Efficiently simulates jump diffusion bridge paths without discretization error.
problem Efficient simulation of jump diffusion bridge sample paths.
method Develops a mathematical framework to simulate finite-dimensional sample path skeletons.
result Simulates (jump) diffusion bridge sample paths without discretization error.
Tensor-based method simplifies causal skeleton discovery.
problem Discover causal relationships between variables.
method Express associations as tensors to reduce dimensionality.
result Causal skeleton can be determined using pair-wise tensors.
Efficiently learns polytrees with known skeleton in polynomial time and sample complexity.
problem Learning polytrees with known skeleton structure.
method Proposes an efficient algorithm for learning d-polytrees in polynomial time and sample complexity when the skeleton is known. result Establishes finite-sample guarantees for efficient learning of d-polytrees. Paper analyzes Bezier simplex fitting risks and optimal sampling.
problem Analyzing risks and optimal sampling for Bezier simplex fitting.
method Two fitting methods: inductive skeleton and all-at-once.
result Optimal subsample ratio for inductive skeleton fitting reduces risk.
The paper computes special values of combinatorial zeta functions to reveal topological properties of manifolds.
problem Counting geodesic paths in triangulations to infer topological invariants.
method Random walks on higher-dimensional skeletons of triangulations.
result Recovery of Betti numbers and linking numbers of manifolds.
Novel hybrid method for Bayesian network structure learning reduces computational time without sacrificing accuracy.
problem Bayesian network structure learning efficiency and accuracy trade-off.
method Partitioned PC (pPC), p-value adjacency thresholding (PATH), hybrid greedy initialization (HGI). result pHGS achieves significant computational reductions compared to the PC algorithm without sacrificing structure learning accuracy.
A method for learning skeleton of Bayesian networks robust to outliers and corruption.
problem Learning the exact skeleton of discrete Bayesian networks from corrupted data.
method Distributionally robust optimization and regression approach, optimizing worst-case risk over distributions within bounded Wasserstein distance or KL divergence.
result Logarithmic sample complexities for successful structure learning of bounded-degree graphs.
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 …
SPOT improves differentiable causal discovery by estimating skeleton posterior for latent confounders.
problem Scalable and accurate estimation of causal skeletons in the presence of latent confounders.
method SPOT (Skeleton Posterior-guided OpTimization) framework that estimates skeleton posterior and integrates it with differentiable causal discovery.
result SPOT enhances differentiable causal discovery by reducing the search space and improving accuracy.
The study examines the topology of complements of polytopal skeletons.
problem Characterizing topological properties of polytopal complexes and their skeletons.
method Constructing a long exact sequence relating homologies of skeleton complements and links of faces.
result Characterizations of Cohen-Macaulay and Leray complexes, stacked balls, and neighbourly spheres in terms of skeleton complements.
Develops theory of Cartan geometries on skeletons and morphisms induced by extension functors.
problem Describing categories of Cartan geometries with additional morphisms.
method Using extension functors to define new categories of Cartan geometries and studying their properties.
result Shows functors between categories of Cartan geometries with morphisms induced by extension functors and categories of Cartan geometries modeled on skeletons.
Criterion for manifold skeletons embeddability in Euclidean space.
problem Embeddability of manifold skeletons in Euclidean space.
method Criterion based on the complement of a submanifold.
result Embeddability of (q−1)-skeleton of a triangulation of an Sp-bundle over Sq into Rp+q. New method for constructing space-filling curves for self-similar sets.
problem Constructing space-filling curves for self-similar sets.
method Skeleton concept and neighbor graph analysis.
result Connected self-similar sets satisfying the finite type condition always possess skeletons.
Geometric quantization extended to arbitrary connected spaces using path integration.
problem Constructing a Prequantum Groupoid for arbitrary connected parasymplectic spaces.
method Define a Total Group of Periods and a Prequantum Groupoid with connected isotropy.
result The Prequantum Groupoid Tω is isomorphic to the group of symmetries of the Dynamical System. Develops a model for causal discovery in path spaces.
problem Discover causal relationships in path spaces using asymmetric independence.
method Theory linking E-separation in DMGs to conditional independence in SDEs, proving global Markov property, characterizing equivalence classes of graphs.
result Each equivalence class of graphs has a greatest element as a parsimonious representation, which can be identified from data.
New triangulations show harder skeletons for hyperbolic orbifolds.
problem Embedding tricky skeletons of hyperbolic orbifolds in Euclidean space.
method Generalized Gromov-Guth inequality for hyperbolic n-orbifolds, finding nearly optimal geodesic triangulations.
result Triangulations of skeletons become increasingly difficult to embed nicely in Euclidean space.
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…
Optimal interventions identified to learn causal graphs.
problem Learning causal graphs with minimum intervention cost.
method Design optimal intervention sets for given causal graph skeletons.
result Polynomial time algorithms for various causal graph skeletons.
Fixed point sets of certain group actions are contractible.
problem Fixed point sets of group actions on specific types of complexes.
method Analyzing group actions on diagrammatically reducible complexes with fine 1-skeleton.
result Fixed point sets are contractible under certain conditions.
Let T be a triangulation of a Riemann surface. We show that the 1-skeleton of T may be oriented so that there is a global bound on the outdegree of the vertices. Our application is to construct extremal metrics on triangulations formed from T by attaching new edges and vertices and subdividing its faces. Such ref…
Paper tackles non-Markovian control problems with new learning methods.
problem Non-Markovian stochastic control problems with unknown parameters.
method Off-model training and importance sampling for deep neural network approximation.
result Quantitative error bounds for adaptive learning under model uncertainty.
Mapper tool preserves graph structures for better visualization.
problem Graphs can be hard to visualize for large datasets.
method Developed a variation of mapper for weighted, undirected graphs.
result Homology-preserving skeletons enable multi-scale visualization.
Skeleton clustering detects clusters in high-dimensional data without needing prototypes.
problem Detecting clusters in high-dimensional data with irregular shapes.
method Skeleton clustering combines prototype methods, density-based clustering, and hierarchical clustering using surrogate density measures.
result Skeleton clustering reliably detects clusters in multivariate and high-dimensional data.
New theorem shows embedding restrictions for manifold skeletons.
problem Embedding restrictions for triangulated manifolds.
method Proves van Kampen-Flores theorem for manifolds with specific Stiefel-Whitney classes.
result Triangulated manifolds with non-trivial Stiefel-Whitney classes cannot embed into R2d. 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.
Paper presents a copula-based method to efficiently generate correlated sample paths from multi-step time series models.
problem Generating realistic correlation structures in multi-step forecast sample paths is expensive and time-consuming.
method Copula-based approach to generate correlated sample paths in one forward pass.
result Improved sample path quality and significant speedup over autoregressive sampling.
New method certifies risks of LLM outputs, improving accuracy and reliability.
problem Uncertain and incorrect outputs from large language models.
method Information-lift certificates using PAC-Bayes bounds and skeleton design.
result Achieves 77.0% coverage at 2% risk, outperforming baselines.
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…
DACNN improves skeleton-based action recognition and segmentation.
problem Lack of spatial relationships and non-uniform temporal scalings in skeleton-based data.
method Introduces deep-aligned convolutional neural network (DACNN) with new filters trained on local subsequences.
result DACNN achieves competitive performance compared to state-of-the-art models.
The paper tackles entity induction and reference in visual storytelling.
problem Coherence in visual storytelling through proper entity introduction and reference.
method Building an entity skeleton, using an encoder-decoder framework, and proposing a glocal hierarchical attention model.
result The proposed models outperform the baseline in automatic evaluation metrics and human preference.
Proposes a neural network for recognizing 3D skeleton-based interactions.
problem Recognizing two-person interactions from 3D skeleton sequences.
method Uses Gaussian distributions and Riemannian geometry of SPD matrices and matrix groups.
result Achieves competitive results on three benchmarks for 3D human activity understanding.
The paper finds and visualizes unique geometric polyhedra and tori with few vertices.
problem Finding and visualizing geometric polyhedra and tori with specific vertex configurations.
method Using Schlegel diagrams and geometric realization in 3D and 4D space.
result Identifies and visualizes 12 triangulations of the 2-torus and 12 triangulations of the 2D projective plane.
We create a 3-skeleton for a symmetric group's classifying space.
problem Classifying space construction for symmetric groups.
method Combining rewriting systems and combinatorial methods.
result Correctness of the constructed 3-skeleton.
A new graph-based approach for estimating complex data with manifold structure.
problem Regression of large-scale, complex data with underlying geometric structure and noises.
method Constructing a skeleton graph to capture geometric structure, defining metrics, and applying nonparametric regression.
result Statistical guarantees and effectiveness demonstrated through simulations and real data examples.
Paper proposes method for generating paths of stochastic volatility CGMY process for option pricing.
problem Generating accurate sample paths for stochastic volatility models for option pricing.
method Monte-Carlo method for European and American options, least square regression for calibration.
result Calibrated model parameters to S\&P 100 index options market using path-dependent options.
Every cubic graph is a bridge trisection's 1-skeleton for a knotted surface.
problem Understanding cubic graphs and their relation to bridge trisections.
method Proving every Tait-colored cubic graph is a 1-skeleton of a bridge trisection.
result Every Tait-colored cubic graph corresponds to a bridge trisection of a knotted surface.
Convex optimisation solves inverse kinematics problems more reliably.
problem Finding the best parameters of a kinematic skeleton from observed joint locations.
method Convex optimisation using semidefinite programming.
result The proposed method significantly outperforms local optimisation methods.
Quantum genetic algorithm optimizes SVM for efficient human action recognition.
problem Efficiently extracting motion features for human skeleton dynamics.
method Quantum genetic algorithm optimization of SVM with joint angles and variance.
result Proposed approach outperforms conventional SVM by 2.3% accuracy.
Study positive scalar curvature on manifolds with skeleton singularities.
problem Positive scalar curvature on manifolds with skeleton singularities.
method Polyhedral comparison theory and edge metrics.
result Edge singularities do not affect the Yamabe type in all dimensions.
The one-skeleton of a G-manifold M is the set of points p in M where dimGp≥dimG−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…
New algorithms sample from complex path measures using neural networks.
problem Sampling from posterior path measures under a general prior process.
method Combines controlled equilibrium dynamics and optimization in infinite-dimensional probability space.
result The algorithms can be integrated with neural networks for learning target trajectory ensembles.
Finite simplicial complexes dominate certain manifolds with a bounded number of simplices.
problem Understanding the finite domination of manifolds by simplicial complexes.
method Proving that a manifold can be dominated by the n-skeleton of a finite simplicial complex with a bounded number of simplices. result The total number of simplices in the n-skeleton is bounded above by a constant depending only on n and the embolic volume of the manifold. The paper defines conditions for Gaussian process sample path regularity.
problem Lack of understanding of Gaussian process sample path regularity.
method Analyzes covariance kernels to determine sample path regularity.
result Necessary and sufficient conditions for Hölder regularity are provided.
Flow Matching enables robust training of CNFs with various probability paths.
problem Training Continuous Normalizing Flows (CNFs) at large scales.
method Flow Matching (FM) is a simulation-free approach for training CNFs by regressing vector fields of conditional probability paths.
result Flow Matching with diffusion paths yields more robust and stable training compared to diffusion-based methods.
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.
Defines a new category structure on Weinstein manifolds using h-principle.
problem Defining a category structure on Weinstein manifolds.
method Defines a co/sheaf of categories on the skeleton of a Weinstein manifold using h-principle.
result Existence and uniqueness of the co/sheaf of categories up to isotopy.
We present a constructive proof that there exists a decomposition of the 2-skeleton of the k-dimensional cross polytope βk into closed surfaces of genus g≤1, each with a transitive automorphism group given by the vertex transitive Z2k-action on βk. Furthermore we show that for each $k \equiv …
The paper introduces negative controls to evaluate causal discovery algorithms, improving their reliability.
problem Lack of a general guideline for evaluating causal discovery algorithms.
method Derive exact distributional results under random guessing for evaluation metrics and propose a pipeline for using negative controls.
result Evaluation metrics can achieve very favorable values under random guessing, highlighting the need for negative control results.