Given a matched pair of Lie groups, we show that the tangent bundle of the matched pair group is isomorphic to the matched pair of the tangent groups. We thus obtain the Euler-Lagrange equations on the trivialized matched pair of tangent groups, as well as the Euler-Poincaré equations on the matched pair of Lie algebra…
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.
168,657 papers · 148 categories
Trend · papers per month
48 results for “matched pair”
We introduce the notion of matched pairs of Courant algebroids and give several examples arising naturally from complex manifolds, holomorphic Courant algebroids, and certain regular Courant algebroids. We consider the matched sum of two Dirac subbundles, one in each of two Courant algebroids forming a matched pair.
Analysis of Vlasov plasma dynamics using matched pair Lie-Poisson formulation.
problem Understanding the dynamics of Vlasov plasma and its kinetic moments.
method Hamiltonian (Lie-Poisson) analysis and matched pair decomposition.
result Observation of mutual interactions between subdynamics in Vlasov plasma.
It is shown that the cotangent bundle of a matched pair Lie group is itself a matched pair Lie group. The trivialization of the cotangent bundle of a matched pair Lie group are presented. On the trivialized space, the canonical symplectic two-form and canonical Poisson bracket are explicitly written. Various symplectic…
A novel graphical matching approach improves pairs trading by reducing portfolio variance and risk-adjusted returns.
problem Common pairs trading methods lead to high portfolio variance and low risk-adjusted returns due to focusing on highly cointegrated assets.
method Model all assets and their cointegration levels with a weighted graph. Select pairs as a maximum weighted matching to ensure no shared assets and lower portfolio variance.
result The matching-based strategy shows a significant improvement in risk-adjusted performance, with a gross Sharpe ratio of 1.23.
The pair-matching problem appears in many applications where one wants to discover good matches between pairs of entities or individuals. Formally, the set of individuals is represented by the nodes of a graph where the edges, unobserved at first, represent the good matches. The algorithm queries pairs of nodes and obs…
FSBM improves matching efficiency with minimal supervision.
problem Scalability vs. minimal supervision in matching frameworks.
method FSBM uses a small portion of pre-aligned pairs as state feedback to guide non-coupled samples.
result FSBM accelerates training and enhances generalization.
Increasingly many real world tasks involve data in multiple modalities or views. This has motivated the development of many effective algorithms for learning a common latent space to relate multiple domains. However, most existing cross-view learning algorithms assume access to paired data for training. Their applicabi…
We introduce Courant algebroids, providing definitions, some historical notes, and some elementary properties. Next, we summarize basic properties of graded manifolds. Then, drawing on the work of Roytenberg and others, we introduce the graded or supergraded language demonstrating a cochain complex / cohomology for (ge…
New MMD estimators detect differences in missing paired data.
problem Handling missing data in matched pairs with complex distributions.
method Maximum mean discrepancy (MMD) estimators for complex data with missing values.
result Valid and consistent estimators detect differences in data distributions.
Matching two different sets of items, called heterogeneous set-to-set matching problem, has recently received attention as a promising problem. The difficulties are to extract features to match a correct pair of different sets and also preserve two types of exchangeability required for set-to-set matching: the pair of …
SIGMA model improves graph matching across various applications.
problem Graph matching problem in different domains.
method Stochastic Iterative Graph Matching (SIGMA) model with multi-step refinement and dummy nodes.
result SIGMA produces significantly improved graph matching results compared to state-of-the-art models.
For every Lie pair of algebroids we construct a dg-manifold structure on the -graded manifold such that the inclusion and the projection are morphisms of dg-manifolds. The vertical tangent bundle then inherit…
Machine learning improves invoice matching speed and accuracy.
problem Efficiently matching similar invoices from various businesses and organizations.
method Combining machine learning with string similarity functions on invoice datasets.
result Neural network and boosted decision tree outperformed existing solutions.
LSDM uses unpaired data to match latent space distributions for generative modeling.
problem Generating high-quality images with limited paired data.
method Two-stage approach: latent space learning from paired and unpaired data, followed by joint distribution matching.
result LSDM enhances geometric fidelity in generated outputs and provides theoretical insights into LDMs.
We consider partial matchings, which are finite graphs consisting of edges and vertices of degree zero or one. We consider transformations between two states of partial matchings. We introduce a method of presenting a transformation between partial matchings. We introduce the notion of the lattice presentation of a par…
A statistical algorithm for categorizing different types of matches and fraud in image databases is presented. The approach is based on a generative model of a graph representing images and connections between pairs of identities, trained using properties of a matching algorithm between images.
We address the problem of image translation between domains or modalities for which no direct paired data is available (i.e. zero-pair translation). We propose mix and match networks, based on multiple encoders and decoders aligned in such a way that other encoder-decoder pairs can be composed at test time to perform u…
Augmented bridge matching preserves coupling information between distributions.
problem Preserving the original empirical pairing in flow and bridge matching processes.
method Augmenting the velocity field with initial sample point information.
result Simple modification recovers coupling information without losing Markovian property.
Li-Bland's correspondence between linear Courant algebroids and Lie -algebroids is explained and shown to be an equivalence of categories. Decomposed VB-Courant algebroids are shown to be equivalent to split Lie 2-algebroids in the same manner as decomposed VB-algebroids are equivalent to 2-term representations up t…
Factorizable Lie bialgebras, quadratic Rota-Baxter Lie algebras and Rota-Baxter Lie bialgebrasmath-ph
The paper connects Lie bialgebras, Rota-Baxter Lie algebras, and their properties.
problem Exploring connections between Lie bialgebras and Rota-Baxter Lie algebras.
method Introducing quadratic Rota-Baxter Lie algebras, matched pairs, bialgebras, and Manin triples.
result Established a correspondence between factorizable Lie bialgebras and quadratic Rota-Baxter Lie algebras.
Optimizes matching in weighted graphs with semi-bandit sampling.
problem Finding optimal pairings in weighted graphs with sequential sampling.
method Leverages rank-1 assumption on adjacency matrix to reduce sample complexity and regret.
result Achieves linear dependency in the number of vertices for sample complexity and regret.
We show that double Lie algebroids, together with a chosen linear splitting, are equivalent to pairs of 2-term representations up to homotopy satisfying compatibility conditions which extend the notion of matched pair of Lie algebroids. We discuss in detail the tangent of a Lie algebroid.
User identity linkage is a task of recognizing the identities of the same user across different social networks (SN). Previous works tackle this problem via estimating the pairwise similarity between identities from different SN, predicting the label of identity pairs or selecting the most relevant identity pair based …
Efficiently matches random graphs with inhomogeneous edge probabilities.
problem Matching latent vertex correspondence between two correlated random graphs with inhomogeneous edge probabilities.
method Inspired by Ding et al. (2021), an efficient matching algorithm is developed with conditions on minimal average degree and minimal correlation.
result An efficient matching algorithm is obtained as long as the minimal average degree is at least and the minimal correlation is at least .
We review a method to construct --instantons over compact --manifolds arising as the twisted connected sum of a matching pair of Calabi-Yau -folds with cylindrical end, based on the series of articles [SE15, SEW15, JMPSE17, MNSE17] by the author and others. The construction is based on gluing $\r…
Paper tackles novelty detection in text classification.
problem Traditional text classification assumes known classes in testing, but often encounters unexpected instances.
method Converts problem to pair-wise matching, uses CNN with embedding matrices.
result Proposed method outperforms state-of-the-art baselines.
We study how a gluing construction, which produces compact manifolds with holonomy G_2 from matching pairs of asymptotically cylindrical G_2-manifolds, behaves under deformations. We show that the gluing construction defines a smooth map from a moduli space of gluing data to the moduli space of torsion-free G_2-structu…
This paper explores combinatorial optimization for problems of max-weight graph matching on multi-partite graphs, which arise in integrating multiple data sources. Entity resolution-the data integration problem of performing noisy joins on structured data-typically proceeds by first hashing each record into zero or mor…
This paper addresses the challenging problem of retrieval and matching of graph structured objects, and makes two key contributions. First, we demonstrate how Graph Neural Networks (GNN), which have emerged as an effective model for various supervised prediction problems defined on structured data, can be trained to pr…
Method finds multiple noisy graph templates in large graphs.
problem Finding multiple graph templates in noisy large graphs.
method Iteratively penalizes node-pair similarity matrix in matched filter algorithm.
result Method can sequentially discover multiple templates under mild model conditions.
Robust Random Graph Matching in Dense Graphs via an Approximate Message Passing Type Algorithmstat.ML
Paper tackles robust graph matching in dense graphs with AMP type algorithm.
problem Matching recovery between correlated Gaussian Wigner matrices with adversarial perturbations.
method Approximate Message Passing (AMP) type iterative algorithm with time-dependent matrix multiplication.
result Algorithm succeeds in polynomial time for non-vanishing correlation and small perturbations.
Framework for precise recall control in spatial conflation tasks.
problem Precise recall control in large-scale spatial conflation tasks to avoid downstream analytics failures and excessive manual review.
method End-to-end framework using equigrid bounding-box filter, CSR representation, neural ranker, and inverse-variance weighted ensemble of threshold estimators.
result Achieves exact recall with sub-percent variance over tens of millions of geometry pairs, runs on a single TPU v3 core.
Improves retrieval accuracy for hierarchical documents, especially for distant matches.
problem Limited expressive power of dual encoder models in hierarchical retrieval.
method Proves feasibility of DEs for HR, introduces pretrain-finetune recipe to improve long-distance retrieval.
result Pretrain-finetune boosts recall on long-distance pairs from 19% to 76%.
Learning disentangled representations that correspond to factors of variation in real-world data is critical to interpretable and human-controllable machine learning. Recently, concerns about the viability of learning disentangled representations in a purely unsupervised manner has spurred a shift toward the incorporat…
Comparing and aligning large datasets is a pervasive problem occurring across many different knowledge domains. We introduce and study MREC, a recursive decomposition algorithm for computing matchings between data sets. The basic idea is to partition the data, match the partitions, and then recursively match the points…
A tacit assumption in linear regression is that (response, predictor)-pairs correspond to identical observational units. A series of recent works have studied scenarios in which this assumption is violated under terms such as ``Unlabeled Sensing and ``Regression with Unknown Permutation''. In this paper, we study the s…
DIAL learns embeddings to maximize recall and accuracy for entity resolution.
problem Low resource settings for entity resolution with large Cartesian product search space.
method DIAL uses an Index-By-Committee framework with pre-trained transformer language models to jointly learn embeddings for recall and accuracy.
result DIAL achieves high precision, recall, and efficiency on benchmark datasets.
Joint matching over a collection of objects aims at aggregating information from a large collection of similar instances (e.g. images, graphs, shapes) to improve maps between pairs of them. Given multiple matches computed between a few object pairs in isolation, the goal is to recover an entire collection of maps that …
In the second of a pair of papers, we complete the construction of Seiberg-Witten-like invariants for smooth four-manifolds equipped with broken fibrations, prove an index formula, and compute some examples.
A new method for flow matching reduces computational costs and improves performance.
problem Efficiently matching flow models to target data distributions.
method Semidiscrete formulation of optimal transport (SD-OT) using SGD and maximum inner product search (MIPS).
result Semidiscrete FM (SD-FM) outperforms batch-OT and traditional flow matching methods.
Unpaired deep learning reconstructs MRI images from accelerated data.
problem Difficulty in acquiring matched fully sampled k-space data for supervised deep learning.
method Optimal transport driven cycleGAN architecture.
result Reconstructs high resolution MR images from accelerated k-space data.
We study the local structure of Lie bialgebroids at regular points. In particular, we classify all transitive Lie bialgebroids. In special cases, they are connected to classical dynamical -matrices and matched pairs induced by Poisson group actions
We consider the connected-sum method of constructing compact Riemannian 7-manifolds with holonomy G_2 developed in math.DG/0012189. The method requires pairs of projective complex threefolds endowed with anticanonical K3 divisors, the latter `matching' via a certain non-holomorphic map. Suitable examples of threefolds …
The strength of association between a pair of data vectors is represented by a nonnegative real number, called matching weight. For dimensionality reduction, we consider a linear transformation of data vectors, and define a matching error as the weighted sum of squared distances between transformed vectors with respect…
Improved graph matching algorithm robust to noise.
problem Finding a bijection between vertex sets of two graphs.
method Uses multistage signature vectors to match vertices.
result Recover matching exactly with high probability for .
Efficiently matches subgraphs in noisy data without node labels.
problem Subgraph isomorphism in noisy, real-valued graphs.
method Two-step approach: extract topology, then expand matches.
result Realistically sub-linear computational efficiency, robustness to noise.
New algorithm achieves almost exact graph matching in almost quadratic time.
problem Graph matching under correlated Erdős-Rényi models.
method Rank-based graph matching using local tree correlation tests.
result Achieves almost exact recovery in almost quadratic time complexity.