7 problems

A Gaussian directed acyclic graph (DAG) model is the statistical model associated with a directed acyclic graph under Gaussian conditional-dependence constraints; its conditional i…

Let $u$ be a finite positive measure on $[0,1]$. The deterministic equivalent is established when $u$ is a finite discrete measure. Continuum-measure extension conjecture. Th…

Consider the Gaussian model with $X_1,\dots,X_n\stackrel{\mathrm{iid}}{\sim}\mathcal{N}(0,I_d)$ and $Z_1,\dots,Z_n\stackrel{\mathrm{iid}}{\sim}\mathcal{N}(0,\sigma^2I_d)$, and let…

Let $\{\boldsymbol{x}^{\mu}\}_{\mu=1}^{n}$ be independent samples from a data distribution on $\mathcal{X}\subset\mathbb{R}^{D}$, and let the centred teacher and student features b…

Random-features/Gaussian-features equivalence conjecture. In the limit $p,n,d\to\infty$ with $p/d\to\psi_1$ and $n/d\to\psi_2$,

Distinct-solutions conjecture. For generic values of $A$, $B$, and $S$, the score equations of $\mathcal{M}_{A,B}$ with sample covariance matrix $S$ have $2n-3$ distinct solutions.

Sturmfels–Timme–Zwiernik conjecture. The ML-degree in this case is $3n^2-9n+7$.