21 problems

A Gaussian directed acyclic graph (DAG) model is the statistical model associated with a directed acyclic graph under Gaussian conditional-dependence constraints; its conditional i…

Let $X_A^{[0,t)}$, $X_B^t$, and $X_C^{[0,t)}$ denote the restrictions and time-$t$ values of the processes indexed by sets $A$, $B$, and $C$, respectively. Local-independence conje…

Asymptotic counting conjecture. The number of compositional graphoids which are representable by $n$ discrete random variables is asymptotically

Hannula et al.'s conjecture. The bounded-cardinality conditional independence implication problem can be easier than the general upper bound suggests, especially when all variables…

Gaussoid-axioms sufficiency conjecture. If $a \perp\!\!\!\perp b \mid C$ holds for every covariance matrix $\Sigma \in \mathcal{M}_{\mathcal{G}, i \perp\!\!\!\perp j\mid K}$, then…

Let $G$ be a DAG and let $\mathcal{S}$ be a support. Say that $\mathcal{S}$ is trivially incompatible with $G$ when some $d$-separation relation of $G$ induces a conditional indepe…

Let $G$ be an mDAG. Write $\textsc{Algebraic}$ for the property that all causal compatibility constraints of $G$ are conditional independence relations, and let…

Let $G$ be a finite Bayesian network, let $P_G$ be its associated prime ideal, and let $I_G$ be the ideal generated by the conditional-independence relations of $G$. The quadratic…

Pearl–Paz conjecture. There exists a finite set of axioms characterizing all valid conditional independence implication statements.

For an infinite-dimensional factored set, one proposed definition says that $X$ and $Y$ are orthogonal given $Z$ if they are orthogonal given $Z$ in some finite-dimensional flatten…

Consider conditional independence tests based on Azadkia–Chatterjee-type coefficients and conditional randomization tests, with local alternatives in which $\mX$ and $Y$ may be dep…

Let $Y$ and $\mZ$ be independent, and let $\xi_n^\#$ be the coefficient defined by … Here $R_i$ and $M(i)$ are the rank and nearest-neighbor index quantities defined for the covari…

Matúš's rational-point conjecture. For any discrete conditional independence model $\mathcal{C}$, there exists a distribution

Four-variable Ingleton conjecture. The sub-cone obtained by adding the Ingleton inequalities to the inequalities defining ${\cal H}(N)$ determines all probabilistic conditional-ind…

Two-global-statement realizability conjecture. All minimal gaussoid extensions of at most two global conditional-independence statements are realizable.

Studený's two-antecedent completeness conjecture. The semigraphoid axioms are complete for those inference rules of discrete conditional independence that have at most two antecede…

Pearl–Paz completeness conjecture. The semigraphoid axioms are complete for the theory of discrete conditional-independence structures.

Conditional-expectation Markov category conjecture. Such a Markov category exists, with conditionals in the sense of the paper's definition, and these conditionals are given by con…

Let $X$, $Y$, and $Z$ be random variables, and let the null hypothesis consist of distributions under which $X$ and $Y$ are conditionally independent given $Z$. A test is required…

Let extended conditional independence be defined for stochastic variables in the presence of a decision variable, and let the separoid axioms be the standard axioms satisfied by co…

Smoothness conjecture. All models obtained by replacing the interactions in $\cg I$ with an adequate replacement in $\cg H$ are smooth everywhere in the parameter space.