74 problems

Roverato's conjecture. For every real number $\delta>0$,

The Letac–Massam conjecture.

Alternative-gauge cancellation conjecture. For some other classes of graphical models, such as those naturally defined on regular lattices, similar cancellations can take place for…

Consider the sufficient convergence bounds for loopy belief propagation (LBP) in graphical models with discrete variables and nonnegative factors, including Corollary … is stronger…

Let a system of causal stochastic differential equations be a class of SDE systems, and suppose that instantaneous cycles are excluded. d-separation Markov-property conjecture. The…

Cardwell's conjecture. Every GL-binomial BMT-derived model derived from a phylogenetic tree with colored nodes must be vertex regular.

The MNIST images are represented on a $28\times 28$ pixel grid, and the estimated conditional independence graph exhibits more diagonal edges in the upper-right-to-lower-left direc…

Let $C_n$ be the cycle with $n$ edges, and let $q(C_n)$ denote its consistency probability. Define … The cycle consistency probability conjecture. The consistency probability of…

Extremal ML threshold relation. For any undirected graph $G$,

Extremal ML degree bound. For any graph $G$,

Higher-order trek-polynomial conjecture. The polynomial is

Let $G$ be a random graph generated according to the Erdős–Rényi model $G(n,c/n)$, where $c$ is a fixed positive real number, and let $d$ be the minimum integer such that $G$ is…

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…

Let $T$ be the integral operator associated with the interaction kernel defining a conditionally specified stationary multivariate time-series model, and let stationarity mean that…

Graphical models on locally tree-like ensembles are expected to have thermodynamic behavior similar to that of graphical models on regular lattices, particularly concerning phase t…

A BMT-derived graph is a graph obtained from the tree model by merging color classes of edges. Two internal nodes are non-adjacent when they are not joined by an edge in the underl…

Let $\mathcal{T}$ be a tree with distinct colors on all internal nodes, and let $L_{\mathcal{T}}^{-1}$ denote the inverse model associated with it. Leaves have the same color when…

A BMT-derived graph is a graph obtained from the construction described in the paper, and its vanishing ideal is the ideal defining the associated model. A graph is toric if this v…

Algebraic–nested Markov equivalence conjecture. Algebraic equivalence can be related to nested Markov equivalence, in a way that would also make the algorithms for deciding algebra…

Let $G$ be the undirected graphical model modelling a generic $n$-player game $X$ with binary choices in normal form. Let $\mathcal{C}=\operatorname{global}(G)$ and let…

Hyperplane-gluing conjecture. This extension also works when the gluing set $S$ is not a clique.

Stabilisation conjecture. For star-shaped graphs, the $\Lambda$-MLE given any $f$-stabilisation of a sample $f$ is a $\Lambda$-MLE given $f$ if either a $\Lambda$-MLE given $f$ exi…

SCCR2 correctness conjecture. For all $n\in\mathbb{N}$, there exists $N\in\mathbb{N}$ such that, with high probability, the SCCR2 algorithm outputs a set $E_C$ satisfying all prope…

Reachability conjecture. For every $(\mathcal{P},\pi)\in\mathcal{S}$, there exist $(\mathcal{P}_0,\pi_0)\in S_6$ and a directed path in $\mathcal{G}$ starting at…

Longest-path optimality conjecture. Starting from any partially ordered partition, following any longest non-self-intersecting directed path in $\mathcal{G}$ eventually reaches an…