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.
Tree Mover's Distance measures graph attributes and improves GNN performance.
Quantum Earth Mover's distance improves stability and efficiency in quantum learning.
New neural method calculates EMD for particle physics data.
While the celebrated Word2Vec technique yields semantically rich representations for individual words, there has been relatively less success in extending to generate unsupervised sentences or documents embeddings. Recent work has demonstrated that a distance measure between documents called \emph{Word Mover's Distance…
The Earth Mover's Distance (EMD) is a state-of-the art metric for comparing discrete probability distributions, but its high distinguishability comes at a high cost in computational complexity. Even though linear-complexity approximation algorithms have been proposed to improve its scalability, these algorithms are eit…
Positive definite kernels are an important tool in machine learning that enable efficient solutions to otherwise difficult or intractable problems by implicitly linearizing the problem geometry. In this paper we develop a set-theoretic interpretation of the Earth Mover's Distance (EMD) and propose Earth Mover's Interse…
Collaborative filtering, a widely-used recommendation technique, predicts a user's preference by aggregating the ratings from similar users. As a result, these measures cannot fully utilize the rating information and are not suitable for real world sparse data. To solve these issues, we propose a novel user distance me…
This paper speeds up WMD computation for multiple queries efficiently.
Diffusion-weighted MR imaging (DWI) is the only method we currently have to measure connections between different parts of the human brain in vivo. To elucidate the structure of these connections, algorithms for tracking bundles of axonal fibers through the subcortical white matter rely on local estimates of the fiber …
We address the problem of defining a network graph on a large collection of classes. Each class is comprised of a collection of data points, sampled in a non i.i.d. way, from some unknown underlying distribution. The application we consider in this paper is a large scale high dimensional survey of people living in the …
This paper presents a unified framework for smooth convex regularization of discrete optimal transport problems. In this context, the regularized optimal transport turns out to be equivalent to a matrix nearness problem with respect to Bregman divergences. Our framework thus naturally generalizes a previously proposed …
Sparse coding (Sc) has been studied very well as a powerful data representation method. It attempts to represent the feature vector of a data sample by reconstructing it as the sparse linear combination of some basic elements, and a norm distance function is usually used as the loss function for the reconstructio…
For localization and mapping of indoor environments through WiFi signals, locations are often represented as likelihoods of the received signal strength indicator. In this work we compare various measures of distance between such likelihoods in combination with different methods for estimation and representation. In pa…
New method for neural networks to predict histogram data.
Computing optimal transport distances such as the earth mover's distance is a fundamental problem in machine learning, statistics, and computer vision. Despite the recent introduction of several algorithms with good empirical performance, it is unknown whether general optimal transport distances can be approximated in …
Many information retrieval algorithms rely on the notion of a good distance that allows to efficiently compare objects of different nature. Recently, a new promising metric called Word Mover's Distance was proposed to measure the divergence between text passages. In this paper, we demonstrate that this metric can be ex…
We present a framework for building unsupervised representations of entities and their compositions, where each entity is viewed as a probability distribution rather than a vector embedding. In particular, this distribution is supported over the contexts which co-occur with the entity and are embedded in a suitable low…
LOT framework speeds up event distance computation in collider physics.
The ability to measure similarity between documents enables intelligent summarization and analysis of large corpora. Past distances between documents suffer from either an inability to incorporate semantic similarities between words or from scalability issues. As an alternative, we introduce hierarchical optimal transp…
As a fundamental problem of natural language processing, it is important to measure the distance between different documents. Among the existing methods, the Word Mover's Distance (WMD) has shown remarkable success in document semantic matching for its clear physical insight as a parameter-free model. However, WMD is e…
Wasserstein Generative Adversarial Networks (WGANs) provide a versatile class of models, which have attracted great attention in various applications. However, this framework has two main drawbacks: (i) Wasserstein-1 (or Earth-Mover) distance is restrictive such that WGANs cannot always fit data geometry well; (ii) It …
Adversarial attacks aim to confound machine learning systems, while remaining virtually imperceptible to humans. Attacks on image classification systems are typically gauged in terms of -norm distortions in the pixel feature space. We perform a behavioral study, demonstrating that the pixel -norm for any $0\le p …
The problem of unsupervised learning node embeddings in graphs is one of the important directions in modern network science. In this work we propose a novel framework, which is aimed to find embeddings by \textit{discriminating distributions of similarities (DDoS)} between nodes in the graph. The general idea is implem…
A new supervised tree-Wasserstein distance improves document classification.
This paper approximates 1-Wasserstein distance using tree-based embedding.
Document alignment aims to identify pairs of documents in two distinct languages that are of comparable content or translations of each other. Such aligned data can be used for a variety of NLP tasks from training cross-lingual representations to mining parallel data for machine translation. In this paper we develop an…
Metric learning has the aim to improve classification accuracy by learning a distance measure which brings data points from the same class closer together and pushes data points from different classes further apart. Recent research has demonstrated that metric learning approaches can also be applied to trees, such as m…
Metric learning has the aim to improve classification accuracy by learning a distance measure which brings data points from the same class closer together and pushes data points from different classes further apart. Recent research has demonstrated that metric learning approaches can also be applied to trees, such as m…
New metric learning approach for tree data reduces computation cost.
The paper tightens bounds on distances between Reeb graphs.
Covariance and histogram image descriptors provide an effective way to capture information about images. Both excel when used in combination with special purpose distance metrics. For covariance descriptors these metrics measure the distance along the non-Euclidean Riemannian manifold of symmetric positive definite mat…
A new tree-Wasserstein distance for high-dimensional data with latent feature hierarchy.
In the last couple of years, several adversarial attack methods based on different threat models have been proposed for the image classification problem. Most existing defenses consider additive threat models in which sample perturbations have bounded L_p norms. These defenses, however, can be vulnerable against advers…
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…
Locally adaptive clustering for tree delineation.
Bayesian optimization with Gaussian processes speeds up searches for stationary points.
This study investigates self-supervised learning with Wasserstein distance on tree structures.
The paper proposes a method to infer differentiation trees from RNA velocity data.
A new k-means algorithm using cover trees accelerates clustering.
Method learns hierarchical representations of samples and features simultaneously.
PhyloVAE learns tree topologies without supervision.
Paper extends tree bijection for hyperbolic surfaces without requiring cusps.
Automated sentiment classification (SC) on short text fragments has received increasing attention in recent years. Performing SC on unseen domains with few or no labeled samples can significantly affect the classification performance due to different expression of sentiment in source and target domain. In this study, w…
This paper introduces a new method to cluster qualitative attribute data using tree structures.
Paper develops a new method to analyze 3D tree-like objects.
Optimal transport induces the Earth Mover's (Wasserstein) distance between probability distributions, a geometric divergence that is relevant to a wide range of problems. Over the last decade, two relaxations of optimal transport have been studied in depth: unbalanced transport, which is robust to the presence of outli…
Optimal algorithms learn Gaussian trees and polytrees from data.
The paper improves decision tree stability for health care applications.