6 problems

Let $C$ be the $\mathbf{\ell}_1$ ball, let $p(w\mid\xi)$ be the posterior density under the uniform prior on $C$, and write $\operatorname{Cov}_{\mathrm{Uni}(C)}(w)$ for the covari…

Consider a Bayesian inference problem with a noise variance parameter, and let AMP be used for estimation. Define the asymptotically Bayes-optimal estimation regime as the set of v…

Let $\boldsymbol{X}=n^{-1}\beta\boldsymbol{\theta}\boldsymbol{\theta}^\top+\boldsymbol{W}$ be a spiked model, where $\beta$ is the signal strength and $\boldsymbol{\theta}$ is the…

Let $\beta_{\mathrm{IT}}$ and $\beta_{\mathrm{wr}}$ denote the information-theoretic and weak-recovery thresholds, respectively, and consider the posterior distribution of the symm…

Let $\boldsymbol{X}\in\mathbb{R}^{n\times p}$ be a design matrix, let $\boldsymbol{y}_0=\boldsymbol{X}\boldsymbol{\theta}+\boldsymbol{\varepsilon}$ with…

Let $\beta_{\text{IT}}$ be the information-theoretic threshold, let $J(\pi_{\Theta})$ denote the set of signal-to-noise parameters for which Bayes AMP is known to achieve asymptoti…