We solve structure learning for cyclic linear causal models using observational data.
problem Learning the structure of cyclic linear causal models from observational data.
method Assuming simple graphs, we use a criterion for distributional equivalence and implement a greedy search method.
result We show that simple cyclic models are of expected dimension and justify score-based methods for structure learning.
Causal Inference over Mixtures models cyclic, evolving causal processes using a mixture of DAGs.
problem Cycles, time evolution, and population differences in causal processes are challenging for traditional graphical models.
method Causal Inference over Mixtures uses a mixture of directed cyclic graphs (DAGs) to model longitudinal data and infer causal relations.
result Improved performance compared to prior approaches in inferring causal relations from a mixture of DAGs.
Unified notion of equivalence for causal graphs, cyclic or acyclic.
problem Defining equivalence for causal graphs with cycles.
method General unified notion of equivalence based on distribution generation.
result Unified notion of equivalence and quasi-equivalence for causal graphs.
New framework for cyclic quantum causal models with graph separation property.
problem Understanding causal relationships in feedback processes and exotic scenarios.
method Introducing a robust probability rule and a novel graph-separation property, p-separation.
result Established graph-separation properties for all consistent cyclic causal models.
Study counterfactuals in cyclic systems with shifts and scales.
problem Counterfactual inference in cyclic systems with shifts and scales.
method Shift-scale interventions in cyclic SCMs.
result Valid inference in cyclic systems with shifts and scales.
We propose two spectral algorithms for partitioning nodes in directed graphs respectively with a cyclic and an acyclic pattern of connection between groups of nodes. Our methods are based on the computation of extremal eigenvalues of the transition matrix associated to the directed graph. The two algorithms outperform …
Develops a new framework for causal models on cyclic graphs, solving unique solvability issues.
problem Challenges in specifying unique probability distributions for cyclic functional causal models.
method Introduces a new probability rule and graph-separation property (p-separation) for cyclic fCMs.
result Proves p-separation is sound and complete for all consistent cyclic fCMs, recovering d-separation for DAGs.
We consider intrinsic linking and knotting in the context of directed graphs. We construct an example of a directed graph that contains a consistently oriented knotted cycle in every embedding. We also construct examples of intrinsically 3-linked and 4-linked directed graphs. We introduce two operations, consistent edg…
The study shows that certain groups can be uniquely identified by their finite abelian summands.
problem Identifying groups based on their finite abelian summands.
method Analyzing hyperbolic groups as graphs of free groups with cyclic edge groups.
result Free products of free and surface groups are profinitely rigid.
A graph product kernel means the kernel of the natural surjection from a graph product to the corresponding direct product. We prove that a graph product kernel of countable groups is special, and a graph product of finite or cyclic groups is virtually cocompact special in the sense of Haglund and Wise. The proof of th…
Develops a model for causal discovery in path spaces.
problem Discover causal relationships in path spaces using asymmetric independence.
method Theory linking E-separation in DMGs to conditional independence in SDEs, proving global Markov property, characterizing equivalence classes of graphs.
result Each equivalence class of graphs has a greatest element as a parsimonious representation, which can be identified from data.
Simplified presentation of symplectic fillings of lens spaces.
problem Symplectic fillings of lens spaces.
method Visual presentation of rational blowdown algorithm using triangulations of convex polygons.
result Organization of symplectic fillings into a graph.
The paper shows that relaxing assumptions about causal graphs can lead to exponentially large equivalence classes.
problem The size of Markov equivalence classes under relaxed assumptions.
method Analytical proofs for three settings: sparse random directed acyclic graphs, uniformly random acyclic directed mixed graphs, and uniformly random directed cyclic graphs.
result Exponentially large lower bounds for the expected size of Markov equivalence classes.
We study the dependence of solutions of equations of the form a0+a1zℓ1+...+amzℓm=0, on the exponents ℓ1,...,ℓm. We apply our results to equations that appear in graph theory, the theory of 3-manifolds fibering over the circle, and the theory of free-by-cyclic groups. In particul…
Let φ be an atoroidal outer automorphism of the free group Fn. We study the Gromov boundary of the hyperbolic group Gφ=Fn⋊φZ. We explicitly describe a family of embeddings of the complete bipartite graph K3,3 into ∂Gφ. To do so, we define the directional Whitehead graph and …
Efficiently learns DAG structures without cycles.
problem Learning DAG structures efficiently with constraints.
method Proposes DAG-NoCurl, a two-step algorithm to find and project acyclic graphs.
result Significantly improves efficiency over existing methods, often by more than one order of magnitude.
New framework learns nonlinear cyclic causal models from data.
problem Challenges in learning causal relationships from real-world, cyclic systems.
method NODAGS-Flow: a novel framework using residual normalizing flows for likelihood estimation.
result Significant performance improvements in structure recovery and predictive performance compared to state-of-the-art methods.
RECLAIM discovers causal graphs in cyclic, noisy systems.
problem Discovering causal relationships in cyclic, noisy systems.
method RECLAIM uses EM with residual normalizing flows to handle cycles and noise.
result RECLAIM effectively discovers causal graphs in both synthetic and real-world datasets.
We introduce a model for causal structure learning from multivariate functional data, even when graphs have cycles.
problem Discovering causal relationships from multivariate functional data with cycles.
method Functional linear structural equation model with a low-dimensional causal embedded space.
result The proposed model is causally identifiable under standard assumptions.
We prove that any isometry of the graph of cyclic splittings of a finitely generated free group FN of rank N≥3 is induced by an outer automorphism of FN. The same statement also applies to the graphs of maximally-cyclic splittings, and of very small splittings.
New 3-manifold spines with unique Whitehead graphs identified.
problem Identifying new 3-manifold spines with specific Whitehead graph types.
method Cyclic presentations and conditions on parameters to show spines of 3-manifolds.
result Examples of 3-manifolds with Whitehead graphs of specific types.
Identifies root causes of outliers in unknown cyclic graphs.
problem Outliers in unknown cyclic graphs with linear structural equations.
method Identifies a short list of potential root causes based on strong perturbation and structural equations.
result The shortlist includes true root causes and their parents on the cycle.
Characterizes non-degenerate cyclic metric Lie algebras.
problem Understanding the structure of non-solvable cyclic metric Lie algebras.
method Using sufficient conditions, cyclic quadruples, and double extension method.
result Complete characterization of non-degenerate cyclic metric Lie algebras.
We define analogues of the graphs of free splittings, of cyclic splittings, and of maximally-cyclic splittings of FN for free products of groups, and show their hyperbolicity. Given a countable group G which splits as G=G1∗⋯∗Gk∗F, where F denotes a finitely generated free group, we identify th…
A new method learns DAGs from Gaussian data without verifying acyclicity.
problem Learning DAGs from Gaussian data without verifying acyclicity.
method Relaxation technique for permutation matrix estimation and cyclic coordinatewise descent for sparse Cholesky factor estimation.
result The method recovers DAGs without verifying acyclicity constraints.
The paper expands Dunwoody's classification of graphs to include all graphs satisfying the first five conditions.
problem Classifying graphs satisfying specific conditions related to Dunwoody manifolds.
method Analyzing the conditions and expanding the scope of Dunwoody's classification.
result All graphs satisfying the first five conditions are classified.
For a signed cyclic graph G, we can construct a unique virtual link L by taking the medial construction and convert 4-valent vertices of the medial graph to crossings according to the signs. If a virtual link can occur in this way then we say that the virtual link is graphical. In the article we shall prove that a virt…
MissNODAG learns cyclic causal graphs from incomplete data.
problem Causal discovery in systems with feedback loops and missing data.
method Differentiable framework integrating additive noise model and expectation-maximization.
result MissNODAG uncovers cyclic structures and missingness mechanisms from partially observed data.
In this paper, we study quandles of cyclic type, which form a particular subclass of finite quandles. The main result of this paper describes the set of isomorphism classes of quandles of cyclic type in terms of certain cyclic permutations. By using our description, we give a direct classification of quandles of cyclic…
This paper proposes an axiomatic for Cyclic Foam Topological Field theories. That is Topological Field theories, corresponding to String theories, where particles are arbitrary graphs. World surfaces in this case are two-manifolds with one-dimensional singularities. We proved that Cyclic Foam Topological Field theories…
Generalized Baumslag-Solitar groups are defined as fundamental groups of graphs of groups with infinite cyclic vertex and edge groups. Forester proved (in "On uniqueness of JSJ decompositions of finitely generated groups", Comment. Math. Helv. 78 (2003) pp 740-751) that in most cases the defining graphs are cyclic JSJ …
We show that the arc graph of Sg1 is a coarse Lipschitz retract of the free splitting complex of F2g. We also show that the arc and curve graph of Sg1 is a coarse Lipschitz retract of both the cyclic splitting graph of F2g and the maximally cyclic splitting graph of F2g.
We start by studying the distribution of (cyclically reduced) elements of the free groups Fn with respect to their abelianization (or equivalently, their integer homology class. We derive an explicit generating function, and a limiting distribution, by means of certain results (of independent interest) on Chebyshev pol…
We outline a representation for discrete multivariate distributions in terms of interventional potential functions that are globally normalized. This representation can be used to model the effects of interventions, and the independence properties encoded in this model can be represented as a directed graph that allows…
Develop a variational framework for statistical inference on cyclic interactions.
problem Estimating and comparing large-scale recurrent organization in directed interactions.
method Represent directed interactions as edge flows on a simplicial complex and evolve under an energy-minimizing dynamical system.
result Separate transient interaction components from persistent harmonic flows, yielding a low-dimensional cycle space.
Study disproves conjecture about quadratic differentials.
problem Apisa-Wright conjecture about branched covers of quadratic differentials.
method Provided counterexamples to the conjecture.
result Found infinite family of non-cyclic 1-cylinder surfaces.
A {\em word labeled oriented graph} (WLOG) is an oriented graph G on vertices X={x1,…,xk}, where each oriented edge is labeled by a word in X±1. WLOGs give rise to presentations which generalize Wirtinger presentations of knots. WLOG presentations, where the underlying graph is a tree are of …
Gaussian BP algorithm converges exponentially under walk summability for cyclic graphs.
problem Convergence rate of Gaussian BP for cyclic graphs.
method Extending known results on walk summability, proving exponential convergence rate.
result Gaussian BP converges exponentially under walk summability for cyclic graphs.
A new framework learns cyclic causal graphs from incomplete data.
problem Learning causal models in systems with feedback loops and missing data.
method MissNODAGS framework, alternating imputation and likelihood maximization.
result Improved performance compared to imputation followed by causal learning.
DCCD-CONF discovers causal graphs with unmeasured confounders.
problem Discovering causal relationships in systems with unmeasured confounders.
method Differentiable learning of nonlinear cyclic causal graphs using interventional data.
result DCCD-CONF outperforms state-of-the-art methods in causal graph recovery and confounder identification.
We discuss 3-manifolds which are cyclic coverings of the 3-sphere, branched over 2-bridge knots and links. Different descriptions of these manifolds are presented: polyhedral, Heegaard diagram, Dehn surgery and coloured graph constructions. Using these descriptions, we give presentations for their fundamental groups, w…
New algorithm efficiently learns sparse causal graphs from time series data.
problem Learning sparse causal graphs from time series data efficiently and automatically selecting the number of edges.
method Cyclical coordinate descent algorithm with two non-parametric error metrics for LASSO coefficient selection.
result State-of-the-art performance on simulated and real datasets.
This paper tackles causal interactions in mixtures of DAGs using interventions.
problem Learning causal interactions among variables governed by a mixture of causal systems.
method Establishes necessary and sufficient conditions for intervention size, designs an adaptive algorithm.
result Identifies true edges in a mixture of DAGs using optimal or near-optimal interventions.
New method selects direct causal parents from large sets of variables.
problem Inferring direct causal parents from many variables, especially nonlinear and cyclic.
method One-vs.-the-rest feature selection approach with theoretical guarantees.
result Significant improvements over existing methods.
We establish causal semantics for SDEs and develop methods to reason about them.
problem Understanding causal relationships in systems modeled by stochastic differential equations.
method We introduce a causal graph framework, Markov properties, and do-calculus for SDEs.
result We prove the σ-separation Markov property and do-calculus for causal SDEs. We study the hairy graph homology of a cyclic operad; in particular we show how to assemble corresponding hairy graph cohomology classes to form cocycles for ordinary graph homology, as defined by Kontsevich. We identify the part of hairy graph homology coming from graphs with cyclic fundamental group as the dihedral h…
Consider a one-ended word-hyperbolic group. If it is the fundamental group of a graph of free groups with cyclic edge groups then either it is the fundamental group of a surface or it contains a finitely generated one-ended subgroup of infinite index. As a corollary, the same holds for limit groups. We also obtain a ch…
We give upper bounds, linear in rank, to the topological dimensions of the Gromov boundaries of the intersection graph, the free factor graph and the cyclic splitting graph of a finitely generated free group.