We define a novel class of distances between statistical multivariate distributions by modeling an optimal transport problem on their marginals with respect to a ground distance defined on their conditionals. These new distances are metrics whenever the ground distance between the marginals is a metric, generalize both…
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48 results for “novel distances”
Novel neural network approximates exact distance for robust classification.
problem Adversarial attacks on neural networks in safety-critical systems.
method Signed Distance Classifiers (SDCs) and Unitary-Gradient Neural Network.
result Approximates exact distance from classification boundary for certifiable predictions.
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.
The paper tightens bounds on distances between Reeb graphs.
problem Certifying quasi-universality of distances between Reeb graphs.
method Establishes tight bi-Lipschitz bounds for various distances.
result Proves strict universality of the functional contortion distance for contour trees and coincides with interleaving distance for merge trees.
A novel criterion selects optimal distance metrics for cell profile analysis.
problem Determining the most accurate distance metric for high-dimensional cell profiles.
method Generalized proposition and corollaries to evaluate and select distance metrics.
result Wasserstein and cosine similarity metrics are optimal for general cases.
A novel method for comparing graphs of different sizes using Wasserstein distance.
problem Comparing non-aligned graphs of varying sizes.
method Optimal transport in graph comparison framework, solving a one-to-many assignment problem.
result Significant improvements in graph alignment and classification tasks.
A new method embeds distributions in a common space for optimal transport comparison.
problem Comparing distributions in different metric spaces.
method Sub-embedding robust Wasserstein (SERW) distance.
result SERW mimics GW distance properties and provides a cost relation.
We define a new family of similarity and distance measures on graphs, and explore their theoretical properties in comparison to conventional distance metrics. These measures are defined by the solution(s) to an optimization problem which attempts find a map minimizing the discrepancy between two graph Laplacian exponen…
Neural networks can learn distance metrics affecting model performance.
problem Understanding how neural networks learn and represent data.
method Experiments with six MNIST architectures, constrained to learn either distance or intensity representations.
result Distance-based learning affects model performance, validating the geometric framework.
Efficient sampling reduces memory usage for Minimax distance analysis.
problem Quadratic memory requirement for existing Minimax distance methods.
method Proposes a novel sampling technique with linear space complexity.
result Demonstrates significant reduction in memory usage for Minimax distances.
Paper presents a novel k-means clustering method using two distance measures for Gaussian data.
problem Improving clustering accuracy and robustness for Gaussian data.
method Integrates within cluster distance (WCD) and inter cluster distance (ICD) into k-means clustering.
result The algorithm provides more accurate clustering and better handles outliers.
A novel clustering method uses torque balance to group objects.
problem Grouping similar objects in various scientific fields.
method Inspired by gravitational interactions, a parameter-free clustering algorithm based on mass and distance.
result The algorithm effectively clusters objects regardless of their shape, size, or density.
Fuzzy clustering of ordinal time series based on two novel distances with economic applicationsstat.ML
Paper introduces novel distances for clustering ordinal time series.
problem Clustering ordinal time series with discrete response.
method Introduces two novel distances and fuzzy clustering algorithms.
result Fuzzy clustering algorithms accurately group series from similar stochastic processes.
We present a novel modulation level classification (MLC) method based on probability distribution distance functions. The proposed method uses modified Kuiper and Kolmogorov-Smirnov distances to achieve low computational complexity and outperforms the state of the art methods based on cumulants and goodness-of-fit test…
A new robust time series distance metric for k-NN classification.
problem Robustness against arbitrary data contamination in time series classification.
method Proposes a novel distance metric with worst-case complexity.
result Demonstrates competitive classification accuracy in k-NN time series classification.
Paper connects surface shape analysis and unbalanced optimal transport.
problem Computing the SRNF shape distance on piecewise linear surfaces.
method Characterizes SRNF shape distance as WFR distance pullback, proposes new algorithm for WFR distance computation.
result Direct computation of SRNF shape distance on piecewise linear surfaces.
Paper tackles robust Euclidean distance estimation with sparse outliers.
problem Estimating point positions from corrupted distance measurements.
method Proposes a novel algorithm using Nyström method and robust PCA.
result Achieves accurate recovery with minimal anchors and sparse outliers.
We present a novel hierarchical distance-dependent Bayesian model for event coreference resolution. While existing generative models for event coreference resolution are completely unsupervised, our model allows for the incorporation of pairwise distances between event mentions -- information that is widely used in sup…
High dimensional structured data such as text and images is often poorly understood and misrepresented in statistical modeling. The standard histogram representation suffers from high variance and performs poorly in general. We explore novel connections between statistical translation, heat kernels on manifolds and gra…
Novel neural network approach on hyperbolic and SPD spaces.
problem Developing neural networks on symmetric spaces of noncompact type.
method Unified formulation of distance from a point to a hyperplane.
result Closed-form expression for point-to-hyperplane distance in higher-rank spaces.
Large scale agglomerative clustering is hindered by computational burdens. We propose a novel scheme where exact inter-instance distance calculation is replaced by the Hamming distance between Kernelized Locality-Sensitive Hashing (KLSH) hashed values. This results in a method that drastically decreases computation tim…
Edit distance, also known as Levenshtein distance, is an essential way to compare two strings that proved to be particularly useful in the analysis of genetic sequences and natural language processing. However, edit distance is a discrete function that is known to be hard to optimize. This fact hampers the use of this …
New distances measure mixtures of Gaussians, useful in machine learning.
problem Comparing distributions with disjoint supports.
method Schoenberg-Rao distances based on concave Rao's entropy.
result Closed-form distances for mixtures of Gaussians.
Clustering is one of the major roles in data mining that is widely application in pattern recognition and image segmentation. Fuzzy C-means (FCM) is the most used clustering algorithm that proven efficient, fast and easy to implement, however, FCM uses the Euclidean distance that often leads to clustering errors, espec…
Improved training boosts certified robustness of L-infinity distance nets.
problem Certified robustness of L-infinity distance nets is not as strong as conventional networks.
method Improved training process combining scaled cross-entropy and clipped hinge loss with a decaying mixing coefficient.
result Certified accuracy of L-infinity distance nets improved from 33.30% to 40.06% on CIFAR-10.
In our work, we propose a novel formulation for supervised dimensionality reduction based on a nonlinear dependency criterion called Statistical Distance Correlation, Szekely et. al. (2007). We propose an objective which is free of distributional assumptions on regression variables and regression model assumptions. Our…
A new metric HCP distance for comparing distributions.
problem Comparing high-dimensional probability distributions efficiently.
method Hilbert curve projection to low-dimensional coupling, followed by transport distance calculation.
result HCP distance is a proper metric for probability measures with bounded supports.
The paper describes distances on Sol-type groups using novel geometric techniques.
problem Understanding distances on Sol-type groups.
method New technique of Euclidean curve surgery to describe uniformly roughly geodesic paths.
result The rough isometry type of distances on Sol-type groups is determined by a specific metric restriction.
Energy distance measures feature heterogeneity in federated learning.
problem Heterogeneity across data sources hinders model aggregation in federated learning.
method Introduced Taylor approximations of energy distance for efficient computation.
result Taylor approximations accurately capture feature discrepancies, improving convergence.
Many mobile robots rely on 2D laser scanners for localization, mapping, and navigation. However, those sensors are unable to correctly provide distance to obstacles such as glass panels and tables whose actual occupancy is invisible at the height the sensor is measuring. In this work, instead of estimating the distance…
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.
Optimal transport theory has recently found many applications in machine learning thanks to its capacity for comparing various machine learning objects considered as distributions. The Kantorovitch formulation, leading to the Wasserstein distance, focuses on the features of the elements of the objects but treat them in…
Preference are central to decision making by both machines and humans. Representing, learning, and reasoning with preferences is an important area of study both within computer science and across the sciences. When working with preferences it is necessary to understand and compute the distance between sets of objects, …
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.
The traditional Minkowski distances are induced by the corresponding Minkowski norms in real-valued vector spaces. In this work, we propose novel statistical symmetric distances based on the Minkowski's inequality for probability densities belonging to Lebesgue spaces. These statistical Minkowski distances admit closed…
WAPPO optimizes feature distributions for better visual transfer in RL.
problem Improving visual transfer in reinforcement learning.
method WAPPO uses Wasserstein Confusion to minimize feature distribution distance.
result WAPPO outperforms previous methods in visual transfer across different environments.
Kernel Trace Distance: Quantum Statistical Metric between Measures through RKHS Density Operatorsstat.ML
A new distance metric compares probability distributions using kernel covariance operators.
problem Comparing probability distributions in machine learning tasks.
method Introduces a novel distance metric based on Schatten norm of kernel covariance operators.
result The new distance metric is more discriminative and robust to hyperparameters.
A novel distance measure aligns time series with feature and temporal variability.
problem Measuring similarity between time series with different features and dynamics.
method Learn a latent global transformation and temporal alignment in a joint optimization problem.
result Framework robustly aligns time series across various invariance classes.
We consider the task of detecting regulatory elements in the human genome directly from raw DNA. Past work has focused on small snippets of DNA, making it difficult to model long-distance dependencies that arise from DNA's 3-dimensional conformation. In order to study long-distance dependencies, we develop and release …
In this paper, we present a novel two-stage metric learning algorithm. We first map each learning instance to a probability distribution by computing its similarities to a set of fixed anchor points. Then, we define the distance in the input data space as the Fisher information distance on the associated statistical ma…
This paper proposes a new method for embedding sequences using Wasserstein distances.
problem Embedding sequences in a metric space for better pattern recognition.
method Develops a deep learning model that embeds sequences as distributions and uses Wasserstein distances for comparison.
result Distributional embeddings using Wasserstein distances outperform traditional vector embeddings.
Detection of Small Holes by the Scale-Invariant Robust Density-Aware Distance (RDAD) Filtrationmath.ST
A new method detects small holes in noisy data.
problem Detecting small holes in high-density regions from noise.
method Robust Density-Aware Distance (RDAD) filtration, incorporating distance-to-measure concept.
result The RDAD filtration prolongs the persistences of small holes, making them distinguishable from noise.
A new method efficiently approximates Gromov-Wasserstein distance.
problem High computational complexity of Gromov-Wasserstein distance.
method Importance sparsification method to construct a sparse coupling matrix.
result Efficient approximation of GW distance with reduced complexity.
This work robustifies Wasserstein distance estimation with MoM estimators for outlier-polluted data.
problem Estimating Wasserstein distance between two distributions with outliers.
method Introducing MoM-based robust estimators for Wasserstein distance.
result Consistent MoM-based estimators for Wasserstein distance with convergence rates.
Spherical Sliced-Wassersteinstat.ML
A new spherical Sliced-Wasserstein distance for data on spheres.
problem Defining Wasserstein distance on manifolds, especially spheres.
method Closed-form solutions of the Wasserstein distance on the circle and a new spherical Radon transform.
result A novel spherical Sliced-Wasserstein (SW) discrepancy for data on spheres.
New slicing methods speed up Gaussian mixture Wasserstein distance computations.
problem High computational cost of the mixture Wasserstein distance.
method Slicing-based approximations to reduce computational complexity.
result Significant reduction in computational complexity while preserving key properties.
New measures assess differences in causal graphs' separations.
problem Evaluating causal discovery algorithms' output.
method Proposes new distance measures capturing causal graphs' separations.
result Proposed distances assess differences in causal graphs' separations.
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.