A new measure of causal influence quantifies intrinsic contributions in DAGs.
problem Quantifying intrinsic causal contributions in Directed Acyclic Graphs (DAGs).
method Recursive decomposition of node contributions, structure-preserving interventions, Shapley symmetrization.
result A measure of intrinsic causal contribution that is invariant to node relabeling.
In this paper we extend some well-known rigidity results for conformal changes of Einstein metrics to the class of generalized quasi-Einstein (GQE) metrics, which includes gradient Ricci solitons. In order to do so, we introduce the notions of conformal diffeomorphisms and vector fields that preserve a GQE structure. W…
We present a numerical approach for approximating unknown Hamiltonian systems using observation data. A distinct feature of the proposed method is that it is structure-preserving, in the sense that it enforces conservation of the reconstructed Hamiltonian. This is achieved by directly approximating the underlying unkno…
We prove an existence result for local and global G-structure preserving affine immersions between affine manifolds. Several examples are discussed in the context of Riemannian and semi-Riemannian geometry, including the case of isometric immersions into Lie groups endowed with a left-invariant metric, and the case of …
A new method learns Hamiltonian functions from noisy data.
problem Learning Hamiltonian functions from noisy observations.
method Structure-preserving kernel ridge regression method.
result The method yields excellent numerical performances.
Structure-preserving GANs learn distributions with group symmetry efficiently.
problem Learning distributions with group symmetry efficiently.
method Developed structure-preserving GANs by reducing the discriminator space and designing structured generators.
result Significantly improved sample fidelity and diversity in small data regimes.
A fast method learns plasma collision kernels from simulations, improving kinetic models.
problem Improving kinetic models for plasma dynamics beyond the weakly coupled regime.
method Data-driven collisional operator, fast spectral separation method.
result Accurately captures plasma dynamics in moderately coupled regime.
New method preserves MHD equations on sphere without costly matrix exponentials.
problem Discretizing MHD equations on sphere for numerical simulations.
method Lie-Poisson discretization, geometric quantization, semi-direct product Lie algebras.
result Preserves Lie-Poisson structure and Casimir functions.
Optimal transport for vector Gaussian mixtures improves efficiency and structure preservation.
problem Optimal mass transport for vector-valued Gaussian mixtures.
method Vectorizing Gaussian mixture models and studying optimal mass transport problems.
result Computational efficiency and structure preservation in optimal mass transport.
New integrators for mechanical systems on Lie groups simplify based on group properties.
problem Designing numerical integrators for mechanical systems on Lie groups.
method Leverage retraction maps and Lie group properties to design structure-preserving integrators.
result Simplified design of integrators for Euler-Poincare and Lie-Poisson equations.
Survey explores cohomology's roles in applied math and sciences.
problem Understanding cohomology's role in solving differential equations.
method Examining differential complexes and structure-preserving discretizations.
result Various fundamental concepts in mechanics are formulated using differential complexes.
Paper proposes G-CRD to improve GNNs by preserving global graph topology.
problem Improving lightweight GNNs for robust performance on large-scale real-world graphs.
method Introduces Graph Contrastive Representation Distillation (G-CRD) using contrastive learning.
result G-CRD consistently boosts GNN performance and robustness, outperforming existing methods.
Estimates joint causal effects using single-variable interventions on nonlinear models.
problem Estimating joint causal effects from single-variable interventions.
method Identifiability result and practical estimator for decomposing causal effects.
result Joint effects can be inferred without joint interventional data for nonlinear additive models.
Develops integrators for nonholonomic systems on Lie groups.
problem Nonholonomic constraints on Lie groups.
method Using retraction maps and Hamel formulation.
result Structure-preserving numerical integrators for nonholonomic systems.
This paper tackles CRL for multi-node interventions, achieving identifiability guarantees.
problem CRL under unknown multi-node interventions, focusing on single-node assumptions.
method Establishes identifiability results for general latent causal models under stochastic interventions.
result Identifiability up to ancestors using soft interventions, perfect identifiability using hard interventions.
This work tackles causal graph discovery with stochastic interventions to minimize the number of interventions.
problem Discovering the true causal graph from observational data with limited interventions.
method Proposes a stochastic intervention model and studies verification and search problems with approximation algorithms.
result Provides approximation algorithms with competitive ratios for verification and search problems.
Causal diagrams based on do intervention are useful tools to formalize, process and understand causal relationship among variables. However, the do intervention has controversial interpretation of causal questions for non-manipulable variables, and it also lacks the power to check the conditions related to counterfactu…
Our goal is to identify beneficial interventions from observational data. We consider interventions that are narrowly focused (impacting few covariates) and may be tailored to each individual or globally enacted over a population. For applications where harmful intervention is drastically worse than proposing no change…
Paper proposes scalable algorithm to estimate intervention targets in linear models.
problem Estimating intervention targets in linear models from observational and interventional data.
method The paper proposes a scalable algorithm that estimates intervention sites from the difference between precision matrices of observational and interventional datasets.
result The algorithm consistently identifies all intervention targets and updates observational Markov equivalence classes to interventional ones.
New method disentangles mixed interventional and observational data in SEMs.
problem Learning causal relationships from mixed interventional and observational data.
method Developed a method to disentangle mixed interventional and observational data in linear SEMs with Gaussian noise.
result The method can identify causal graphs up to their interventional Markov Equivalence Class.
The paper presents a method to estimate joint interventional distributions from marginal interventional data.
problem Estimating joint interventional distributions from marginal interventional data.
method The paper extends the Causal Maximum Entropy method to use interventional data and employs Lagrange duality to prove the solution lies in the exponential family.
result The method allows for causal feature selection and inference of joint interventional distributions.
We develop a method to describe laws of random surfaces using surface holonomy.
problem Describing laws of random surfaces with structure.
method Introduce surface holonomy and develop expected surface developments.
result Expected surface development provides a structured description of random surface laws.
Bayesian method for causal discovery from unknown general interventions.
problem Learning causal DAGs from unknown interventions that modify parent sets.
method Bayesian approach with MCMC for approximating posterior DAGs and intervention targets.
result Bayesian method can identify DAGs and intervention targets up to equivalence classes.
We classify nilmanifolds with an invariant symplectic half-flat structure. We solve the half-flat evolution equations in one example, writing down the resulting Ricci-flat metric. We study the geometry of the orbit space of 6-manifolds with an SU(3)-structure preserved by a U(1) action, giving characterizations in the …
Interventional data helps identify latent factors without distributional assumptions.
problem Identifying latent factors from interventional data without distributional assumptions.
method Leveraging geometric signatures of latent factors' support from interventional data.
result Latent causal factors can be identified up to permutation and scaling given data from perfect do-interventions.
New Wasserstein divergence improves generative model robustness and structure preservation.
problem Improving generative model robustness and structure preservation.
method Introduces a novel Wasserstein-1 path-space divergence and a WUP theorem.
result Derives robustness and generalization bounds for flow-based models.
Paper tackles imbalanced time series classification with a novel oversampling method.
problem Imbalanced time series classification challenges due to high dimensionality and correlation.
method Density-ratio based clustering followed by shrinkage technique for covariance estimation, then generating synthetic samples.
result OHIT outperforms state-of-the-art methods in F1, G-mean, and AUC metrics.
Develops neural networks that follow thermodynamics principles.
problem Learning physical systems from data while respecting thermodynamics.
method Uses feedforward neural networks and the GENERIC formalism to enforce metriplectic structure.
result Predictions comply with first and second principles of thermodynamics.
IntDC framework uncovers causal relationships from non-interventional data.
problem Detecting causal relationships in non-interventional complex systems.
method Interventional Embedding Entropy (IEE) for causal strength measurement.
result IEE accurately finds causal edges and quantifies causal strength robustly.
Algorithm detects causal change points quickly with adaptive interventions.
problem Detecting changes in causal models with interventions.
method Centralization technique, Kullback-Leibler divergence for intervention selection, adaptive intervention policy.
result Theoretical first-order optimality and validation through simulations and real-world studies.
A quantum state generation method that respects physical constraints.
problem Generating quantum states with complex-valued Hermitian, positive semi-definite, and trace one properties.
method Mirror diffusion model with von Neumann entropy to enforce structural constraints.
result Demonstrated effective generation of quantum states with conditional guidance.
Method learns causal effects from multiple interventions in presence of unobserved confounders.
problem Disentangling causal effects from sets of interventions in the presence of unobserved confounders.
method Non-linear structural causal models with additive, multivariate Gaussian noise; algorithm that learns causal model parameters by pooling data from different regimes and maximizing combined likelihood.
result Identification proofs demonstrate that causal effects of single interventions can be learned from sets of interventions, even with unobserved confounders.
New algorithms improve causal graph discovery with adaptive interventions, even under worst-case interventional costs.
problem Discover causal relationships from data with adaptive interventions and node-dependent costs.
method Define new benchmarks and provide adaptive search algorithms for causal graph discovery.
result Logarithmic approximations achieved under various settings: atomic, bounded size interventions and generalized cost objectives.
We address the problem of optimal Central Bank intervention in the exchange rate market when interventions create feedback in the rate dynamics. In particular, we extend the work done on optimal impulse control by Cadenillas and Zapatero to incorporate temporary market reactions, of random duration and level, to Bank i…
Algorithm learns latent variables for thermodynamically-consistent deep neural networks.
problem Predicting time evolution of large-scale physical systems with thermodynamic consistency.
method Sparse autoencoders and structure-preserving neural networks.
result Method conserves total energy and entropy inequality for both conservative and dissipative systems.
GIT uses gradient estimators to target interventions for causal discovery.
problem Challenges in inferring causal structure from observational data.
method GIT uses gradient estimators to target interventions for causal discovery.
result GIT performs on par with competitive baselines, surpassing them in low-data regimes.
Paper relaxes faithfulness assumption for causal discovery using interventions.
problem Violation of faithfulness assumption in natural systems leads to incorrect causal structure identification.
method Use intervention-immediacy faithfulness assumption to identify causal structures with hard interventions.
result Interventions contain information about causal structure that can identify causal structures when faithfulness is violated.
Derives stochastic and dissipative dynamics preserving Gibbs measure.
problem Understanding and deriving structure-preserving stochastic systems.
method Extension of Hamilton-Pontryagin principle, symmetry reduction, and inclusion of dissipation.
result New derivation of double-bracket dissipation.
Eigen-GNN enhances GNNs by preserving graph structures.
problem Existing shallow GNNs fail to effectively preserve graph structures.
method Integrates eigenspace of graph structures into GNNs as a dimensionality reduction module.
result Eigen-GNN boosts GNNs' ability to preserve graph structures without increasing depth.
FMI uses matching to mimic interventions for causal feature learning.
problem Challenges in causal discovery from observational data.
method Feature Matching Intervention (FMI) using matching to emulate perfect interventions.
result FMI outperforms in identifying causal features from observational data.
Develops integrators for Hamiltonian systems in Jacobi manifolds.
problem Modeling conservative systems with dissipative and thermodynamic phenomena.
method Constructs structure-preserving integrators for Hamiltonian systems in Jacobi manifolds.
result Proposes a numerical integration technique compatible with Jacobi dynamics.
CDSPP learns domain-specific projections for heterogeneous domain adaptation.
problem Heterogeneous domain adaptation problems where source and target domains have different modalities or feature dimensions.
method Cross-Domain Structure Preserving Projection (CDSPP) algorithm that learns domain-specific projections to map features into a common subspace.
result CDSPP achieves superior performance in both supervised and semi-supervised HDA compared to state-of-the-art methods.
BaCaDI discovers causal structures from unknown interventions.
problem Inferring causal structures from unknown interventions with limited data.
method Bayesian framework with gradient-based variational inference.
result BaCaDI outperforms related methods in identifying causal structures and intervention targets.
Graph-coupled causal Bayesian optimization transfers information across related interventions.
problem Optimizing expensive systems where interventions are costly and causal effects are confounded.
method Ties intervention effects together through shared causal parameters, improving estimation.
result Information-gain and regret bounds show improved performance with shared mechanisms.
The paper tackles matching a desired mean in causal systems through shift interventions.
problem Matching a desired mean in causal systems.
method Defining Markov equivalence classes, proposing active learning strategies, deriving lower bounds.
result Proposed active learning strategies require fewer interventions than previous approaches, especially for certain graph classes.
We establish a connection between recent developments in the study of vortices in the abelian Higgs models, and in the theory of structure-preserving discrete conformal maps. We explain how both are related via conformal mapping problems involving prescribed linear combinations of the curvature and volume form, and sho…
Intervention loss stabilizes GAN training and reduces mode collapse.
problem Stabilizing GAN training and mitigating mode collapse.
method Intervention loss regularization term introduced into GAN objective.
result Improved GAN training stability and reduced mode collapse.
Model identifies causal structure from paired observational and interventional data with unknown soft interventions.
problem Identifying causal structure from observational and interventional data with unknown soft interventions.
method Proposes a scalable causal discovery model that aggregates subset-level PDAGs and applies contrastive cross-regime orientation rules.
result The model asymptotically recovers the identifiable PDAG and can orient additional edges compared to non-contrastive subset-restricted methods.