Directed acyclic graphs are the basic representation of the structure underlying Bayesian networks, which represent multivariate probability distributions. In many practical applications, such as the reverse engineering of gene regulatory networks, not only the estimation of model parameters but the reconstruction of t…
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48 results for “uniform acyclicity”
No 5D aspherical manifolds can have uniformly positive scalar curvature.
problem Proving the non-existence of metrics with positive scalar curvature on certain 5D manifolds.
method Uniform acyclicity and toric symmetrization of stable μ-bubbles.
result Compact aspherical 5-manifolds cannot have metrics with uniformly positive scalar curvature.
Paper constructs unfaithful probability distributions in binary causal graphs.
problem Unfaithful probability distributions in binary causal graphs.
method Constructs unfaithful probability distributions in binary causal graphs.
result Examples of unfaithful probability distributions in binary causal graphs.
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.
Polynomial-time methods count and sample DAGs from equivalence classes.
problem Counting and sampling DAGs from Markov equivalence classes.
method Polynomial-time algorithms for DAGs.
result Counting and sampling can be done in polynomial time.
We explore non-acyclic GFlowNets in discrete settings.
problem Training and understanding non-acyclic GFlowNets in discrete environments.
method Relaxing acyclicity assumption, simpler theoretical framework, novel theoretical insights, experimental validation.
result Theoretical and experimental validation of non-acyclic GFlowNets in discrete environments.
COSMO learns DAG structure without acyclicity constraints.
problem Learning DAG structure from data efficiently and without constraints.
method Differentiable approximation of smooth orientation matrix.
result COSMO converges to acyclic solutions without evaluating acyclicity.
Acyclicity proven for curve complex on surfaces.
problem Acyclicity of curve complex on surfaces.
method Analyzing homologous curves on surfaces of genus g.
result Complex is (g-3)--acyclic.
We show a relationship between the non-acyclic Reidemeister torsion and a zero of the acyclic Reidemeister torsion for a lambda-regular SU(2) or SL(2, C)-representation of a knot group. Then we give a method to calculate the non-acyclic Reidemeister torsion of a knot exterior. We calculate a new example and investigate…
We study a family of regularized score-based estimators for learning the structure of a directed acyclic graph (DAG) for a multivariate normal distribution from high-dimensional data with . Our main results establish support recovery guarantees and deviation bounds for a family of penalized least-squares estima…
New method learns DAGs from data without acyclicity constraint.
problem Learning DAGs from data without imposing acyclicity.
method Sparse matrix factorization and -penalized optimization.
result Empirical success in recovering true graphs and almost-DAG graphs.
The main contribution of this article is a new prior distribution over directed acyclic graphs, which gives larger weight to sparse graphs. This distribution is intended for structured Bayesian networks, where the structure is given by an ordered block model. That is, the nodes of the graph are objects which fall into …
We report a scalable hybrid quantum-classical machine learning framework to build Bayesian networks (BN) that captures the conditional dependence and causal relationships of random variables. The generation of a BN consists of finding a directed acyclic graph (DAG) and the associated joint probability distribution of t…
ALIAS uses RL to learn DAGs without acyclicity constraints.
problem Efficiently learning DAGs from observational data without acyclicity constraints.
method ALIAS employs RL to generate DAGs in a single step with optimal complexity, bypassing acyclicity constraints.
result ALIAS outperforms state-of-the-art methods in causal discovery.
Develops a new method for learning non-parametric DAGs using RKHS.
problem Challenges of learning non-parametric causal models with large combinatorial search space.
method Uses reproducing kernel Hilbert spaces (RKHS) and sparsity-inducing regularization terms based on partial derivatives to enforce acyclicity.
result Shows improved performance through simulations and data analyses.
The acyclic group dichotomymath.GR
Two extremal classes of acyclic groups are discussed. For an arbitrary group G, there is always a homomorphism from an acyclic group of cohomological dimension 2 onto the maximum perfect subgroup of G, and there is always an embedding of G in a binate (hence acyclic) group. In the other direction, there are no nontrivi…
In this note we derive enumerative formulas for several types of labelled acyclic directed graphs by slight modifications of the familiar recursive formula for simple acyclic digraphs. These considerations are motivated by, and based upon, recent combinatorial results in geometric topology obtained by S.Choi, who estab…
ENCOD learns causal graphs efficiently without acyclicity constraints.
problem Learning causal graphical models from observational and interventional data.
method ENCOD uses optimization of edge likelihoods with separate orientation parameters.
result ENCOD efficiently recovers large graphs (hundreds of nodes) without acyclicity constraints.
We give a Dehn-Nielsen type theorem for the homology cobordism group of homology cylinders by considering its action on the acyclic closure, which was defined by Levine, of a free group. Then we construct an additive invariant of those homology cylinders which act on the acyclic closure trivially. We also describe some…
New results on relative simplicial volume using bounded acyclicity.
problem Understanding relative simplicial volume in bounded cohomology.
method Equivariant nerve pairs, relative classifying spaces, and small relative amenable category.
result Vanishing results for -Betti numbers and mapping degrees.
The paper explores conditions for homology spheres to bound acyclic smooth manifolds and symplectic fillings.
problem Conditions for integral homology 3-spheres to bound acyclic smooth 4-manifolds and their symplectic fillings.
method Structural results and analysis of smooth embeddings of lens spaces in .
result Smooth embeddings of connected sums of lens spaces in cannot be upgraded to Stein embeddings.
Proposes an approach to ensure acyclic graphs in Bayesian structure learning.
problem Ensuring acyclic graphs in Bayesian structure learning.
method Integration of knowledge from topological orderings to constrain acyclicty.
result Outperforms related Bayesian score-based approaches in experiments.
We consider finite groups which admit a faithful, smooth action on an acyclic manifold of dimension three, four or five (e.g. euclidean space). Our first main result states that a finite group acting on an acyclic 3- or 4-manifold is isomorphic to a subgroup of the orthogonal group O(3) or O(4), respectively. The analo…
We determine which 3-manifolds admit a unitary representation such that the corresponding twisted chain complex is acyclic.
Proposes an evolutionary approach to fitting acyclic VAR models.
problem Cycles in multivariate time series systems obscure hierarchical analysis.
method Evolutionary approach to fitting acyclic VAR processes with hierarchical representation.
result Outperforms unconstrained models and captures key structural properties.
Solves linearity problem for acyclic groups, bounds Cheeger-Gromov ρ-invariants.
problem Linearity problem for acyclic groups and Cheeger-Gromov ρ-invariants.
method Quantitative algebraic and geometric techniques over simplicial classifying spaces.
result Universal linear bound for Cheeger-Gromov ρ-invariants of PL (4k-1)-manifolds.
In terms of Turaev's shadows, we provide a sufficient condition for a compact, smooth, acyclic 4-manifold with boundary the 3-sphere to be diffeomorphic to the standard 4-ball. As a consequence, we prove that if a compact, smooth, acyclic 4-manifold with boundary the 3-sphere has shadow-complexity at most 2, then it is…
DAGMA learns DAGs faster and more accurately using log-determinant acyclicity.
problem Learning directed acyclic graphs from data efficiently and accurately.
method DAGMA uses M-matrices and log-determinant acyclicity to optimize DAG learning.
result DAGMA achieves faster and more accurate DAG learning compared to existing methods.
What discuss the problem of obtaining new manifold invariants via different analogues of 6j-symbols and the torsion of acyclic complexes.
The paper tackles learning varying DAG structures based on contextual features.
problem Learning a single DAG for the entire population from observational data.
method A neural network that maps contextual features to a weighted adjacency matrix of a DAG, with a projection layer to ensure acyclicity.
result The new approach can recover context-specific DAGs where existing methods fail.
Rational acyclic resolutionsmath.GT
Let X be a compactum such that dim_Q X < n+1, n>1. We prove that there is a Q-acyclic resolution r: Z-->X from a compactum Z of dim < n+1. This allows us to give a complete description of all the cases when for a compactum X and an abelian group G such that dim_G X < n+1, n>1 there is a G-acyclic resolution r: Z-->X fr…
ProDAG uses variational inference to learn DAGs with uncertainty quantification.
problem Statistical and computational challenges in learning a single DAG from data.
method Bayesian variational inference framework with novel distributions.
result ProDAG outperforms state-of-the-art alternatives in accuracy and uncertainty quantification.
New invariant from non-acyclic flat connections.
problem Constructing a higher-loop perturbative invariant.
method Integral of a Chern-Simons volume form over moduli space of flat connections.
result Generalization of Chern-Simons invariant to non-acyclic connections.
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.
DAGgr aggregates multiple DAGs to stabilize causal structure learning.
problem Stability in learning causal structure from data.
method Model averaging of candidate DAGs weighted by predictive likelihood, with acyclicity enforced.
result DAGgr consistently outperforms individual DAGs and bootstrap-aggregation baselines.
We provide a correction to the expression for scoring Gaussian directed acyclic graphical models derived in Geiger and Heckerman [Ann. Statist. 30 (2002) 1414-1440] and discuss how to evaluate the score efficiently.
We show that standard cyclic actions on Brieskorn homology 3-spheres with non-empty fixed set do not extend smoothly to any contractible smooth 4-manifold it may bound. The quotient of any such extension would be an acyclic -manifold with boundary a related Brieskorn homology sphere. We briefly discuss well known in…
We show that there can be no algorithm to decide whether infinite recursively described acyclic aspherical 2-complexes are contractible. We construct such a complex that is contractible if and only if the Collatz conjecture holds.
A combination of Bestvina--Brady Morse theory and an acyclic reflection group trick produces a torsion-free finitely presented Q-Poincaré duality group which is not the fundamental group of an aspherical closed ANR Q-homology manifold. The acyclic construction suggests asking which Q-Poincaré duality groups act freely …
Supplement to "Reversible MCMC on Markov equivalence classes of sparse directed acyclic graphs"stat.ML
This supplementary material includes three parts: some preliminary results, four examples, an experiment, three new algorithms, and all proofs of the results in the paper "Reversible MCMC on Markov equivalence classes of sparse directed acyclic graphs".
Study non-acyclic SL2-representations of twist knots and their L-functions.
problem Characterize SL2-representations of twist knots and their properties.
method Character variety, Reidemeister torsion, Chebyshev polynomials, and L-functions.
result Non-acyclic SL2-representations lie on the line x=y in character variety, and their orders are related to (-3)-Dehn surgery.
Proves conditions for separating regions in homogeneous spaces without trivial topology.
problem Separating regions in homogeneous, locally compact spaces without trivial topology.
method Analyzes properties of closed subsets and their boundaries in Čech cohomology.
result Conditions for irreducible separation without trivial topology.
Neural networks with DAGs show linearity as width increases.
problem Understanding linearity in neural networks with arbitrary DAG structures.
method Analyzing the transition to linearity in networks with arbitrary DAGs, characterizing width by minimum in-degree.
result General neural networks with DAGs exhibit linearity as width approaches infinity.
Study embeddings of manifolds via acyclic maps and surgery.
problem Relationship between embeddings of manifolds in spheres.
method Solve Poincaré duality variant, apply surgery machine, focus on homology spheres.
result Deduce results about homotopy type of embedding spaces.
Shelling-type orderings of regular CW-complexes and acyclic matchings of the Salvetti complexmath.CO
Motivated by the work of Salvetti and Settepanella we introduce certain total orderings of the faces of any shellable regular CW-complex (called `shelling-type orderings') that can be used to explicitly construct maximum acyclic matchings of the poset of cells of the given complex. Building on an application of this me…
We show that a finite type duality group of dimension is the fundamental group of a -manifold with rationally acyclic universal cover. We use this to find closed manifolds with rationally acyclic universal cover and some nonvanishing -Betti numbers outside the middle dimension, which contradicts a rat…
We prove that every acyclic normal one-dimensional real Ambrosio-Kirchheim current in a Polish (i.e. complete separable metric) space can be decomposed in curves, thus generalizing the analogous classical result proven by S. Smirnov in Euclidean space setting. The same assertion is true for every complete metric space …
We show that the rational Novikov conjecture for a group of finite homological type follows from the mod 2 acyclicity of the Higson compactifcation of an E. We then show that for groups of finite asymptotic dimension the Higson compactification is mod p acyclic for all p, and deduce the integral Novikov conjectu…