11 problems

General congruence transformation to a diagonal-noise adjacency representation
arXiv@arxiv
General diagonal-noise representation conjecture. There exists a general adjacency matrix
Conjectureopencausal-discovery structural-equation-models
0
Containment of the model induced by a DAG in the model induced by its explicit-confounder expansion
arXiv@arxiv
Model-containment conjecture. Even though the two models are different, the model obtained from $G$ is always contained in the one obtained from $G'$ .
Conjectureopencausal-discovery structural-equation-models
1
The conjectured relation between algebraic and nested Markov equivalence
arXiv@arxiv
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…
Conjectureopenalgebraic-statistics causal-discovery graphical-models
0
The Tiered FCI soundness conjecture for cyclic DSCMs
arXiv@arxiv
Tiered FCI soundness conjecture. Tiered FCI is sound for cyclic DSCMs, and applying it to the evaluated DSCM $\mathcal{M}_{\operatorname{ev}(t)}$ , followed by mapping its output ba…
Conjectureopencausal-discovery cyclic-models structural-causal-models
0
Extension of tiered-background-knowledge results to PAGs
arXiv@arxiv
A PAG (partial ancestral graph) represents an equivalence class of maximal ancestral graphs, and tiered background knowledge specifies an ordering of variables into tiers that rest…
Conjectureopenancestral-graphs background-knowledge causal-discovery
1
High-probability correctness conjecture for the SCCR2 algorithm
arXiv@arxiv
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…
Conjectureopencausal-discovery graphical-models strongly-connected-components
0
Reachability conjecture for the six-vertex state space
arXiv@arxiv
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…
Conjectureopencausal-discovery graphical-models graph-theory
0
Longest-path optimality conjecture for partially ordered partitions
arXiv@arxiv
Longest-path optimality conjecture. Starting from any partially ordered partition, following any longest non-self-intersecting directed path in $\mathcal{G}$ eventually reaches an…
Conjectureopencausal-discovery graphical-models optimization
0
Richardson's conjecture on PAG representations of FCI output
arXiv@arxiv
A partial ancestral graph (PAG) is a graph representation used to compactly encode a set of hypothetical maximal ancestral graphs, and the Fast Causal Inference (FCI) algorithm was…
Conjecturesolvedcausal-discovery partial-ancestral-graphs
1
The large dense network challenge for causal discovery algorithms
arXiv@arxiv
Causal network discovery algorithms evaluate conditional mutual informations over candidate causal parents and conditioning subsets; in dense networks, the number of such tests can…
Conjectureopencausal-discovery computational-complexity network-science
0
Single-path-faithfulness conjecture for linear models
arXiv@arxiv
Single-path-faithfulness conjecture. The single-path-faithfulness assumption is satisfied for all linear models.
Conjectureopencausal-discovery graphical-models linear-models
0