Related papers: Euclidean Ideal Point Estimation From Roll-Call Da…
This paper describes continuous-space methodologies to estimate the collision probability, Euclidean distance and gradient between an ellipsoidal robot model and an environment surface modeled as a set of Gaussian distributions.…
The majority of classic tensor CP decomposition models are designed for squared loss, employing Euclidean distance as a local proximal term. However, the Euclidean distance is unsuitable for the generalized loss function applicable to…
Existing deep embedding methods in vision tasks are capable of learning a compact Euclidean space from images, where Euclidean distances correspond to a similarity metric. To make learning more effective and efficient, hard sample mining is…
Existing approaches to estimating politicians' latent positions along specific dimensions often fail when relevant data is limited. We leverage the embedded knowledge in generative large language models (LLMs) to address this challenge and…
The need for efficiently comparing and representing datasets with unknown alignment spans various fields, from model analysis and comparison in machine learning to trend discovery in collections of medical datasets. We use manifold learning…
Accurate source localization in Multi-Platform Radar Networks (MPRNs) benefits from exploiting both range and angle measurements under robust estimation. In this paper, we propose a robust Euclidean distance matrix (EDM) optimization model…
Distance metrics and their nonlinear variant play a crucial role in machine learning based real-world problem solving. We demonstrated how Euclidean and cosine distance measures differ not only theoretically but also in real-world medical…
Ideal point estimation methods face a significant challenge when legislators engage in protest voting -- strategically voting against their party to express dissatisfaction. Such votes introduce attenuation bias, making ideologically…
This paper addresses the problem of estimating the positions of points from distance measurements corrupted by sparse outliers. Specifically, we consider a setting with two types of nodes: anchor nodes, for which exact distances to each…
Laplacian-based methods are popular for the dimensionality reduction of data lying in $\mathbb{R}^N$. Several theoretical results for these algorithms depend on the fact that the Euclidean distance locally approximates the geodesic distance…
The problem of determining the configuration of points from partial distance information, known as the Euclidean Distance Geometry (EDG) problem, is fundamental to many tasks in the applied sciences. In this paper, we propose two algorithms…
Selecting representatives based on voters' preferences is a fundamental problem in social choice theory. While cardinal utility functions offer a detailed representation of preferences, ordinal rankings are often the only available…
The construction of $r$-nets offers a powerful tool in computational and metric geometry. We focus on high-dimensional spaces and present a new randomized algorithm which efficiently computes approximate $r$-nets with respect to Euclidean…
This paper studies the problem of estimation from relative measurements in a graph, in which a vector indexed over the nodes has to be reconstructed from pairwise measurements of differences between its components associated to nodes…
The classification loss functions used in deep neural network classifiers can be grouped into two categories based on maximizing the margin in either Euclidean or angular spaces. Euclidean distances between sample vectors are used during…
Repeated sampling is a standard way to spend test-time compute, but its benefit is controlled by the latent distribution of correctness across examples, not by one-call accuracy alone. We study the binary correctness layer of repeated LLM…
A new method is proposed for variable screening, variable selection and prediction in linear regression problems where the number of predictors can be much larger than the number of observations. The method involves minimizing a penalized…
Random geometric graphs are a popular choice for a latent points generative model for networks. Their definition is based on a sample of $n$ points $X_1,X_2,\cdots,X_n$ on the Euclidean sphere~$\mathbb{S}^{d-1}$ which represents the latent…
Robust local feature representations are essential for spatial intelligence tasks such as robot navigation and augmented reality. Establishing reliable correspondences requires descriptors that provide both high discriminative power and…
The 2-Wasserstein distance (or RMS distance) is a useful measure of similarity between probability distributions that has exciting applications in machine learning. For discrete distributions, the problem of computing this distance can be…