相关论文: Integral representations of one dimensional projec…

One of the fundamental problems in machine learning is the estimation of a probability distribution from data. Many techniques have been proposed to study the structure of data, most often building around the assumption that observations…

We show that the requirement of manifest coordinate invariance of perturbatively defined quantum-mechanical path integrals in curved space leads to an extension of the theory of distributions by specifying unique rules for integrating…

We introduce differentiable indirection -- a novel learned primitive that employs differentiable multi-scale lookup tables as an effective substitute for traditional compute and data operations across the graphics pipeline. We demonstrate…

We consider the problem of computing L1-distances between every pair ofcprobability densities from a given family. We point out that the technique of Cauchy random projections (Indyk'06) in this context turns into stochastic integrals with…

Parametric projections let analysts embed new points in real time, but input variations from measurement noise or data drift can produce unpredictable shifts in the 2D layout. Whether and where a projection is locally stable remains largely…

In this work, we generalize the Cram\'er-von Mises statistic via projection-averaging to obtain a robust test for the multivariate two-sample problem. The proposed test is consistent against all fixed alternatives, robust to heavy-tailed…

Approximate solutions of linear and nonlinear integral equations using methods related to an interpolatory projection involve many integrals which need to be evaluated using a numerical quadrature formula. In this paper, we consider…

The technique coined as NDIM - Negative Dimensional Integration Method by their discoverers, relies on a three-pronged basis: Gaussian integration, series expansion and analytic continuation. The technique has been successfully applied to…

The core of a projective dimension one module is computed explicitly in terms of Fitting ideals. In particular, our formula recovers previous work by R. Mohan on integrally closed torsionfree modules over a two-dimensional regular local…

Interferometers play an increasingly important role for spatially resolved observations. If employed at full potential, interferometry can probe an enormous dynamic range in spatial scale. Interpretation of the observed visibilities…

t-Distributed Stochastic Neighbor Embedding (t-SNE) for the visualization of multidimensional data has proven to be a popular approach, with successful applications in a wide range of domains. Despite their usefulness, t-SNE projections can…

This article discusses a prescription to compute polarized dimensionally regularized amplitudes, providing a recipe for constructing simple and general polarized amplitude projectors in D dimensions that avoids conventional Lorentz tensor…

A powerful data transformation method named guided projections is proposed creating new possibilities to reveal the group structure of high-dimensional data in the presence of noise variables. Utilising projections onto a space spanned by a…

In this manuscript a unified framework for conducting inference on complex aggregated data in high dimensional settings is proposed. The data are assumed to be a collection of multiple non-Gaussian realizations with underlying undirected…

In this paper, the estimation of the Integrated Covariance matrix from high-frequency data, for high dimensional stock price process, is considered. The Hayashi-Yoshida covolatility estimator is an improvement over Realized covolatility for…

We consider mechanics of composite materials in which thin inclusions are modeled by lower-dimensional manifolds. By successively applying the dimensional reduction to junctions and intersections within the material, a geometry of…

We propose a new approach that allows for the separate numerical calculation of the real and imaginary parts of finite loop integrals. We find that at one-loop the real part is given by the Loop-Tree Duality integral supplemented with…

Kadison's Pythagorean theorem (2002) provides a characterization of the diagonals of projections with a subtle integrality condition. Arveson (2007), Kaftal, Ng, Zhang (2009), and Argerami (2015) all provide different proofs of that…

The paper investigates the problem of performing correlation analysis when the number of observations is very large. In such a case, it is often necessary to combine the random observations to achieve dimensionality reduction of the…

Implicit neural representations (INRs) have emerged as a powerful tool for compressing large-scale volume data. This opens up new possibilities for in situ visualization. However, the efficient application of INRs to distributed data…