arXiv research

SPOT improves differentiable causal discovery by estimating skeleton posterior for latent confounders.

We consider the problem of learning a causal graph over a set of variables with interventions. We study the cost-optimal causal graph learning problem: For a given skeleton (undirected version of the causal graph), design the set of interventions with minimum total cost, that can uniquely identify any causal graph with…

Tensor-based method simplifies causal skeleton discovery.

The paper introduces negative controls to evaluate causal discovery algorithms, improving their reliability.

This paper presents a new open source Python framework for causal discovery from observational data and domain background knowledge, aimed at causal graph and causal mechanism modeling. The 'cdt' package implements the end-to-end approach, recovering the direct dependencies (the skeleton of the causal graph) and the ca…

New algorithm reduces regret in combinatorial causal bandits without graph structure.

FMCIT accelerates CI tests for causal discovery, maintaining power and efficiency.

It is commonplace to encounter heterogeneous or nonstationary data, of which the underlying generating process changes across domains or over time. Such a distribution shift feature presents both challenges and opportunities for causal discovery. In this paper, we develop a framework for causal discovery from such data…

We introduce a new approach to functional causal modeling from observational data, called Causal Generative Neural Networks (CGNN). CGNN leverages the power of neural networks to learn a generative model of the joint distribution of the observed variables, by minimizing the Maximum Mean Discrepancy between generated an…

Local approach learns causal structure of linear Gaussian polytree models from interventional data.

New method discovers causal relationships in large-scale data.

ML4C uses binary classification to infer causal structures from latent vicinity.

Develops a method to efficiently learn causal DAGs using directed clique trees.

Study designs experiments to identify causal graph structure with cycles and latent confounders.

A significant theoretical advantage of search-and-score methods for learning Bayesian Networks is that they can accept informative prior beliefs for each possible network, thus complementing the data. In this paper, a method is presented for assigning priors based on beliefs on the presence or absence of certain paths …

The study examines the topology of complements of polytopal skeletons.

Develops a model for causal discovery in path spaces.

Criterion for manifold skeletons embeddability in Euclidean space.

Skeleton is a new notion designed for constructing space-filling curves of self-similar sets. It is shown in [Dai, Rao and Zhang, Space-filling curves of self-similar sets (II): Edge-to-trail substitution rule,https://doi.org/10.1088/1361-6544/ab1275] that for a connected self-similar set, space-filling curves can be c…

We have completely rewritten the paper, and corrected the proofs. We construct an exponential map at any point in the (n-1)-skeleton minus the (n-2)-skeleton of an n-dimensional Riemannian polyhedron. We have added allover the extra-assumption that the exponential map is totally geodesic at points in the (n-1)-skeleton…

This paper tackles causal interactions in mixtures of DAGs using interventions.

The extension functors between categories of Cartan geometries can be used to define different categories of Cartan geometries with additional morphisms. The Cartan geometries modeled on skeletons can be used for the description of such categories of Cartan geometries and therefore we develop the theory of Cartan geome…

Algorithm recovers causal graphs from data with fewer tests.

Fixed point sets of certain group actions are contractible.

Skeleton clustering detects clusters in high-dimensional data without needing prototypes.

Bayesian method models binary response and covariates for two groups, estimating causal relationships.

Efficiently learns polytrees with known skeleton in polynomial time and sample complexity.

New theorem shows embedding restrictions for manifold skeletons.

The Bezier simplex fitting is a novel data modeling technique which exploits geometric structures of data to approximate the Pareto front of multi-objective optimization problems. There are two fitting methods based on different sampling strategies. The inductive skeleton fitting employs a stratified subsampling from e…

Node-link diagrams are a popular method for representing graphs that capture relationships between individuals, businesses, proteins, and telecommunication endpoints. However, node-link diagrams may fail to convey insights regarding graph structures, even for moderately sized data of a few hundred nodes, due to visual …

Our main theorem identifies a class of totally geodesic subgraphs of the 1-skeleton of the pants complex, each isomorphic to the product of two Farey graphs. We deduce the existence of many convex planes in the 1-skeleton of the pants complex.

Researchers study learning polytree graphs from linear SEMs with exact recovery conditions.

We are enveloped by stories of visual interpretations in our everyday lives. The way we narrate a story often comprises of two stages, which are, forming a central mind map of entities and then weaving a story around them. A contributing factor to coherence is not just basing the story on these entities but also, refer…

New method certifies risks of LLM outputs, improving accuracy and reliability.

The present paper is devoted to the joint motion of two immiscible incompressible liquids in porous media. The liquids have different densities and initially separated by a surface of strong discontinuity (free boundary). We discuss the results of numerical simulations for exact free boundary problems on the microscopi…

Proposes a neural network for recognizing 3D skeleton-based interactions.

The paper finds and visualizes unique geometric polyhedra and tori with few vertices.

We create a 3-skeleton for a symmetric group's classifying space.

A new graph-based approach for estimating complex data with manifold structure.

A method for learning skeleton of Bayesian networks robust to outliers and corruption.

We consider the problem of learning causal networks with interventions, when each intervention is limited in size under Pearl's Structural Equation Model with independent errors (SEM-IE). The objective is to minimize the number of experiments to discover the causal directions of all the edges in a causal graph. Previou…

We show that closed arithmetic hyperbolic n-dimensional orbifolds with larger and larger volumes give rise to triangulations of the underlying spaces whose 1-skeletons are harder and harder to embed nicely in Euclidean space. To show this we generalize an inequality of Gromov and Guth to hyperbolic n-orbifolds and find…

Every cubic graph is a bridge trisection's 1-skeleton for a knotted surface.

On a Weinstein manifold, we define a constructible co/sheaf of categories on the skeleton. The construction works with arbitrary coefficients, and depends only on the homotopy class of a section of the Lagrangian Grassmannian of the stable symplectic normal bundle. The definition is as follows. Take any, possibly high …

The one-skeleton of a G-manifold M is the set of points p in M where $\dim G_p \geq \dim G -1$; and M is a GKM manifold if the dimension of this one-skeleton is 2. Goresky, Kottwitz and MacPherson show that for such a manifold this one-skeleton has the structure of a ``labeled" graph, $(Γ, α)$, and that the equivariant…

Finite simplicial complexes dominate certain manifolds with a bounded number of simplices.

We present a constructive proof that there exists a decomposition of the 2-skeleton of the k-dimensional cross polytope $β^k$ into closed surfaces of genus $g \leq 1$, each with a transitive automorphism group given by the vertex transitive $\mathbb{Z}_{2k}$-action on $β^k$. Furthermore we show that for each $k \equiv …

Study Monge-Ampère equations on Calabi-Yau hypersurfaces, proving unique solutions and implications for special Lagrangian fibrations.