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…
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48 results for “structural-equation models”
Graphical notation simplifies complex polynomial constraints in linear models.
problem Complex polynomial constraints in linear structural equation models are impractical.
method Developed a graphical notation to represent these constraints.
result The graphical notation simplifies the representation of many polynomial constraints.
New method uses SEMs to uncover cause-effect in manufacturing processes.
problem Complex cause-and-effect relationships in manufacturing processes.
method Using Structural Equation Models with non-linear relationships.
result More informative cause-effect relationships derived from data.
Identifiability of Gaussian Structural Equation Models with Dependent Errors Having Equal Variancesstat.ML
In this paper, we prove that some Gaussian structural equation models with dependent errors having equal variances are identifiable from their corresponding Gaussian distributions. Specifically, we prove identifiability for the Gaussian structural equation models that can be represented as Andersson-Madigan-Perlman cha…
The paper reviews identifiability in linear and nonlinear models, from Gaussian to non-Gaussian.
problem Identifiability issues in latent-variable and structural-equation models, especially in nonlinear cases.
method Review of identifiability theory for linear and nonlinear models, including factor analysis and structural equation models.
result Even nonparametric nonlinear models can be estimated with additional assumptions.
In a variety of disciplines such as social sciences, psychology, medicine and economics, the recorded data are considered to be noisy measurements of latent variables connected by some causal structure. This corresponds to a family of graphical models known as the structural equation model with latent variables. While …
In a variety of disciplines such as social sciences, psychology, medicine and economics, the recorded data are considered to be noisy measurements of latent variables connected by some causal structure. This corresponds to a family of graphical models known as the structural equation model with latent variables. While …
Book introduces ML and AI for causal inference.
problem Uncertainty in causal relationships.
method Structural equation models, DAGs, SCMs, and Double/Debiased Machine Learning.
result Improved inference in causal models using predictive tools.
Despite their popularity, many questions about the algebraic constraints imposed by linear structural equation models remain open problems. For causal discovery, two of these problems are especially important: the enumeration of the constraints imposed by a model, and deciding whether two graphs define the same statist…
In this work, we consider the identifiability assumption of Gaussian linear structural equation models (SEMs) in which each variable is determined by a linear function of its parents plus normally distributed error. It has been shown that linear Gaussian structural equation models are fully identifiable if all error va…
We describe a method for solving the Maurer-Cartan structure equation associated with a Lie algebra that isolates the role of the Jacobi identity as an obstruction to integration. We show that the method naturally adapts to two other interesting situations: local symplectic realizations of Poisson structures, in which …
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.
In this paper we build the structure equations and the integrable systems for a discrete centroaffine indefinite surface in . At the same time, some centroaffine invariants are obtained according to the structure equations. Using these centroaffine invariants, we study the Laplacian operator and the convexity of …
New method identifies extreme risk propagation in financial networks.
problem Understanding extreme risk in financial networks.
method Max-linear structural equation model, hard-thresholding, Hamming distance.
result Sparse DAG for extreme risk propagation estimated.
We explicitly determine the structure equations of 5-dimensional Levi 2-nondegenerate CR hypersurfaces, using our recently constructed canonical Cartan connection for this class of CR manifolds. We also give an outline of the basic properties of absolute parallelisms and Cartan connections, together with a brief discus…
New neural approach for estimating SEMs with provable convergence.
problem Estimating structural parameters in SEMs.
method Formulated as a min-max game with neural networks, learned using stochastic gradient descent.
result Global convergence in overparametrized regime, improving state-of-the-art.
Consistent Bayesian causal discovery for structural equation models with equal error variancesmath.ST
Bayesian method recovers causal structure in SEMs with equal error variances.
problem Recovering causal structure in SEMs with equal error variances.
method Bayesian DAG selection method using g-priors and the key property of minimum expected squared errors.
result The method consistently recovers the true graph without additional distributional assumptions.
New probabilistic approaches offer recourse recommendations even when causal models are imperfect.
problem Limited causal knowledge makes guaranteeing algorithmic recourse impossible.
method Two probabilistic approaches: Bayesian model averaging and average effect computation.
result Probabilistic approaches lead to more reliable recourse recommendations.
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…
Superintegrable systems on surfaces are classified geometrically.
problem Classifying superintegrable systems on conformal surfaces.
method Geometric structures on conformal surfaces, conformal covariant structural equations.
result Explicit set of algebraic equations defining superintegrable systems on all constant curvature surfaces.
Researchers study learning polytree graphs from linear SEMs with exact recovery conditions.
problem Learning polytree graphs from linear SEMs with exact recovery conditions.
method Study Gaussian polytree models, derive sufficient and necessary conditions for sample sizes, and establish estimation error bounds.
result Sharp characterization of difficulty with matching sufficient and necessary conditions.
Identifies patient-specific root causes of disease using structural equation models.
problem Detecting significant variables in complex diseases that differ between patients.
method Defining patient-specific root causes as exogenous errors in a structural equation model, quantifying predictivity using Shapley values, and developing a fast algorithm called Root Causal Inference.
result Significant improvements in accuracy by uncovering root causes with large effect sizes at the individual level but clinically insignificant effect sizes at the group level.
Proposes KAR for nonlinear causal discovery using kernel methods.
problem Learning causal relationships in nonlinear settings.
method Kernel anchor regression (KAR) with improved three-stage nonparametric regression.
result KAR outperforms existing methods in nonlinear causal discovery.
Introduces pqc structures, generalizing para 3-Sasakian geometry.
problem Generalizing and studying para 3-Sasakian geometry.
method Defines pqc structures, derives a distinguished linear connection, and presents structure equations.
result Para 3-Sasakian spaces are pqc manifolds and pqc-Einstein.
Complex systems can be modelled at various levels of detail. Ideally, causal models of the same system should be consistent with one another in the sense that they agree in their predictions of the effects of interventions. We formalise this notion of consistency in the case of Structural Equation Models (SEMs) by intr…
Paper bridges AI/ML and causal modeling to reduce bias.
problem Difficulty in combining methods from different assumptions.
method Integrates system dynamics and structural equation modeling.
result Unified mathematical framework for AI/ML and causal modeling.
Geometrodynamics based on geodesic equation with Cartan structural equation on Riemannian manifoldsmath.DG
Motivated by the geospin matrix as a new variable in Riemannian geometry. Then, we use four real dynamical variables to show the dynamical essence of Cartan structural equation, we obtain the geometrodynamics on Riemannian manifolds that can be expressed below \begin{align} & Θ/d{{t}^{2}}…
We give an elegant formulation of the structure equations (of Cartan) and the Bianchi identities in terms of exterior calculus without reference to a particular basis and without the exterior covariant derivative. This approach allows both structure equations and the Bianchi identities to be expressed in terms of forms…
Study curvature of piecewise metrics using moving frames.
problem Deriving a curvature measure for piecewise-smooth Riemannian metrics.
method Used moving frame techniques to derive curvature, showing it satisfies Cartan structure equations and gauge transformation law.
result Equivalence of the derived curvature to existing densitized distributional curvature.
Multi-scanner Antivirus systems provide insightful information on the nature of a suspect application; however there is often a lack of consensus and consistency between different Anti-Virus engines. In this article, we analyze more than 250 thousand malware signatures generated by 61 different Anti-Virus engines after…
New model identifies patient-specific disease root causes.
problem Identifying root causes of complex diseases varying between patients.
method Generalized Root Causal Inference (GRCI) algorithm for heteroscedastic noise model.
result GRCI accurately extracts patient-specific root causes.
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.
Quaternionic differential geometry expands geometric concepts using quaternions.
problem Generalizing geometric concepts to quaternionic constraints.
method Generalizing curves and surfaces, curvature, torsion, differential forms, and directional derivatives to quaternionic constraints.
result Quaternionic formalism provides a suitable language for differential geometry.
The classical Cartan's structural equations show in a compact way the relation between a connection and its curvature, and reveals their geometric interpretation in terms of moving frames. In order to study the mathematical properties of singularities, we need to study the geometry of manifolds endowed on the tangent b…
New methods discover causal relationships from multiple related data views.
problem Causal discovery from non-Gaussian data.
method Multi-view linear Structural Equation Model (SEM) with weak assumptions.
result Identifiability of acyclic SEMs and successful causal graph estimation.
The paper proves isometric embedding equations in low Sobolev regularity.
problem Proving isometric embedding equations in low Sobolev regularity.
method Proving Cartan's and Gauss's equations for frames and deducing the Gauss equation for isometric embeddings.
result Gauss equation holds for isometric embeddings.
Structural equation models and Bayesian networks have been widely used to analyze causal relations between continuous variables. In such frameworks, linear acyclic models are typically used to model the data-generating process of variables. Recently, it was shown that use of non-Gaussianity identifies the full structur…
We improve robust parameter estimation in causal models from observational data.
problem Robustly estimating parameters in linear structural equation models from observational data.
method Extending Sankararaman et al. (2019) to a broader class of models, providing sufficient conditions for robust identifiability.
result For a large set of parameters, robust identifiability holds and existing algorithms achieve robust identifiability.
Boosting method for causal SEMs from observational data.
problem Learning causal order among variables from observational data.
method Boosting-based approach with early stopping and component-wise gradient descent.
result Boosting with early stopping consistently favors the true causal ordering.
Lévy driven term structure models have become an important subject in the mathematical finance literature. This paper provides a comprehensive analysis of the Lévy driven Heath-Jarrow-Morton type term structure equation. This includes a full proof of existence and uniqueness in particular, which seems to have been lack…
We propose two nonlinear regression methods, named Adversarial Orthogonal Regression (AdOR) for additive noise models and Adversarial Orthogonal Structural Equation Model (AdOSE) for the general case of structural equation models. Both methods try to make the residual of regression independent from regressors while put…
Study combines SEM, OLS, and DML for robustness checks in survey-based research.
problem Stability of SEM findings under alternative estimation frameworks.
method Staged robustness analysis framework connecting SEM, OLS, and DML.
result Identifies stable and unstable relationships across SEM, OLS, and DML checks.
New method identifies root causes in presence of latent confounding.
problem Identifying root causes in the presence of latent variables.
method Extract Errors with Latents (EEL) procedure for inferring root causes.
result Superior accuracy and robustness compared to previous methods.
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.
The paper explores reductions of self-dual conformal structure equations.
problem Integrating the general local form of self-dual conformal structure.
method Using Lax pair, hierarchy structure, and dressing scheme to discuss reductions.
result Constructs solutions for the SDCS equations and presents type B SDCS system.
SLEM: Machine Learning for Path Modeling and Causal Inference with Super Learner Equation Modelingstat.ML
SLEM uses machine learning to improve causal inference from observational data.
problem Improving causal inference from observational data using non-linear relationships.
method Super Learner Equation Modeling integrating machine learning ensembles.
result SLEM provides consistent and unbiased estimates of causal effects.
Paper introduces a new identifiability criterion for DAGs using conditional variances.
problem Challenges in discovering causal relationships from observational data.
method Introduces a novel identifiability criterion for DAGs using conditional variances. Uses weak majorization on Cholesky factor of covariance matrix for learning DAGs.
result Demonstrates effectiveness of the new approach in recovering DAGs through simulations and real data analysis.
In this paper we obtain the structure equation of a contact-complex Riemannian submersion and give some applications of this equation in the study of almost cosymplectic manifolds with Kaehler fibres.