5 problems

Sparse PCA threshold conjecture. There exists a critical sparsity threshold $\gamma^*\in(0,1)$ such that, if $\gamma\geq\gamma^*$, both the information-theoretic and computational…

Consider the spiked Wigner inference problem with signal-to-noise parameter $\beta_{\bM}$ and threshold $\beta_{\bM}$ as used in the paper. Let $\beta_{\bM}$ denote the scaled post…

In the spiked Wigner inference problem, let annealed Glauber dynamics refer to the Markov chain studied in the paper, and let weak recovery mean achieving nonzero correlation with…

BBP transition conjecture. The instability of the identity-denoiser state-evolution fixed point when $\lambda(\bm{\Delta})>1$ corresponds to the BBP transition for $\tilde{\bm{Y}}$…

Type-I error conjecture. The formula for the Type-I error, and hence the preceding formula for the limiting optimal error and total variation distance, should be correct up to…