12 problems

Let $\mu$ be a distribution and let $\mathcal{F}[\mu,\psi]$ denote the relevant concentration objective for a coordinate $\psi$. Given $n$ samples, let $\hat{\psi}_n$ be a data-dri…

NP optimality of geometric neutral zones. The reliability score induces a monotone likelihood-ratio ordering: whenever $R_1>R_2$,

Let $c$ denote the collinearity parameter, $\Delta$ the correlation parameter, and $p$ the number of variables in the latent linear-regression framework described above. Proposed f…

Quantum–classical learning-coefficient conjecture. The functions $K$ and $K^Q$ behave similarly under the fundamental conditions; equivalently,

Quantum regularity conjecture. If $(q(x),p(x\mid\theta))$ is regular, then $(\rho,\sigma(\theta))$ is also quantum regular.

Let $\Phi_d^{(G)}$ be the free entropy of the Gaussian-equivalent matrix generalized linear model, with $\bS^\star\sim\mcW_{m,d}$, and let $Q_0$, $\alpha$, $J_q$, and $\Psi$ have t…

Let $A\in\mathbb{R}^{\alpha N\times N}$ have independent standard Gaussian entries, and consider the set of $\sigma\in\{-1,+1\}^N$ satisfying $A\sigma>0$ entrywise. The largest sol…

Variance conjecture.

Let $n$ be the sample size, let $\cF$ be a function class, and let $\mathbb P$ be a probability distribution. Write $\widehat f_n$ for the empirical risk minimizer,…

Let $(\hat{F}_t)_{t\geq 0}$ be the infinitesimal gradient boosting trajectory, let $\beta\geq 0$ be the tree-randomization parameter, let $\mathcal{P}_d(F^*)$ denote the projection…

EGD statistical-radius conjecture. There exist universal constants $C_{3},C_{4},C_{5}$ such that, whenever $n\geq C_{3}(d\log(d/\delta))^{4}$ and…

Let $N$ be the size of the finite sample space and let $k$ be the dimension of an exponential family. For a class $\mathcal{H}$ of exponential families, define … In particular, let…