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.
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.
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.
We propose three measures of mutual dependence between multiple random vectors. All the measures are zero if and only if the random vectors are mutually independent. The first measure generalizes distance covariance from pairwise dependence to mutual dependence, while the other two measures are sums of squared distance…
In a recently published paper [1], it is shown that deep neural networks (DNNs) with random Gaussian weights preserve the metric structure of the data, with the property that the distance shrinks more when the angle between the two data points is smaller. We agree that the random projection setup considered in [1] pres…
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.
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.
For any pseudo-Anosov diffeomorphism on a closed orientable surface S of genus greater than one, it is known by the work of Bers and Thurston that the topological entropy agrees with the translation distance on the Teichmüller space with respect to the Teichmüller metric. In this paper, we consider random walks on th…
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.
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.
We present a methodology for clustering N objects which are described by multivariate time series, i.e. several sequences of real-valued random variables. This clustering methodology leverages copulas which are distributions encoding the dependence structure between several random variables. To take fully into account …
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.
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.
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.
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.
Consider a weighted or unweighted k-nearest neighbor graph that has been built on n data points drawn randomly according to some density p on R^d. We study the convergence of the shortest path distance in such graphs as the sample size tends to infinity. We prove that for unweighted kNN graphs, this distance converges …
Optimal transport (\OT) theory defines a powerful set of tools to compare probability distributions. \OT~suffers however from a few drawbacks, computational and statistical, which have encouraged the proposal of several regularized variants of OT in the recent literature, one of the most notable being the \textit{slice…
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.
BERET improves binary expansion test for multivariate independence.
problem Testing independence of random vectors in arbitrary dimensions.
method Ensemble approach using sum of squared symmetry statistics and distance correlation.
result Improves power while preserving interpretability.
We provide a simple method and relevant theoretical analysis for efficiently estimating higher-order lp distances. While the analysis mainly focuses on l4, our methodology extends naturally to p = 6,8,10..., (i.e., when p is even). Distance-based methods are popular in machine learning. In large-scale applications, sto…
A new graph-based clustering method for moderate-dimensional data.
problem Performance degradation of existing graph-based clustering methods in high dimensions.
method Introduces UN-CCDs using NND-based MC-SRT for covering radii determination.
result UN-CCDs provide stable and competitive performance in moderate-sized datasets.
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.
Optimizes sample reweighting to match laws under covariate shift using Wasserstein distance.
problem Matching laws of samples with different distributions under covariate shift.
method Minimizes Wasserstein distance between empirical measures of samples using Nearest Neighbors weights.
result Consistent reweighting leads to asymptotic convergence of empirical measures.
Two new methods reduce random forest latency and improve accuracy.
problem High latency and memory demands in deep random forest models.
method DiNo and RanBu convert shallow random forests into efficient predictors.
result RanBu matches or exceeds full-depth random forest accuracy with up to 95% reduction in time.
Tensorized random projections reduce high-dimensional tensor size efficiently.
problem Efficiently reducing the dimension of very high-dimensional tensors.
method Proposes two tensorized random projection maps using TT and CP decompositions.
result TT format offers superior performance in terms of required random projection size.