retrieval problem with unknown measurement-noise variance.
