14 problems

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…

High-dimensional arboreal-gas conjecture. In dimensions $d\geq 5$, the supercritical arboreal gas contains infinitely many infinite trees.

The edge-negative association conjecture. For every such graph $G$, the random forest $\Phi$ is edge-negatively associated. This is a longstanding problem concerning negative depen…

Let $I(\infty)=\{0\}\times\mathbb Z$ be the source axis of the directed IDLA forest ${\mathcal F}_{\infty}$. The forest consists of infinitely many trees rooted at points of…

Let ${\mathcal T}_{\infty}$ be the infinite IDLA tree rooted at the origin and let ${\mathcal F}_{\infty}$ be the directed IDLA forest. For fixed $R$, consider their restrictions t…

Simply generated forest conjecture. Lemma should also hold when the generating function has radius of convergence $0$.

Let a base learner predict by randomly selecting and averaging over points in a set $A$, and let $k$ denote the number of selected points. Write $\zeta_s$ and $\zeta_1$ for the cor…

Consider a random-forest setting with sample size $n$ and feature vector $\mathbf{x}\in\mathbb{R}^p$. Assume that $n\ll p$, that only a small proportion of the coordinates of…

Let $a$ of the $n$ observations be selected either by subsampling or by the $a$ out of $n$ bootstrap, and consider the corresponding pure forests. Table describes the relevant comp…

Update-stable zero-one conjecture. For every update-stable Borel set $\mathscr A\subseteq \{0,1\}^E$, the probability that $\mathfrak F$ belongs to $\mathscr A$ is either zero or o…

High-dimensional C2-minimax PRF conjecture. PRF models reaching $C^2$-minimax rates of convergence could also be derived in dimension $d$.

Proportional-size partitioning conjecture. Such a partitioning scheme should perform better than the BPRF scheme and could reach the minimax rate for $C^2$ functions.

PURF bias conjecture. The result for the PURF model should be the same as the result for the toy model.

Let $G=(U,A)$ be a weighted digraph, let $K_p$ be the complete graph with vertex set $[p]$, and let $H=G\times K_p$ be their Cartesian product. A rooted forest of $H$ has a $G$-pro…