23 problems

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…

The one-pass setting requires controlling the smoothness of the empirical risk at each iteration, which can impose substantially stronger dimension-dependent conditions than in bat…

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

Let $S(r,q)$ be a binary softmax function with elements $S_1(r,q)$ and $S_2(r,q)$ that minimize the prevalence-weighted cross-entropy objective in the infinite-sample limit, where…

Let $H$ be a hypothesis concerning the values of a non-linear function of the model parameters, such as a hypothesis about a ratio. False-confidence conjecture. False confidence te…

Let $\alpha$ be the significance level, which fixes the tolerated error, and let $\psi\in{\mathscr F}$ be a non-conformity score embodying modeling assumptions. Conjecture. The ana…

Sleep spindle annotation and the exploration of spindle dynamics use the synchrosqueezing transform (SST) together with the proposed bootstrap-based uncertainty quantification. Unc…

Sleep spindle durations and instantaneous-frequency dynamics are difficult to estimate from electroencephalogram signals because of their thin-tail structure and background noise.…

Fractional-posterior uncertainty-quantification conjecture. Choosing $alpha<1$ might automatically accommodate the inflation needed for posterior credible regions to be asymptotica…

Single-integral reduction conjecture. The polar-coordinate collision-probability expression should be reducible to a single integral, including for anisotropic uncertainty.

K-means/center stability conjecture. This averaging effect makes the method much more stable and facilitates capturing the overall shape of the cluster by avoiding certain irregula…

The LAMP and MMT data sets arise from complex dynamical systems, and the study compares models using functional inputs with models using reduced-order-model coefficient inputs. Dim…

Sufficiency conjecture. The upper bound of Lemma should suffice to invoke the cited matrix-completion result, although with larger residual terms and a lower probability of success…

The model predictive probability density function is to be represented in a localized functional space. Gaussian RKHS conjecture. The Gaussian reproducing kernel Hilbert space (RKH…

Uniform-distribution effect conjecture. The faster convergence of IVR-LW relative to IVR-IW and IVR, and the lack of substantial gains for US-LW over US, are due to the fact that s…

Limited-error conjecture. This kind of error in the reconstructed power density is not too significant, probably because the features across all the power densities corresponding t…

Let $\varphi$ be the deterministic mapping from an initial mesh to a deformed mesh, and let the stochastic effects at mesh points be modeled by stochastic Itô processes $p^{(i)}$.…

Weak-correlation conjecture. If the correlations among the data for the individual constraints are weak, one should use individual ellipsoids that are later aggregated.

PDD interaction conjecture. The component functions arising in the function decomposition should exhibit insignificant $S$-variate interactions when $S\to N$, leading to useful low…

Conjecture on alternative exact approaches. The lack of faster convergence for BMCMC appears to be due to inaccurate estimation of the kernel mean, and alternative exact approaches…

Sample-complexity conjecture. The number of samples needed for accurate Monte Carlo estimates of the activity scores $\alpha_i$ may be smaller than the number of samples needed for…

Let $y(\mathbf{X})$ be a stochastic response with mean $y_{\emptyset}$, and let $\hat{y}_{S}(\mathbf{X})$ denote its $S$-variate functional dimensional decomposition approximation.…

Noise-sensitivity conjecture. The sensitivity to noise in the present problem is related to its time-dependent character: the effect of instantaneously small noise levels may be co…