Bayesian method clusters vectorial and network data together.
problem Clustering vectorial and network data simultaneously.
method General probabilistic model with Bayesian inference via MCMC.
result New method outperforms traditional alternatives.
On-device research index
arXiv research
A locally-built, LLM-digested index of recent arXiv papers in quant finance, geometry/topology, and statistical ML — keyword search served straight from SQLite on this machine.
169,341 papers · 148 categories
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48 results for “Vectorial Data”
A new embedding method extracts dataset-scale metric distribution into vectorial representation for graph data.
problem Classifying graph-structured data based on overall dataset-scale discrepancies.
method MetricDistribution2vec embedding strategy.
result Significant improvement in supervised prediction tasks on real-world graph datasets.
VEC-SBM detects communities using side information like texts and images.
problem Community detection in social networks with side information.
method Proposes a novel algorithm based on iterative refinement techniques.
result Optimally recovers latent communities with side information.
The vectorial fundamental transformation for the Darboux equations is reduced to the symmetric case. This is combined with the orthogonal reduction of Lame type to obtain those vectorial Ribaucour transformations which preserve the Egoroff reduction. We also show that a permutability property holds for all these transf…
Classifies Riemannian manifolds with specific torsion properties.
problem Classifying Riemannian manifolds with parallel, non-twistorial torsion.
method Classifies complete simply connected Riemannian manifolds with a metric connection having parallel torsion, non-zero vectorial component, and zero twistorial component.
result Classifies complete simply connected Riemannian manifolds with the specified torsion properties.
Paper reinterprets marginal productivity theory using vectorial products, challenging traditional ethical interpretations.
problem Challenges traditional ethical interpretations of marginal productivity theory.
method Formulates marginal productivity theory using vectorial marginal products, contrasting with traditional scalar approach.
result Vectorial marginal products conflict with traditional distributive shares picture of property.
In this paper we develop the vectorial Ribaucour transformation for Euclidean submanifolds. We prove a general decomposition theorem showing that under {appropriate} conditions the composition of two or more vectorial Ribaucour transformations is again a vectorial Ribaucour transformation. An immediate consequence of t…
Overview of structured data representation methods.
problem Structured data lacks vectorial form, complicating machine learning.
method Various approaches including kernel, distance, neural networks, and graph convolutional networks.
result New approaches like metric learning and recurrent decoder networks have emerged.
The study explores connections with vectorial torsion on manifolds, linking curvature and spinor fields.
problem Properties and relationships of metric connections with vectorial torsion on semi-Riemannian manifolds.
method Analyzes curvature, spinor fields, and connections on manifolds with vectorial torsion.
result Connections with vectorial torsion on warped products match given curvature properties, and existence of -parallel spinor fields implies specific curvature conditions.
Asymptotically almost periodic solutions to parabolic equations on the real hyperbolic manifoldmath.AP
Study asymptotically almost periodic solutions on real hyperbolic manifolds.
problem Existence and asymptotic behavior of solutions to parabolic equations.
method Dispersion and smoothing estimates, fixed point argument.
result Existence and uniqueness of asymptotically almost periodic solutions.
A new framework for structured prediction on non-vectorial spaces.
problem Structured prediction on non-vectorial output spaces.
method Defining a suitable geometry for implicit loss functions.
result Efficient algorithmic framework with sharp statistical analysis.
The present note deals with the dynamics of metric connections with vectorial torsion, as already described by E. Cartan in 1925. We show that the geodesics of metric connections with vectorial torsion defined by gradient vector fields coincide with the Levi-Civita geodesics of a conformally equivalent metric. By pullb…
Proposes a new method for optimizing functions over non-vectorial domains using similarity scores.
problem Optimizing functions over non-vectorial domains with only similarity scores defined.
method Analogical-based Bayesian Optimization, which generalizes Gaussian Processes to handle similarity-based optimization.
result Demonstrates efficient optimization over high-dimensional data using batch query strategies.
Enhances motion data analysis using metric learning for DTW.
problem Improving classification accuracy in motion capture data analysis.
method Extends LMNN principle to DTW, treating component-wise dissimilarity values as features.
result Significantly enhances classification accuracy in motion capture data analysis.
TES-AE uses tree grammars to speed up autoencoding for tree data.
problem Challenges in autoencoding tree data due to its non-vectorial and discrete nature.
method TES-AE combines reservoir computing with tree grammars for faster training.
result TES-AE outperforms D-VAE in speed and accuracy for tree data.
Sharp inequality for -harmonic maps with new optimal constant.
problem Deriving the sharp vectorial Kato inequality for -harmonic mappings.
method Analyzing the inequality for -harmonic mappings and comparing with scalar valued cases.
result Established the optimal constant for -harmonic maps and enhanced the range of values for regularity.
On the basis of Liouville theorem the generalization of the Nambu mechanics is considered. For three-dimensional phase space the concept of vector hamiltonian and vector lagrangian is entered.
This work proposes a dissimilarity projection method for tractography data.
problem Tractography data cannot be directly represented in a vectorial space.
method Adopting dissimilarity representation with prototype selection and scalable approximation.
result Characterizes the use of dissimilarity projection on tractography data.
On the basis of Liouville theorem the generalization of the Nambu mechanics is considered. Is shown, that Poisson manifolds of n-dimensional multi-symplectic phase space have inducting by (n-1) Hamiltonian k-vector fields, each of which requires of (k)-hamiltonians.
We study geometric structures of -type in the sense of A. Gray on a Riemannian manifold. If the structure group $\mathrm{G} \subset \SO(n)$ preserves a spinor or a non-degenerate differential form, its intrinsic torsion is a closed 1-form (Proposition \ref{dGamma} and Theorem \ref{Fixspinor}). Using …
Study global solutions for Boussinesq systems on curved manifolds.
problem Global existence and uniqueness of solutions to Boussinesq systems on non-compact Riemannian manifolds with gravitational fields.
method Used dispersive and smoothing estimates of a vectorial matrix semigroup to establish global existence and uniqueness of mild solutions for linear systems. Then, applied fixed point arguments to semilinear systems. Proved exponential stability using Gronwall's inequality.
result Established global existence, uniqueness, and exponential stability of mild solutions to the Boussinesq systems on non-compact Riemannian manifolds with gravitational fields.
Study compactifies representations space of hyperbolic surfaces.
problem Compactify the space of maximal representations of hyperbolic surfaces.
method Vectorial length compactification, geometric interpretation, dual tree-graded space.
result Identify boundary with sphere of measured geodesic laminations.
New connections found with specific torsion properties.
problem Understanding metric connections with specific torsion properties.
method Described Lorentzian manifolds with metric connections having parallel, skew-symmetric torsion.
result Found new Lorentzian manifolds with metric connections having parallel, skew-symmetric torsion.
Survey on Allen-Cahn equations and systems, focusing on multiplicity results and geometric interpretation.
problem Multiplicity results for Allen-Cahn equations and systems in singular perturbation regime.
method Photography method, variational-topological approach based on localized approximate solutions and barycenter maps.
result Encoding of topology into multiplicity results through variational-topological approach.
Study of online learning for structured prediction problems.
problem Structured prediction in online learning settings.
method Developed algorithms for structured prediction in online learning, generalizing from supervised learning.
result Achieved the same excess risk upper bound for non-i.i.d. data and bounded the stochastic regret for non-stationary data.
The paper proposes using feature side-information to improve model prediction performance.
problem Improving model prediction performance using feature side-information.
method A framework that incorporates feature side-information during the learning process of general model families, controlling model structures to reflect feature similarities.
result Significant predictive performance gains over baselines using feature side-information.
Enhances sparse coding for motion data classification.
problem Efficiently decompose motion data into sparse combinations.
method Combines DTW and kernelized sparse coding with non-negative constraints.
result Effective in motion capture data interpretation and discrimination.
The B-quadrilateral lattice (BQL) provides geometric interpretation of Miwa's discrete BKP equation within the quadrialteral lattice (QL) theory. After discussing the projective-geometric properties of the lattice we give the algebro-geometric construction of the BQL ephasizing the role of Prym varieties and the corres…
New algorithm optimizes multi-objective outcomes in uncertain environments.
problem Optimizing global concave rewards in online Markov decision processes with multiple actions.
method No-regret algorithm based on online convex optimization and UCRL2, with a gradient threshold procedure.
result Non-stationary policy diversifies outcomes to optimize the global concave reward.
Adversarial edit attacks improve machine learning model security for tree data.
problem Improving security of machine learning models for tree-structured data.
method Extends adversarial attacks to tree-structured data using tree edit distance and black-box queries.
result Many tree classifiers can be effectively attacked, demonstrating the vulnerability of these models.
New spinor fields reveal local or global geometric properties of manifolds.
problem Characterizing spinor fields on manifolds.
method Analyzing generalized imaginary Spin^c-Killing spinors and their associated vector fields.
result Local or global geometric descriptions of manifolds based on spinor fields.
The paper classifies second-order superintegrable systems with torsion and semi-degeneracy.
problem Classifying second-order superintegrable systems with torsion and semi-degeneracy.
method Information-geometric structure and geometric conditions for non-degeneracy.
result A -parameter potential is non-degenerate if a certain trace-free tensor field vanishes.
Proves existence of multiple solutions to a multiphasic equation on manifolds.
problem Existence of multiple solutions to a multiphasic equation with a small volume constraint.
method Lusternik-Schnirelmann and infinite-dimensional Morse theories, combined with isoperimetric theory and transversality theorem.
result Lower bound for the number of solutions depending on topological invariants.
We study 5-dimensional Riemannian manifolds that admit an almost contact metric structure. We classify these structures by their intrinsic torsion and review the literature in terms of this scheme. Moreover, we determine necessary and sufficient conditions for the existence of metric connections with vectorial, totally…
We study the irreducible decomposition under Sp(2n, R) of the space of torsion tensors of almost symplectic connections. Then a description of all symplectic quadratic invariants of torsion-like tensors is given. When applied to a manifold M with an almost symplectic structure, these instruments give preliminary insigh…
New framework learns blood sample MTS representations with missing data.
problem Missing data in clinical time series.
method Combines autoencoder with TCK kernel for missing data.
result Improved classification of blood samples with missing data.
This paper presents a kernel-based discriminative learning framework on probability measures. Rather than relying on large collections of vectorial training examples, our framework learns using a collection of probability distributions that have been constructed to meaningfully represent training data. By representing …
New transformation preserves constant curvature submanifolds in space forms.
problem Constructing and understanding submanifolds of constant curvature.
method Vectorial Ribaucour transformation reduction and decomposition theorems.
result Derives Bianchi-cube theorem for constructing families of submanifolds.
In this article we present a continuous time model for natural gas and crude oil future prices. Its main feature is the possibility to link both energies in the long term and in the short term. For each energy, the future returns are represented as the sum of volatility functions driven by motions. Under the risk neutr…
New algorithm clusters sparse, high-dimensional texts efficiently.
problem Clustering very short texts with high dimensions and sparsity.
method Linear algebra-based subspace clustering algorithm.
result Algorithm performs competitively on text categorization tasks.
We propose a non-parametric regression methodology, Random Forests on Distance Matrices (RFDM), for detecting genetic variants associated to quantitative phenotypes representing the human brain's structure or function, and obtained using neuroimaging techniques. RFDM, which is an extension of decision forests, requires…
TTPUDR uses tensor-train decomposition for high-dimensional data analysis.
problem High-dimensional data analysis challenges.
method Tensor-train decomposition and manifold optimization.
result TTPUDR significantly outperforms past methods and state-of-the-art methods.
In this short note we study flat metric connections with antisymmetric torsion . The result has been originally discovered by Cartan/Schouten in 1926 and we provide a new proof not depending on the classification of symmetric spaces. Any space of that type splits and the irreducible factors are compact simple…
Modern datasets are becoming heterogeneous. To this end, we present in this paper Mixed-Variate Restricted Boltzmann Machines for simultaneously modelling variables of multiple types and modalities, including binary and continuous responses, categorical options, multicategorical choices, ordinal assessment and category…
This paper reviews the functional aspects of statistical learning theory. The main point under consideration is the nature of the hypothesis set when no prior information is available but data. Within this framework we first discuss about the hypothesis set: it is a vectorial space, it is a set of pointwise defined fun…
A new method reduces high-dimensional parameter spaces for faster numerical tasks.
problem Efficiently reducing high-dimensional parameter spaces for numerical tasks.
method Local Active Subspaces (LAS) combining active subspaces with clustering techniques.
result Significant speed-up in numerical tasks through efficient dimension reduction.
In this paper, we characterize the dynamic of every abelian subgroups of GL(, ), or . We show that there exists a -invariant, dense open set in saturated by minimal orbits with a union of at most …
New scalable methods for learning with indefinite kernels.
problem Learning with indefinite kernels, especially for structured data.
method Derivation of Nyström method, efficient eigendecomposition, scalable learning methods.
result Principled and theoretically well-founded means for large-scale learning problems.