Local causal structure learning aims to discover and distinguish direct causes (parents) and direct effects (children) of a variable of interest from data. While emerging successes have been made, existing methods need to search a large space to distinguish direct causes from direct effects of a target variable \emph{T…
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48 results for “directional structure”
DiMMSB models directed mixed membership networks, identifying distinct community structures.
problem Modeling directed mixed membership networks with distinct community structures.
method Directed Mixed Membership Stochastic Blockmodel (DiMMSB) with DiSP algorithm.
result DiSP algorithm is asymptotically consistent and outperforms competitors.
We endow projective (resp. direct) limits of Banach tensor structures with Fréchet (resp. convenient) structures and study adapted connections to -structures in both frameworks. This situation is illustrated by a lot of examples.
During the last two decades, we easilly see that the World Wide Web's link structure is modeled as the directed graph. In this paper, we will model the World Wide Web's link structure as the directed hypergraph. Moreover, we will develop the PageRank algorithm for this directed hypergraph. Due to the lack of the World …
We equip the direct limit of tangent bundles of paracompact finite dimensional manifolds with a structure of convenient vector bundle with structural group .
We classify six-dimensional Lie groups which admit a left-invariant half-flat SU(3)-structure and which split in a direct product of three-dimensional factors. Moreover, a complete list of those direct products is obtained which admit a left-invariant half-flat SU(3)-structure such that the three-dimensional factors ar…
Structural restrictions in local causal discovery: identifying direct causes of a target variablestat.ME
We identify direct causes of a target variable from observational data without full DAG identifiability.
problem Learning direct causes of a target variable from observational data.
method Developed algorithms under relaxed identifiability assumptions for one environment without interventions.
result Identifiable set of direct causes from observational data under specific assumptions.
Study coKähler structures on Lie algebras using Fino-Vezzoni correspondence.
problem Characterize coKähler structures on Lie algebras.
method Use Fino-Vezzoni correspondence to relate coKähler Lie algebras to Kähler Lie algebras.
result Complete the flat case for odd-dimensional Lie algebras, proving coKähler structures exist.
This work improves structured prediction by learning the balance between signal and random noise.
problem Structured prediction with random perturbations.
method Learning the variance of randomized structured predictors to balance signal and noise.
result Learning the balance improves structured prediction effectiveness.
Introduces zebra structures on surfaces for directional foliation.
problem Finding canonical representatives of homotopy classes on surfaces.
method Introduces zebra structures and uses triangulations with edge connections to prove existence.
result Canonical representatives exist for homotopy classes on surfaces with specific triangulations.
New Ricci flow method for directed graphs with balancing factor.
problem Analyzing asymmetry in directed networks.
method Rigorous formulation of Ricci flow on directed weighted graphs with balancing factor.
result Existence and uniqueness of discrete Ricci flow solutions.
The paper studies volumes of direct images for high tensor powers of ample bundles.
problem Understanding asymptotics of Monge-Ampère volumes for high tensor powers of ample line bundles.
method Analyzes the leading term of asymptotics and classifies bundles saturating a topological bound.
result Provides a characterization of bundles admitting projectively flat Hermitian structures in the case of high symmetric powers of ample vector bundles.
Circular Directional Flow Decomposition of Networksphysics.soc-ph
CDFD analyzes circularity and directionality in weighted directed networks.
problem Analyzing circularity and directionality in weighted directed networks.
method CDFD framework separates flow into circular and acyclic components.
result CDFD yields a normalized circularity index capturing flow in cycles and directionality.
Bayesian ARMA model with directional shifts captures structural breaks in compositional time series.
problem Structural breaks in compositional time series due to external shocks or policy changes.
method Developed a Bayesian Dirichlet ARMA model augmented with a directional-shift intervention mechanism.
result The model captures structural breaks through interpretable parameters and produces coherent probabilistic forecasts.
Unified framework for clustering and learning causal graphs across subjects.
problem Bias and obscured subpopulation-specific dependencies in multivariate systems.
method Directed Acyclic Graph-based Dependency Clustering via Alternating Direction Method of Multipliers (DAG-DC-ADMM) integrated with Structural Equation Modeling (SEM).
result Unified framework recovers cluster-specific causal dependency structures with high true positive rate and low false discovery rate.
A new pruning method reduces neural network computation without retraining.
problem Efficiently reduce neural network computation while maintaining accuracy.
method Structured directional pruning via perturbation orthogonal projection.
result Achieves state-of-the-art pruned accuracy without retraining.
A new metric based on hitting probabilities for directed graphs and Markov chains.
problem Lack of metrics specifically adapted to asymmetric structure of directed graphs and Markov chains.
method Metric based on hitting probabilities, insensitive to shortest and average walk distances.
result New structural theory of directed graphs and utility for various applications.
CAT method learns causal structure of directed trees efficiently.
problem Learning causal structure from directed trees.
method Chu-Liu-Edmonds algorithm for fast and scalable structure learning.
result Consistency in asymptotic regime with vanishing identifiability gap for Gaussian errors.
No direct generalized complex structure can be induced from 's nearly Kähler structure.
problem Existence of generalized complex structures on .
method Defined integrability in terms of the Dorfman bracket and studied 's nearly Kähler structure.
result No generalized complex structure can be induced from 's nearly Kähler structure.
We consider structural equation models in which variables can be written as a function of their parents and noise terms, which are assumed to be jointly independent. Corresponding to each structural equation model, there is a directed acyclic graph describing the relationships between the variables. In Gaussian structu…
Local discovery method uncovers direct unfairness in complex systems.
problem Identifying causal pathways of unfairness in complex domains.
method Local discovery for direct discrimination (LD3) method.
result LD3 returns a valid adjustment set (VAS) for assessing unfairness.
Proposes a copula-based model for multi-view clustering with directional dependency.
problem Challenges in integrating multi-source datasets with directional dependency.
method Copula-based multi-view clustering model accounting for directional dependence.
result Ignoring directional dependence negatively impacts clustering performance.
Algebraic Dead Directions in LayerNorm Transformers: A Forward-Pass-Only Diagnostic at LLM Scalecs.LG
LayerNorm transformers have dead directions that can be read from their parameters alone.
problem Locating dead directions in LayerNorm transformers
method Using the inverse-scale direction of LayerNorm affine parameters
result Predicted dead direction matches measured bottom singular direction
Directed graphs occur throughout statistical modeling of networks, and exchangeability is a natural assumption when the ordering of vertices does not matter. There is a deep structural theory for exchangeable undirected graphs, which extends to the directed case via measurable objects known as digraphons. Using digraph…
New method identifies causal parameters in tree-shaped linear models using cycles.
problem Identifying causal parameters from correlations in tree-shaped linear models.
method Investigates tree-shaped linear models, uses missing cycles to identify causal parameters, solves quadratic equations.
result Shows how missing cycles can be combined to obtain a unique solution for causal parameters.
Study on residual Monge-Ampère mass of complex functions with directional Lipschitz continuity.
problem Estimating the residual Monge-Ampère mass of plurisubharmonic functions.
method General decomposition formula under Sasakian structure, -apriori estimate, upper-bound estimate on residual mass.
result Upper-bound estimate on residual mass for uniformly directional Lipschitz continuity confirmed.
Novel technique reduces Bayesian network complexity while preserving inference accuracy.
problem Complexity reduction in Bayesian networks for efficient inference.
method Directed convex hull structure and polynomial-time algorithm for identifying minimum localized networks.
result High dimension reduction capability and improved inference efficiency in real networks.
New method computes affine normal directions efficiently for sparse polynomials.
problem Computing affine normal directions is computationally expensive in high dimensions.
method Reduces third-order tensor contraction to matrix-free formulation using log-determinant gradient.
result Scalable implementations with near-linear scaling in dimension and sparsity.
TSAM predicts directed temporal links using GCN and self-attention.
problem Predicting links in directed temporal networks.
method GCN, self-attention mechanism, autoencoder architecture, graph attentional layers, graph convolutional layers, graph recurrent unit layer.
result TSAM outperforms benchmarks on four realistic networks.
We consider learning the possible causal direction of two observed variables in the presence of latent confounding variables. Several existing methods have been shown to consistently estimate causal direction assuming linear or some type of nonlinear relationship and no latent confounders. However, the estimation resul…
Proposes a new neural head for asymmetric representation learning.
problem Asymmetric representation learning in directed relations.
method Role-aware neural convex divergence head.
result Role-aware projections improve directional accuracy over plain ICNN-Bregman heads.
The main approach to defining equivalence among acyclic directed causal graphical models is based on the conditional independence relationships in the distributions that the causal models can generate, in terms of the Markov equivalence. However, it is known that when cycles are allowed in the causal structure, conditi…
Novel approach for SEM in small samples with .
problem Small sample size and issues in factor-based SEM.
method Reformulates covariance structure into self-covariance and cross-covariance, defines a feasible set with relative error constraint.
result Improved stability and directional information in small-sample settings.
Bayesian Out-Treescs.LG
A Bayesian treatment of latent directed graph structure for non-iid data is provided where each child datum is sampled with a directed conditional dependence on a single unknown parent datum. The latent graph structure is assumed to lie in the family of directed out-tree graphs which leads to efficient Bayesian inferen…
We extend to the -dimensional case a recent theorem establishing the validity of the Huygens' envelope principle for wavefronts in Finsler spaces. Our results have direct applications in analogue gravity models, for which the Fermat's principle of least time naturally gives origin to an underlying Finslerian geometr…
Develops neural network for directed hypergraphs for node classification.
problem Irregular data structure, particularly directed graphs.
method Directed hypergraph neural network and semi-supervised learning method.
result Novel directed hypergraph neural network achieves highest accuracies on node classification tasks.
CCHM algorithm learns BN structure with latent variables, improving causal effect measurement.
problem Latent variables cause spurious relationships in BN structure learning.
method Hybrid approach combining constraint-based and score-based learning, incorporating do-calculus.
result CCHM outperforms state-of-the-art in reconstructing true BN structure.
In this paper, we provide a method to learn the directed structure of a Bayesian network using data. The data is accessed by making conditional probability queries to a black-box model. We introduce a notion of simplicity of representation of conditional probability tables for the nodes in the Bayesian network, that we…
The paper proposes a new model to analyze directed networks and accurately estimate community memberships.
problem Modeling and estimating community memberships in directed networks with heterogeneous degrees.
method Directed Degree Corrected Mixed Membership (DiDCMM) model and DiMSC algorithm.
result The proposed DiMSC algorithm is asymptotically consistent and provides error bounds for community membership vectors.
New method improves speed of estimating bivariate functional data.
problem Estimating bivariate functional data at faster rates.
method Adapting to directional regularity of bivariate processes.
result Faster rates of convergence achieved through change-of-basis.
We study a class of Riemannian manifolds with respect to the covariant derivative of their curvature tensors. We introduce geometrically the class of directed Riemannian manifolds of pointwise constant relative sectional curvature and give a tensor characterization for such manifolds. We prove that all rotational hyper…
Recent work suggests goal-driven training of neural networks can be used to model neural activity in the brain. While response properties of neurons in artificial neural networks bear similarities to those in the brain, the network architectures are often constrained to be different. Here we ask if a neural network can…
We provide a characterization of two types of directed homology for fully-connected, feedforward neural network architectures. These exact characterizations of the directed homology structure of a neural network architecture are the first of their kind. We show that the directed flag homology of deep networks reduces t…
Reparameterization of variational auto-encoders with continuous random variables is an effective method for reducing the variance of their gradient estimates. In the discrete case, one can perform reparametrization using the Gumbel-Max trick, but the resulting objective relies on an operation and is non-dif…
Hallmarks of Optimization Trajectories in Neural Networks: Directional Exploration and Redundancycs.LG
The study analyzes optimization trajectories in neural networks to reveal redundancy and redundancy-reducing strategies.
problem Understanding the directional structure and redundancy in neural network optimization.
method Introducing natural notions of complexity for optimization trajectories and analyzing their directional nature.
result Training only scalar batchnorm parameters can match the performance of training the entire network, indicating potential for hybrid optimization schemes.
Study on Kuranishi spaces of complex structures and vector bundles, showing isomorphisms and counterexamples.
problem Understanding Kuranishi spaces of complex structures and vector bundles.
method Analyzing Kuranishi spaces of pairs of compact Kähler manifolds and vector bundles.
result Isomorphisms and counterexamples of Kuranishi spaces of pairs of nilmanifolds and trivial vector bundles.
We investigate probabilistic graphical models that allow for both cycles and latent variables. For this we introduce directed graphs with hyperedges (HEDGes), generalizing and combining both marginalized directed acyclic graphs (mDAGs) that can model latent (dependent) variables, and directed mixed graphs (DMGs) that c…
This dissertation uses ILP to learn Bayesian network structures efficiently.
problem Learning the structure of Bayesian networks from data.
method Integer Linear Programming formulation with cluster constraints and cutting planes.
result The approach finds feasible solutions for Bayesian network structures efficiently.