相关论文: Geometric mean method for judgement matrices: Form…

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…

We discuss the correspondence between Gaussian process regression and Geometric Harmonics, two similar kernel-based methods that are typically used in different contexts. Research communities surrounding the two concepts often pursue…

Understanding Earth's subsurface is critical for energy transition, natural hazard mitigation, and planetary science. Yet subsurface analysis remains fragmented, with separate models required for structural interpretation, stratigraphic…

We consider the problem of minimizing a strongly convex smooth function where the gradients are subject to additive worst-case deterministic errors that are square-summable. We study the trade-offs between the convergence rate and…

This study presents the development and application of a scalable non-ergodic ground motion model (NGMM) for the Los Angeles area. The NGMM is trained and validated on physics-based simulated ground-motion data from a recent Statewide…

Traditional sparse and dense retrieval methods struggle to leverage general world knowledge and often fail to capture the nuanced features of queries and products. With the advent of large language models (LLMs), industrial search systems…

Geometric perception problems are fundamental tasks in robotics and computer vision. In real-world applications, they often encounter the inevitable issue of outliers, preventing traditional algorithms from making correct estimates. In this…

This article presents maximum likelihood estimators (MLEs) and log-likelihood ratio (LLR) tests for the eigenvalues and eigenvectors of Gaussian random symmetric matrices of arbitrary dimension, where the observations are independent…

In the context of first-order algorithms subject to random gradient noise, we study the trade-offs between the convergence rate (which quantifies how fast the initial conditions are forgotten) and the "risk" of suboptimality, i.e.…

A general framework based on Gaussian models and a MAP-EM algorithm is introduced in this paper for solving matrix/table completion problems. The numerical experiments with the standard and challenging movie ratings data show that the…

The standard regression tree method applied to observations within clusters poses both methodological and implementation challenges. Effectively leveraging these data requires methods that account for both individual-level and sample-level…

Scientific machine learning increasingly uses spectral methods to understand physical systems. Current spectral learning approaches provide only point estimates without uncertainty quantification, limiting their use in safety-critical…

This paper introduces GEMBA-MQM, a GPT-based evaluation metric designed to detect translation quality errors, specifically for the quality estimation setting without the need for human reference translations. Based on the power of large…

Finding an unconstrained and statistically interpretable reparameterization of a covariance matrix is still an open problem in statistics. Its solution is of central importance in covariance estimation, particularly in the recent…

Characterising the noise of an airborne electromagnetic (AEM) system is critical in correctly imaging the earth's subsurface conductivity. Deterministic and probabilistic geophysical inversion algorithms require foreknowledge of the system…

Quantum algorithm is a key tool for cryptanalysis. At present, people are committed to building powerful quantum algorithms and tapping the potential of quantum algorithms, so as to further analyze the security of cryptographic algorithms…

Solving Bayesian inference problems approximately with variational approaches can provide fast and accurate results. Capturing correlation within the approximation requires an explicit parametrization. This intrinsically limits this…

The geometric-mean method is often used to estimate the spatial resolution of a position-sensitive detector probed by tracks. It calculates the resolution solely from measured track data without using a detailed tracking simulation and…

A popular approach for estimating an unknown signal from noisy, linear measurements is via solving a so called \emph{regularized M-estimator}, which minimizes a weighted combination of a convex loss function and of a convex (typically,…

The generalized uncertainty principle (GUP) corrected modified relativistic particle model has been derived in curved space-time. From this modified model, the equation of motion (EM) has been constructed relativistically in terms of the…