Differentially private data structures for estimating distances between strings.
problem Estimating distances between query strings and database strings while ensuring privacy.
method Proposes differentially private data structures for Hamming and edit distances using randomized response technique.
result Efficient data structures that provide accurate distance estimates with strong privacy guarantees.
A new distance combines features and structure of objects.
problem Comparing structured machine learning objects.
method Fused Gromov-Wasserstein distance combining features and structure.
result Mathematical framework and properties established.
A new metric compares true and learned causal graphs considering data and graph structure.
problem Comparing true and learned causal graphs accurately.
method Continuous Structural Intervention Distance (CSID) using conditional mean embeddings and maximum mean discrepancy.
result Validated the CSID with synthetic data, showing its effectiveness in comparing causal graphs.
The paper examines convergence of distances in Lipschitz structures on manifolds.
problem Convergence of distances in Lipschitz vector fields and norms on manifolds.
method Analysis of convergence of distances associated to converging structures of Lipschitz vector fields and norms.
result Under mild controllability assumption, distances converge locally uniformly to the limit Carnot-Carathéodory distance.
The moduli space of projective structures on a surface has unusual hermitian structures and no distances.
problem Characterizing distances on the moduli space of complex projective structures.
method Analyzing the canonical complex structure and pseudodistances on the space.
result The moduli space does not carry any distance structure.
New distances for causal graphs improve evaluation of learned structures.
problem Difficulty in evaluating graphs learned by causal discovery algorithms.
method Developed a framework for causal distances, including new reachability algorithms.
result Improved distances are faster and more scalable than existing methods.
The paper identifies clusters in the World Trade Network using communicability distances.
problem Identifying clusters in the World Trade Network.
method Uses Estrada and vibrational communicability distances to find clusters maximizing a modularity function.
result Identifies specific distance thresholds that maximize modularity, revealing unique relationships between countries.
Generates valid Euclidean distance matrices for molecular structures.
problem Generating point clouds in arbitrary rotations and translations is challenging.
method Developed a neural network architecture that produces valid Euclidean distance matrices invariant to rotations and translations.
result The architecture can generate molecular structures in a one-shot fashion by producing Euclidean distance matrices with a three-dimensional embedding.
New network distance based on Laplacian flow captures structure.
problem Measuring similarity between network objects.
method Introducing Laplacian flow to define a new diffusion distance.
result Demonstrated utility and advantage over existing distances.
Predicting RNA base distances using a large language model.
problem Accurately predicting RNA structural information, especially distance maps.
method Using a large pretrained RNA language model coupled with a transformer.
result The model can accurately infer RNA base distances from sequence data.
Revisits Isomap, showing it constructs Euclidean representations of geodesic structure.
problem Nonlinear dimension reduction of manifold data.
method Revisits Isomap's rationale, clarifying its approach to constructing Euclidean representations of geodesic structure.
result Convexity is not required for shortest path distances to converge to Riemannian distances.
Improved image ranking model using ordinal distance metric learning and multidimensional scaling.
problem Ranking images based on known ranked images.
method Proposes an improved linear ordinal distance metric learning approach using multidimensional scaling.
result Demonstrates improved ranking performance and speed over the linear distance metric learning model.
Paper explains distance-based classifiers using neural network structures.
problem Making distance-based classifiers explainable.
method Uncovering latent neural network structures in distance-based classifiers.
result Novel explanation approach outperforms baselines.
Study sequences of static spacetimes using null distance convergence.
problem How to define convergence for sequences of spacetimes.
method Define null distance metric space structure compatible with Lorentzian structure.
result Prove VADB theorem for sequences of static spacetimes with null distance.
kdiff measures distances for time series and structured data.
problem Estimating distances between time series and structured data.
method kdiff uses non-linear kernel distances based on matching overlapping distributions.
result kdiff is more robust to noise and partial occlusions.
Study on surfaces of genus g≥1 in 3D contact sub-Riemannian manifolds, proving finiteness or infiniteness of induced distance.
problem Determining the finiteness of the induced distance on surfaces of genus g≥1 in 3D contact sub-Riemannian manifolds.
method Analyzing the structural stability of the finiteness/not-finiteness of the induced distance on closed surfaces of genus g≥1.
result Closed surfaces of genus g≥1 can be embedded in such a way that the induced distance is either always finite or always infinite.
Causal inference relies on the structure of a graph, often a directed acyclic graph (DAG). Different graphs may result in different causal inference statements and different intervention distributions. To quantify such differences, we propose a (pre-) distance between DAGs, the structural intervention distance (SID). T…
Enhances graph comparison by incorporating edge features using Fused Gromov-Wasserstein distance.
problem Graph distances overlook edge attributes, limiting their effectiveness.
method Introduced Fused Gromov-Wasserstein distance for graph comparison with edge features. Proposed algorithms for distance and barycenter computation.
result Empirically validated the effectiveness of the novel distance in graph learning tasks.
Introduces Wasserstein Transform for updating distance structures.
problem Enhancing features and denoising data sets.
method Representing data points as probability measures and updating distances via Wasserstein distance.
result GT is computationally cheaper and has a closed-form solution for ℓ2-Wasserstein distance. Model tracks structural changes in Brownian particle configurations on a sphere.
problem Tracking structural changes in Brownian particle configurations on a sphere.
method Introduces Frustrated Distance Matrix (FDM) model for dynamic distance matrices on S^2.
result Preserves static BBS template with dynamics as redistributed spectral mass.
The aim of this article is to generalize the notion of the cut locus and to get the structure theorem for it. For this purpose, we first introduce a class of 1-Lipschitz functions, each member of which is called an {\it almost distance function}. Typical examples of an almost distance function are the distance function…
We propose a new class of metrics on sets, vectors, and functions that can be used in various stages of data mining, including exploratory data analysis, learning, and result interpretation. These new distance functions unify and generalize some of the popular metrics, such as the Jaccard and bag distances on sets, Man…
Paper proposes a method to recover point configurations from noisy distance data.
problem Recovering point configurations from noisy distance data.
method Robust Euclidean Distance Geometry via Dual Basis (RoDEoDB) algorithm.
result Exact recovery guarantees for point configuration and Gram matrix under mild conditions.
New algorithm trains generative networks using explicit optimal transport distances.
problem Training generative networks with flexible distance metrics.
method Uses an auxiliary neural network to express optimal transport map and trains generative networks with explicit transportation cost functions.
result Allows training with any transportation cost function, including image-centered distances.
Research explores Lorentzian distances on a specific geometric plane.
problem Investigating Lorentzian structures on a 2D geometric plane.
method Analyzes sectional curvature, attainable sets, and Lorentzian length maximizers.
result Describes distance properties and spheres in the context of Lorentzian geometry.
Note on the computational complexity of Gromov-Wasserstein distance.
problem Computational difficulty of Gromov-Wasserstein distance.
method Analysis of the optimization problem structure and providing explicit examples.
result Gromov-Wasserstein distance optimization problem is non-convex quadratic.
New theory connects string theory to swampland distance conjecture.
problem Connecting string theory to swampland distance conjecture.
method Deformations of the heterotic superpotential, treating separately for large fluxes or large distances, integrating out fields to obtain a new field theory.
result New holomorphic theory defined, connects to swampland distance conjecture.
Framework uses Minimax distances for unsupervised feature extraction.
problem Extracting features from unlabeled data.
method Develops a framework for computing Minimax distances and embedding them into a vector space.
result Minimax distances effectively capture underlying patterns and structures in data.
New metric learning approach for tree data reduces computation cost.
problem Efficiently computing distances between ordered labeled trees.
method Introduced pq-grams and a differentiable weighted pq-gram distance, combined with LMNN for optimization.
result Significantly reduces computation time for tree classification problems.
Introduces MSW distances to improve SW metrics.
problem Redundant projections in SW distance.
method Imposes Markov structure on projecting directions.
result MSW distances improve SW metrics.
Kernel measures similarity of nonlinear causal structures in heterogeneous populations.
problem Learning causal structure in populations with diverse underlying structures.
method Distance covariance-based kernel for measuring similarity of causal structures.
result Kernel enables clustering of homogeneous subpopulations for causal structure learning.
DAG-WGAN learns causal structures using Wasserstein distance.
problem Learning causal structures from data with combinatorial challenges.
method Combines Wasserstein distance, auto-encoder, and acyclicity constraint.
result Demonstrates good performance compared to state-of-the-art models.
Wasserstein t-SNE embeds hierarchical datasets considering within-unit distributions.
problem Exploring hierarchical datasets where units are compared based on means of sample distributions.
method Uses Wasserstein distance metric for 2D embeddings of units, approximating Gaussian distributions for efficiency.
result Demonstrates effective embedding of hierarchical datasets, uncovering meaningful structure.
Upper bound for Hausdorff distance between hyperbolic space and its medianization.
problem Calculating the Hausdorff distance between hyperbolic space and its medianization.
method Using de Sitter space to model finite-dimensional hyperbolic space and its medianization, calculating the Hausdorff distance.
result An upper bound for the Hausdorff distance between hyperbolic space and its medianization is calculated.
Study geodesic curvature in Heisenberg group, interpreting it as distance correction.
problem Interpreting geodesic curvature in the Heisenberg group.
method Analyzing smooth horizontal curves in the Heisenberg group, interpreting curvature as distance correction.
result Geodesic curvature in Heisenberg group is the first term in distance expansion.
In the economic literature, geographic distances are considered fundamental factors to be included in any theoretical model whose aim is the quantification of the trade between countries. Quantitatively, distances enter into the so-called gravity models that successfully predict the weight of non-zero trade flows. Howe…
Bayesian nonparametric models improve OOD detection, especially with complex covariance structures.
problem Improving out-of-distribution detection methods, especially in complex scenarios.
method Proposes Bayesian nonparametric mixture models with hierarchical priors that generalize the Mahalanobis distance score.
result Bayesian nonparametric methods outperform existing OOD methods, especially in complex scenarios.
Robustly aligns datasets with partial GW distance to handle contamination.
problem Aligning contaminated datasets using Gromov-Wasserstein distances.
method Proposes a partial GW distance estimator to minimize distortion from outliers.
result The partial GW distance estimator is minimax optimal and near-optimal in finite samples.
Null distance encodes causal structure in spacetimes.
problem Encoding causal structure in Lorentzian manifolds.
method Using null distance defined by Sormani and Vega, and proving causal structure is encoded by null distance.
result Lorentzian isometry between spacetimes with bijective map preserving null distance and cosmological time function.
The paper introduces a statistical test to assess and rank distance measures.
problem Assessing the relative information retained by different distance measures.
method Developed a statistical test to compare distance measures.
result Identifies the most informative distance measure among candidates.
GT is a new method for denoising and enhancing datasets using Gaussian density estimates.
problem Improving latent structures in datasets.
method GT is an iterative method that generates a new distance function by computing the ℓ2-Wasserstein distance between Gaussian density estimates. result GT is stable under perturbations and asymptotically ellipsoidal neighborhoods in the continuous case.
This research improves classification performance by learning a distance metric from balanced data.
problem Data imbalance in learning methods.
method Extracts a low-dimensional manifold, learns local neighborhood relationships, and optimizes distance metric.
result The proposed method outperforms other approaches, especially in imbalanced datasets.
This study investigates self-supervised learning with Wasserstein distance on tree structures.
problem Improving self-supervised learning methods using Wasserstein distance.
method Utilized Tree-Wasserstein distance (TWD) and Jeffrey divergence regularization for training.
result A simple combination of softmax function and Tree-Wasserstein distance outperforms cosine similarity-based methods.
New model improves data augmentation for causal tasks.
problem Optimizing causal models robustly under Wasserstein distances.
method Proposes a new G-Causal Normalizing Flow architecture.
result Empirically outperforms standard generative models.
GRNF embeds graphs into vectors preserving distances.
problem Representing graph data in a vector space while preserving distances.
method Graph Random Neural Features (GRNF) using graph neural networks.
result GRNF preserves graph metric structure and distances.
In high-dimension, low-sample size (HDLSS) data, it is not always true that closeness of two objects reflects a hidden cluster structure. We point out the important fact that it is not the closeness, but the "values" of distance that contain information of the cluster structure in high-dimensional space. Based on this …
Study extends null distance concept to Lorentzian length spaces for spacetime analysis.
problem Understanding spacetime convergence and topology in Lorentzian geometry.
method Extend null distance concept to Lorentzian length spaces, study Gromov-Hausdorff convergence.
result First results on compatibility of null distance with synthetic curvature bounds in warped product Lorentzian length spaces.
This work considers the problem of computing distances between structured objects such as undirected graphs, seen as probability distributions in a specific metric space. We consider a new transportation distance (i.e. that minimizes a total cost of transporting probability masses) that unveils the geometric nature of …