5 problems

Ergodicity conjecture. As $N\uparrow\infty$, $\{\hat{d}_n(\mathbf{Y}_1):n\in[N]\}$ is ergodic.

Sparse-signal lower-bound conjecture. When $p\geq 8/m$, if the risk of an adaptive sensing and test procedure is less or equal to $b5$, then necessarily

Interpolation conjecture. The lower bound for general values of $p$ should interpolate between the bounds at $p=0$ and $p=1$.

Let $n$ denote the signal dimension, and consider adaptive sensing procedures for recovering sparse supports near the estimation threshold. The sample complexity lower bounds are i…

Let $n$ be the ambient dimension, let $s$ denote the cardinality of the support, and consider adaptive estimators for recovering structured sparse sets when the signal magnitude is…