Landmark-based node embeddings approximate shortest path distances in random graphs.
problem Capturing global graph distances in node representations.
method Landmark-based node embeddings using shortest path distances from a subset of reference nodes (landmarks).
result Random graphs require lower dimensions in landmark-based embeddings compared to worst-case graphs.
We propose fast approximations for the generalized sliced-Wasserstein distance.
problem Efficient approximation of the generalized sliced-Wasserstein distance in high dimensions.
method Deterministic approximations using random projections and concentration of measure results.
result One-dimensional projections of high-dimensional random vectors are approximately Gaussian.
New measures quantify mutual dependence between multiple random vectors.
problem Measuring mutual dependence between multiple random vectors.
method Proposes three measures based on generalized distance covariance.
result Empirical and simplified empirical measures effectively test mutual independence.
There have lately been several suggestions for parametrized distances on a graph that generalize the shortest path distance and the commute time or resistance distance. The need for developing such distances has risen from the observation that the above-mentioned common distances in many situations fail to take into ac…
Topology helps estimate chromatic numbers of random graphs on spheres.
problem Estimating chromatic numbers of random graphs on spheres.
method Topology, specifically connectivity of Lóvasz's neighborhood complex.
result Connectivity bound is useful in dimensions 1 and 2, but generally poor.
Authors disagree with recent findings on random Gaussian weights in DNNs.
problem The relationship between angle and distance shrinkage in DNNs with random Gaussian weights is incorrect.
method Comparison of recent findings with new observations on random Gaussian weights in DNNs.
result Theorem 3 and Figure 5 in the recent paper are not accurate.
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…
New method beats volumetric barrier for manifold recovery.
problem Reconstructing latent geometry from noisy distances.
method Orthogonal Ring Distance Estimation Routine (ORDER).
result Achieves pointwise distance estimation of order n−2/(d+5). A new method approximates the Sliced-Wasserstein distance without random projections.
problem Efficiently approximating the Sliced-Wasserstein distance for machine learning applications.
method Utilizing the concentration of measure phenomenon to develop a deterministic approximation.
result The approximation error goes to zero as the dimension increases, under a weak dependence condition.
Method uses random forest with distance covariance for transfer learning in healthcare.
problem Transfer learning in random forests with sparse differences between source and target.
method Distance covariance-based feature weights in residual random forest.
result Upper bound on mean square error rate for transfer learning in RF.
Improved unsupervised anomaly detection using Random Forest.
problem Enhancing unsupervised anomaly detection accuracy.
method Training Random Forest to distinguish real and synthetic data, then applying transformed distances.
result Significant improvement in anomaly detection accuracy compared to other methods.
This work proposes unsupervised learning by predicting random distances in neural networks.
problem Lack of labelled data in unsupervised learning tasks.
method Train neural networks to predict random distances in a randomly projected space, optimizing for genuine class structures.
result Learned representations outperform state-of-the-art methods in anomaly detection and clustering.
RS-Del provides robustness for sequence classifiers against edit distance attacks.
problem Certifying robustness of discrete sequence classifiers against edit distance attacks.
method Randomized deletion (RS-Del) for discrete sequence classifiers, focusing on edit distance-bounded adversaries.
result Achieved a certified accuracy of 91% at an edit distance radius of 128 bytes on malware detection.
This paper shows how to estimate distances in latent space of random graphs using entropic OT.
problem Estimating distances between groups of nodes in latent space of random graphs.
method Entropic Optimal Transport (OT) with stability results for perturbations of the cost matrix.
result Consistent estimation of entropic OT distances between groups of nodes in latent space.
The study examines lower and upper bounds of Wasserstein distances for affine transformations of random vectors.
problem Understanding Wasserstein distances for affine transformations of random vectors.
method Lower and upper bounds for affine transformations of random vectors in Rn are derived using Bures metric and compositions of affine maps. result Concrete lower bounds and upper bounds for affine transformations are derived and applied to various distributions.
Random Forest proximity distances reveal feature contributions in black-box models.
problem Understanding feature contributions in complex, opaque machine learning models.
method Observing changes in input affecting proximity distances and instance movement in decision space.
result Each feature's independent contribution to model decisions can be calculated and analyzed.
Estimates distances between latent points in random geometric graphs.
problem Estimating distances between latent points in random geometric graphs.
method Spectral estimator of pairwise distances.
result Rate of convergence is the same as nonparametric estimation on the sphere, up to a logarithmic factor.
New Random Forest variants estimate heterogeneous treatment effects using Wasserstein distances.
problem Estimating heterogeneous treatment effects in complex situations.
method Proposes natural variants of Random Forests using Wasserstein distances.
result Natural variants of Random Forests are well-suited for estimating conditional distributions.
Efficient algorithm approximates discrete random variables with minimal Kolmogorov distance.
problem Estimating the probability of missing deadlines in series-parallel schedules.
method An efficient algorithm that computes a random variable with minimal Kolmogorov distance to a given discrete random variable.
result The algorithm efficiently approximates the probability of missing deadlines with minimal Kolmogorov distance.
This paper compares distances between copulas for clustering multivariate time series.
problem Clustering multivariate time series with dependence information.
method Comparison of Fisher-Rao geodesic distance, related divergences, and optimal transport.
result Optimal transport distance outperforms other distances in clustering multivariate time series.
Reconstructs a manifold from noisy intrinsic distances.
problem Reconstructing a smooth Riemannian manifold from intrinsic distances of points.
method Uses random sample points and noisy distances to construct an approximation of the manifold.
result It is possible to construct an approximation of the Riemannian manifold with high probability when N is large enough. New method calculates Ricci curvature from distances between weighted volumes.
problem Calculating Ricci curvature for weighted Riemannian manifolds.
method Asymptotic retrieval of generalized Ricci tensor from scaled metric derivatives of Wasserstein 1-distances.
result Limiting coarse curvature of random graphs converges to generalized Ricci tensor.
We introduce a new framework for comparing parametric network families.
problem Comparing and analyzing data modeled as parameterized families of networks.
method A Gromov-Wasserstein variant of optimal transport for defining distances.
result Established foundational properties and theoretical approximation guarantees for the new distances.
Sharp threshold found for Frechet mean of inhomogeneous graphs.
problem Finding the Frechet mean of inhomogeneous Erdos-Renyi random graphs.
method Thresholding the expected adjacency matrix of the ensemble.
result The Frechet mean graph of inhomogeneous Erdos-Renyi random graphs exhibits a sharp threshold.
Random forest can be adapted for open-set recognition with improved performance.
problem Handling unknown classes in real-world classification tasks.
method Incorporating distance metric learning and distance-based open-set recognition into random forest.
result The proposed method outperforms state-of-the-art open-set recognition methods.
Simplified proof for dimension reduction of polygonal curves.
problem Preserving the continuous Fréchet distance of polygonal curves.
method Sparse oblivious subspace embeddings for generalized dissimilarity measures.
result Generalized dimension reduction technique works for various distance measures.
Abstract: Nonlinear random walk with distributionally robust transition probabilities.
problem Modeling nonlinear random walks with robust transition probabilities.
method Scaling limit and nonlinear semigroup approach.
result Explicit computation of the generator and corresponding PDE.
Random walks on mapping class groups have topological entropy that matches drift.
problem Understanding the topological entropy of random walks on mapping class groups.
method Defined topological entropy and proved it almost surely matches drift.
result Topological entropy of random walks on mapping class groups almost surely equals drift.
Logarithmic growth in random walk projections and shortest curves in mapping tori.
problem Understanding the growth of random walk projections and shortest curves in mapping tori.
method Analyzing random walks and their projections, applying to hyperbolic groups and Out(F_n).
result The shortest geodesic in a mapping torus has length on the order of 1/ log^2(n).
We introduce an universum of the Polish (=complete separable metric) space - the convex cone of distance matrices and study its geometry. It happened that the generic Polish spaces in this sense of this universum is so called Urysohn spaces defined by P.S.Urysohn in 20-th, and generic metric triple (= metric space with…
Bounds on Gaussian approximation for neural networks with novel smoothing techniques.
problem Approximating the distribution of wide random neural networks.
method Stein's method, Gaussian smoothing, Laplacian operators, Cameron-Martin space.
result First bounds on Gaussian approximation of wide random neural networks.
Random walks on hyperbolic spaces follow predictable large deviation principles.
problem Understanding the behavior of random walks on hyperbolic spaces.
method Large deviation principles for displacement and translation distances.
result Translation and displacement distances satisfy large deviation principles with the same rate function.
This research proposes a new distance metric using Isolation Forests.
problem Approximating spatial distance between data points.
method Isolation Forests for outlier detection, transforming separation depth into a distance metric.
result The method produces a distance metric invariant to variable scales and capable of handling non-linear relationships.
Bounds neural network output distribution to Gaussian for random initialization.
problem Quantifying the distribution of randomly initialized deep neural networks.
method Quantitative Gaussian approximation using quadratic Wasserstein distance.
result Explicit inequalities show how network sizes affect Gaussian behavior.
Modified cosine distance improves similarity performance in data with variance and correlation.
problem Limitations of traditional cosine similarity in random variable spaces with variance and correlation.
method Proposed a variance-adjusted cosine distance metric to overcome limitations of traditional cosine similarity.
result Modified cosine distance shows 100% test accuracy in KNN model on the Wisconsin Breast Cancer Dataset.
D2KE converts distance metrics to kernels for machine learning.
problem Machine learning with structured inputs often lacks vector representations.
method Proposes a framework to derive kernels from dissimilarity measures.
result Functions in the RKHS are Lipschitz-continuous with respect to the distance metric.
Optimal transport is #P-hard when components are independent, even with approximate solutions.
problem Computational complexity of optimal transport with independent marginals.
method Proved #P-hardness and developed a pseudo-polynomial time approximation algorithm.
result Optimal transport is #P-hard even with independent components and approximate solutions.
TTRP method preserves distances in high-dimensional data with reduced storage and speed.
problem Preserving distances in high-dimensional datasets efficiently and accurately.
method Tensor train random projection (TTRP) using TT-ranks of one.
result TTRP is an expected isometric projection with bounded variance.
The paper bounds solutions to complex optimization problems with uncertain data.
problem Distributionally robust optimization problems with multivariate uncertainty sets.
method Conditions and bounds derived for multivariate and univariate Wasserstein distances, Bregman-Wasserstein divergences, and signed Choquet integrals.
result Computable lower and upper bounds for DRO problems, derived from scalar-valued aggregation functions and Wasserstein distances.
Random walk speed on Teichmüller space is a proper function.
problem Understanding the speed of random walks on Teichmüller space.
method Adaptation of Gouëzel's pivoting techniques to Teichmüller space.
result Speed of random walk is a proper function on Teichmüller space.
WWe define the notion of a random metric space and prove that with probability one such a space is isometricto the Urysohn universal metric space. The main technique is the study of universal and random distance matrices; we relate the properties of metric (in particulary universal) space to the properties of distance …
SMERF improves distance learning with decision forests.
problem Subpar inference and prediction due to poor distances.
method Decision forest algorithm for distance learning.
result Empirically demonstrates ability to approximate arbitrary distances and identify features.
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.
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.
New method improves Wasserstein distance for large-scale data.
problem High computational cost of Wasserstein distance for large-scale machine learning.
method Augmented Sliced Wasserstein Distances (ASWDs) using neural network mappings.
result ASWDs significantly outperform other Wasserstein variants in synthetic and real-world problems.
Uniform approximations for RHTs improve kernel approximation and distance estimation.
problem Theoretical guarantees for RHTs in low-dimensional applications.
method Proved uniform convergence of average of function over RHTs entries.
result Improved guarantees for kernel approximation and distance estimation.
A new tree-sliced Wasserstein distance improves optimal transport computations.
problem Computational and statistical drawbacks in optimal transport.
method Introducing tree metrics and averaging Wasserstein distances using random tree metrics.
result Tree-sliced Wasserstein distance outperforms other methods on benchmarks.
We develop methods to cluster financial time series using distances between dependent random variables.
problem Inaccurate covariance matrices and difficulty in estimating them from empirical data.
method We propose a new approach to clustering financial time series by using distances between cross-dependent random processes.
result Our method is statistically consistent and can be applied to a broader range of financial analyses.