Decomposes financial networks to reveal cause-effect hierarchies during crises.
problem Complex financial networks are hard to interpret due to Granger causality.
method Helmholtz-Hodge-Kodaira decomposition to separate networks into rotational and gradient components.
result Precious metals and pharmaceutical products are identified as causal drivers during crises.
The study quantifies the information needed for causal queries at different levels of Pearl's hierarchy.
problem How much additional information is needed for interventional and counterfactual queries compared to observational queries?
method Formalized via query-class description length, using Kolmogorov complexity of answer oracles induced by SCMs.
result Binary acyclic SCMs show a quadratic gap between observational and interventional descriptions, and a logarithmic gap between interventional and counterfactual descriptions.
New causal distances improve evaluation of causal discovery algorithms.
problem Evaluating causal discovery algorithms using graphical distances is limited.
method Defined causal distances based on causal distributions rather than graphical structure.
result Improved evaluation of causal discovery algorithms on synthetic and real-world datasets.
The causal compatibility question asks whether a given causal structure graph -- possibly involving latent variables -- constitutes a genuinely plausible causal explanation for a given probability distribution over the graph's observed variables. Algorithms predicated on merely necessary constraints for causal compatib…
The full causal ladder of spacetimes is constructed, and their updated main properties are developed. Old concepts and alternative definitions of each level of the ladder are revisited, with emphasis in minimum hypotheses. The implications of the recently solved ``folk questions on smoothability'', and alternative prop…
Unified tensor model disentangles object appearance factors.
problem Representing hierarchical intrinsic and extrinsic causal factors of object appearance.
method Compositional hierarchical tensor factorization.
result Interpretable object representation robust to occlusion and reduced training data requirements.
TRAM-DAG models bridge interpretability and flexibility in causal modeling.
problem Modeling causal relationships in diverse data types while maintaining interpretability.
method Using transformation models (TRAMs) within structural causal models (SCMs) to handle various data types and maintain interpretability.
result TRAM-DAG models achieve equal or superior performance in causal queries across different levels of the causal hierarchy.
POSCMs extend SCMs for causal modeling with latent contexts.
problem Causal modeling with latent contexts and endogenous mechanisms.
method Kolmogorov-Arnold-Sprecher edge-functional decomposition for explicit parametrization.
result Identifiability of structure and mechanisms under latent context.
Unified multilinear model for causal factor disentanglement.
problem Disentangling causal factors from complex data without direct manipulation.
method Hierarchical block multilinear factorization (M-mode Block SVD) and incremental approach.
result Interpretable object representation robust to occlusion and reduced training data.
The paper proposes a method to transfer knowledge across different settings using causal theory.
problem Learning transfer across similar but different settings.
method Bayesian perspective of causal theory induction, integrating instance-level associative learning and abstract-level structural causal knowledge.
result The proposed model achieved transfer behavior across trials and learning situations, unlike RL algorithms.
Recent interest in the external validity of prediction models (i.e., the problem of different train and test distributions, known as dataset shift) has produced many methods for finding predictive distributions that are invariant to dataset shifts and can be used for prediction in new, unseen environments. However, the…
Paper simplifies complex causal identifiability problems with exogenous isomorphism.
problem Achieving consistent answers to causal questions in Structural Causal Models.
method Introducing exogenous isomorphism and proposing ∼EI-identifiability. result Unified and generalized theories for practical applications in counterfactual reasoning.
Unified approach to causal representation learning using invariance principles.
problem Identifying latent causal variables from high-dimensional observations.
method Guiding identification of causal variables with invariance principles rather than causal hierarchies.
result Unified method that mixes causal and non-causal assumptions improves treatment effect estimation.
Recently ({\em Class. Quant. Grav.} {\bf 20} 625-664) the concept of {\em causal mapping} between spacetimes --essentially equivalent in this context to the {\em chronological map} one in abstract chronological spaces--, and the related notion of {\em causal structure}, have been introduced as new tools to study causal…
Causal deep learning tackles causal inference using tensor factor analysis.
problem Addressing causal questions in data using neural networks.
method Tensor factor analysis and neural network architectures (causal capsules, tensor transformer, multilinear projection algorithm).
result Derives deep neural networks for causal inference with tensor factor analysis.
Study evaluates large language models' ability to understand probabilistic real-world distributions.
problem Understanding how LLMs grasp probabilistic knowledge of real-world distributions.
method Developed a benchmark to test LLMs' ability to learn and represent empirical distributions across various domains.
result LLMs perform poorly in understanding real-world statistics and do not naturally internalize these distributions.
Eight different refinements of trapped surfaces are proposed, of three basic types, each intended as potential stability conditions. Minimal trapped surfaces are strictly minimal with respect to the dual expansion vector. Outer trapped surfaces have positivity of a certain curvature, related to surface gravity. Increas…
Modeling uncertainty in deep neural networks, despite recent important advances, is still an open problem. Bayesian neural networks are a powerful solution, where the prior over network weights is a design choice, often a normal distribution or other distribution encouraging sparsity. However, this prior is agnostic to…
Generates counterfactuals in target domain from source domain observations.
problem Cross-domain learning with domain shifts and lack of parallel datasets.
method Unsupervised, Neural Causal Models, Joint Causal Graphs, Effect-Intrinsic vs Domain-Intrinsic Variables.
result Framework generates counterfactuals that closely match ground truth.
Study reveals which startup valuation factors are most critical.
problem Understanding the complex factors influencing startup valuations.
method Hierarchical prediction models using decision trees and random forests.
result Identifies which factors most significantly impact startup valuations.
Constructs integrable hierarchies for generalized Frobenius manifolds with non-flat unity.
problem Integrable hierarchies for generalized Frobenius manifolds with non-flat unity.
method Constructs a bihamiltonian integrable hierarchy of hydrodynamic type.
result Integrable hierarchy possesses Virasoro symmetries and a tau structure.
Study identifies pitfalls in assessing hierarchies for multi-class classification.
problem Lack of understanding in selecting hierarchies for multi-class classification.
method Analyzed and compared popular approaches to extracting hierarchies.
result Hierarchy quality becomes irrelevant when using powerful classifiers.
Super tau-covers extend bihamiltonian hierarchies' symmetries.
problem Extending symmetries of bihamiltonian hierarchies.
method Constructing super tau-covers for bihamiltonian integrable hierarchies.
result Symmetries of bihamiltonian hierarchies extended to super tau-covers.
Hydrodynamic hierarchy deformed using conservation laws.
problem Deforming a hydrodynamic hierarchy with non-vanishing Nijenhuis torsion.
method Using a chain of conservation laws to deform the hierarchy.
result The resulting hierarchy has non-vanishing Nijenhuis torsion but vanishing Haantjes tensor.
Legendre transformations link related integrable hierarchies.
problem Understanding relationships between integrable hierarchies.
method Legendre-type transformations of generalized Frobenius manifolds.
result Linear reciprocal transformations link related hierarchies.
Twisted U- and twisted U/K-hierarchies are soliton hierarchies introduced by Terng to find higher flows of the generalized sine-Gordon equation. Twisted O(J)×O(J)O(J,J)-hierarchies are among the most important classes of twisted hierarchies. In this paper, interesting first and higher flows of twi…
Derive bihamiltonian structure for rational reduction of 2D-Toda hierarchy
problem Derive bihamiltonian structure for rational reduction of 2D-Toda hierarchy
method Direct computations
result Derive local bihamiltonian structure
We propose a formally completely integrable extension of heat hierarchy based on the space of symmetries isomorphic to the Weyl algebra A1. The extended heat hierarchy will be the basic model for the analysis of the extension of KP hierarchy, and other integrable equations.
Wise's Quasiconvex Hierarchy Theorem classifying hyperbolic virtually compact special groups in terms of quasiconvex hierarchies played an essential role in Agol's proof of the Virtual Haken Conjecture. Answering a question of Wise, we construct a new virtual quasiconvex hierarchy for relatively hyperbolic virtually co…
New hierarchies derived from KP hierarchy using non-formal operators and Yang-Mills action.
problem Formal solutions of KP hierarchy and their non-formal counterparts.
method Developed new hierarchies of non-linear equations on non-formal pseudo-differential operators.
result Expressed one hierarchy as Yang-Mills action minimization.
Symmetry reduction of Painlevé IV to Flaschka-Newell Painlevé II
problem Isomonodromic deformation problem associated with rank-two meromorphic connections
method Symmetry Ψ(−λ)=σ1Ψ(λ)σ1 result Induced isomonodromic dynamics coincides with Flaschka-Newell Painlevé II hierarchy
Scroll structures on solutions of 4D integrable equations are involutive and governed by a dispersionless hierarchy.
problem Characterizing the geometry of solutions to 4D integrable equations.
method Defining rational normal scrolls and showing their involutivity.
result Involutive scroll structures are governed by a dispersionless integrable hierarchy.
Constructs tri-Hamiltonian structure and Frobenius manifold for asymmetric gAL hierarchy
problem Tri-Hamiltonian structure and Frobenius manifold for asymmetric gAL hierarchy
method Local tri-Hamiltonian structure construction and Frobenius manifold construction
result Dispersionless limits of flows belong to Principal Hierarchy
A relation between the Goldstein-Petrich hierarchy for plane curves and the Toda lattice hierarchy is investigated. A representation formula for plane curves is given in terms of a special class of τ-functions of the Toda lattice hierarchy. A representation formula for discretized plane curves is also discussed.
HAKE embeds entities in polar coordinates to model semantic hierarchies in knowledge graphs.
problem Lack of modeling semantic hierarchies in knowledge graph embeddings.
method HAKE embeds entities in a polar coordinate system, where the radial coordinate represents hierarchy levels and the angular coordinate distinguishes entities at the same level.
result HAKE significantly outperforms existing methods on link prediction tasks in knowledge graphs.
New integrable deformations for topological hierarchies from Frobenius manifolds.
problem Integrable deformations of topological hierarchies from Frobenius manifolds.
method Construction of integrable deformations with polynomial tau-structures.
result Conjecture of universal object for Riemann--Hopf hierarchy.
We introduce two families of soliton hierarchies: the twisted hierarchies associated to symmetric spaces. The Lax pairs of these two hierarchies are Laurent polynomials in the spectral variable. Our constructions gives a hierarchy of commuting flows for the generalized sine-Gordon equation (GSGE), which is the Gauss-Co…
Paper investigates methods to improve classification by inducing a hierarchy from flat labels.
problem Improving classification performance on datasets lacking a natural hierarchy.
method The approach involves clustering conditional distributions and using a hierarchical classifier with the induced hierarchy.
result The methods can discover latent hierarchies and improve accuracy in various applications.
We compute the central invariants of the bihamiltonian structures of the constrained KP hierarchies, and show that these integrable hierarchies are topological deformations of their hydrodynamic limits.
We prove that the extended Toda hierarchy of \cite{CDZ} admits nonabelian Lie algebra of infinitesimal symmetries isomorphic to the half of the Virasoro algebra. The generators Lm, m≥−1 of the Lie algebra act by linear differential operators onto the tau function of the hierarchy. We also prove that the tau fu…
Paper addresses limitations of traditional hierarchical clustering methods.
problem Traditional hierarchical clustering methods face limitations in binary trees and ultrametrics.
method Introduces the notion of a valid hierarchy and a two-step algorithm to construct a binary tree and prune it to enforce validity.
result Proposes a method to recover the finest valid hierarchy, which is not constrained to binary structures.
We present the Lax pair formalism for certain extension of the continuous limit of the classical Toda lattice hierarchy, provide a well defined notion of tau function for its solutions, and give an explicit formulation of the relationship between the CP1 topological sigma model and the extended Toda hierarchy. We al…
New diffiety theory leads to a well-posed KP hierarchy.
problem Formalizing diffieties for better hierarchy analysis.
method Definition of diffiety based on Frolicher structures.
result Formation of a well-posed Kadomtsev-Petviashvili hierarchy.
We propose an extension of the differential system for constant mean curvature (CMC) surfaces in a three dimensional space form to an associated hierarchy of evolution equations by the higher-order commuting symmetries. The infinite sequence of higher-order conservation laws of CMC surfaces admit the corresponding exte…
This is the third in a series of papers attempting to describe a uniform geometric framework in which many integrable systems can be placed. A soliton hierarchy can be constructed from a splitting of an infinite dimensional group L as positive and negative subgroups L_+, L_- and a commuting sequence in the Lie algebr…
Investigate the evolving structure of cryptocurrency interactions using high-frequency returns.
problem Evolution of cryptocurrency interactions
method Construct directed and weighted networks from Granger causal relationships between cryptocurrency log-returns.
result Normalized returns exhibit heavy-tailed distributions.
Study bihamiltonian structures and Frobenius manifolds for specific Toda hierarchies.
problem Local bihamiltonian structures and Frobenius manifolds for asymmetric rational reductions of 2D-Toda hierarchy.
method Construct three-dimensional generalized Frobenius manifold, relate to other hierarchies via transformations.
result Explicit relation between RR2T and bi-graded Toda and constrained KP hierarchies.
We observe that the modular class of a Poisson-Nijhenhuis manifold has a canonical representative and that, under a cohomological assumption, this vector field is bi-hamiltonian. In many examples the associated hierarchy of flows reproduces classical integrable hierarchies.