6 problems

Let ${\boldsymbol{Y}}$ be the observation matrix and let ${\boldsymbol{\theta}}_*$ be the rank-one signal direction. Define … and set … Here $\rho_{\text{\tiny \rm alg}}$ is the ac…

In the block-structured spiked model, let $\beta_*$ denote the threshold governing the performance of spectral and approximate message passing algorithms, and let $\beta$ be the si…

Polynomial-time tensor completion conjecture. No polynomial-time algorithm will be successful if the sample complexity is less than order $n^{3/2}$.

Let $\boldsymbol{\mathscr{\widehat{A}}}_{\textup{SSN}}$ and $\boldsymbol{\mathscr{\widehat{A}}}_{\textup{MN}}$ denote the SSN and MN estimators, respectively, and let their error r…

Let $X$ have prior distribution $P_0$, and consider the symmetric rank-one matrix estimation model with signal-to-noise parameter $\lambda$. For $\eta>0$, define … and set … Here…

Let $X$ have prior distribution $P_0$, and consider the rank-one symmetric matrix estimation model … where $Z_{i,j}$ are standard Gaussian noises. Assume $\mathbb{E}_{P_0}[X]=0$ an…