4 problems

Let $q\in[0,1]$, and let $\hat{\mathcal{S}}$ estimate the principal subspace $\mathcal{S}$ under the same conditions as in the column sparse upper-bound corollary, with $R_q$ repla…

Sparse PCA runtime conjecture. For any $\lambda$ in the hard regime

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…

Consider the single-spike model with dimension $p$, sample size $n$, spike support size $k$, and signal strength $\beta$. Let $\mathbf{z}$ denote the sparse spike, and let…