10 problems

Chunk-energy sufficiency conjecture. Restricting weights to depend on $\mathbf{x}$ only through the chunk-energy vector is sufficient without loss of optimality for the step-$d$ sl…

Let $\Delta_k$ denote the optimal asymptotic MSE constant within the generalized grouping (GG) family for groups of size $k$. Monotonicity conjecture. … i.e., the optimal asymptoti…

Let $W_{\rho}^{\alpha,2}(\mathbb{R})$ be the one-dimensional $\rho$-weighted Sobolev space, and consider trapezoidal rules combined with the boundary-damping importance sampling me…

The rejection sampling steps are considered in the importance fine-tuning procedure for diffusion models, with the objective referred to as the one from the DEFT paper. Rejection-s…

subMIDAS convergence conjecture. The subsampling algorithm subMIDAS satisfies similar convergence properties to those described in Theorem, depending on the choice of $\lambda_n$,…

Let $\mathbf{m}^*$ be the optimal mean-shift vector and let $\mathbf{d}^*_1$ be the leading eigenvector of the matrix $\Sigma^*$, with estimators $\hat{\mathbf{m}}$ and…

The self-approximating method uses a marginal importance sampler, and some simulated draws may fall outside the support of $Z_t\mid Z_{t-1}=z$ for a given $z$, so they are not used…

Let $(X_n,Y_n)_{n\in\mathbb{N}}$ be an augmented Metropolis-Hastings Markov chain with stationary initial distribution, so that $X_1\sim\mu$, and let $f\colon G\to\mathbb{R}$ be bo…

The model has dimension $d$, and the representation established in the cited one-dimensional setting is the representation described above for the relevant subsolution and large-de…

Consider the multiscale diffusion in the zero-temperature regime, with $\beta\gg 1$, and let $\widetilde{f}$, $\widetilde{h}$, and $\widetilde{\alpha}$ be the averaged coefficients…