11 problems

Embedding index conjecture. This assumption should hold for a broad class of RKHS with eigenvalue decay rate $b2>1$.

Let $K$ be a kernel on $\mathbb{R}$, let $\mathbb{P}_K$ be the associated point-process law, and let a discrete subset of $\mathbb{R}$ mean a subset with no finite accumulation poi…

Probabilistic representer conjecture. There exists an $\mathbb{F}$-measure $\nu$ on $X$, with support contained in the support of $\mu$, such that

Let $H^2_d$ be the Drury--Arveson space on the unit ball in $\mathbb{C}^d$. If $I$ is a homogeneous ideal of polynomials, let $M$ be its closure in $H^2_d$, and define … Write…

Let $K_\lambda$ be a stationary kernel with lengthscale parameter $\lambda$, let $X=\{x_1,\ldots,x_n\}\subset\mathbb{R}$, and let $X_\lambda=\{x_1/\lambda,\ldots,x_n/\lambda\}$. Su…

Let $X$ be a Gaussian process with reproducing-kernel Hilbert spaces $H(K_0)$, $H(K_1)$, and $H(K_2)$ associated with kernels $K_0$, $K_1$, and $K_2$, respectively. Let…

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…

Sobolev rate conjecture. The detection boundary should be of order

Lyons–Peres conjecture. For $\mathbb{P}_K$-almost every $X\in\operatorname{Conf}(E)$,

Let $P_k$, $A$, $A^{*\mathbf a}$, $C^{*}$, and $\mathbf e_k$ be the operators and multi-index notation defined in the paper, and let $e_{*}$ be the distinguished vector. The operat…

Let $\mathcal{H}$ be a reproducing kernel Hilbert space, and for each point $z$ let $k_z^{\mathcal{H}}$ be its kernel function and $\widetilde{k}_z^{\mathcal{H}}$ the corresponding…