99 problems

For $\kappa\in\mathbb{R}$, let $\delta_{\mathrm{s}}(\kappa)$ denote the phase-transition threshold for the existence of $\kappa$-margin solutions, and let…

The data consist of a highly dependent time series with change-points, and the proposed algorithm estimates both the number and locations of the change-points without relying on ra…

Structural convergence-rate gap conjecture. The gap in convergence rates between the smooth regime $\beta>d/2$ and the rough regime $\beta\leq d/2$ is structural rather than an art…

Consider the Gaussian multi-index model with hidden indices $\{\boldsymbol{w}_1^\star,\ldots,\boldsymbol{w}_M^\star\}$ satisfying the separation condition required in Theorem 1 of…

Let $d$ be the ambient dimension, $n$ the sample size, and $v_i$ the strength of feature $i$. In the non-overfitting regime, let $\textsc{Adam}$ denote the training algorithm and l…

Bayesian online learning updates the posterior sequentially and therefore requires an approximation at each step. Under the one-pass constraint, the data are processed sequentially…

FSD extension conjecture. Incorporating the FSD framework into the classical analysis of the population excess risk of PCR should extend both Theorem and Theorem to spectral method…

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 a PLS estimator use a specified number of PLS directions, and let its degrees of freedom be denoted by DoF. PLS degrees-of-freedom conjecture. The degrees of freedom of PLS alw…

The target domain consists of observations from a hospital or other target population, and the transfer-learning standard random forest (TL SRF) method uses a calibration step base…

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…

Let CEStGM denote the conditionally specified graphical model for stationary multivariate time series, with parameters $Phi_{\ell}^{(a,b)}$ and a process-wide conditional independe…

Under analogous small-noise and smoothness assumptions for dynamic treatment regimes with multiple categorical treatments per stage, the regret rate … should be minimax-optimal. La…

Voronoi-loss conjecture. The novel loss should satisfy

Let A1 and A5 denote the assumptions introduced for the model, and let Theorem … should hold even without assumption A5. The authors state that they do not know how to prove this.…

The estimated density flow map $t\mapsto \widehat R_t$ is compared with the ground-truth map $t\mapsto R_t^\ast$ through the integrated squared Hellinger distance … The preceding r…

Let $\lambda_2$ be the quadratic regularization parameter in the empirical KLIEP loss with an elastic net penalty, and let the sample sizes and dimensions be fixed. Fixed-small-…

Tuning-parameter conjecture. The observed differences in tuning bias may be due to the large number of parameters tuned in these methods.

Asymptotic quasi-Bayesian learning conjecture. Results analogous to these posterior-concentration and coverage conditions can be established in the quasi-Bayesian context of the ar…

Kernel-basis approximation conjecture. The choice of kernel functions as basis functions can be very useful for the $n$-dimensional space of Gibbs distributions to accurately appro…

Let $s>2$ denote the source smoothness parameter, let $\beta$ be the eigenvalue-decay parameter, and let $n$ be the sample size. Kernel ridge regression (KRR) is tuned through its…

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.

Gaitonde et al.'s moment-matrix necessity conjecture. Boundedness of certain moment matrices is necessary for learning throughout the entire high-temperature regime.