6 problems

Let the setting be that of the preceding result, with transformed empirical Fréchet means and a steep variational inequality of exponent $\beta$. The steep variational inequality i…

Nie-Gollakota-Srivastava's conjecture. No polynomial-time algorithm achieves optimal error for $\mathcal{P}_{\mathrm{subgaussian}}$.

Monotonicity conjecture. The function $g_{tT}(\theta)$ is strictly increasing.

Statistical estimation and detection both address inference from data, and statistical similarity measures quantify relationships between probability distributions or statistical m…

Let $N$ denote the number of measurements in the estimation problem, and consider the dense and sparse moment relaxations. Ambiguity conjecture. When $N$ is small, the estimation p…

Let $n$ be the ambient dimension, let $\boldsymbol{\mu}\in\mathbb{R}^n$ be a $k$-sparse mean with $k\ll n^{1/2}$, and suppose samples from the identity-covariance Gaussian with mea…