相关论文: Map Projections Minimizing Distance Errors
Solving the trust-region subproblem (TRS) plays a key role in numerical optimization and many other applications. The generalized Lanczos trust-region (GLTR) method is a well-known Lanczos type approach for solving a large-scale TRS. The…
We consider the problem of discrimination between two pure quantum states. It is well known that the optimal measurement under both the error-probability and log-loss criteria is a projection, while under an ``erasure-distortion'' criterion…
The seminal result of Johnson and Lindenstrauss on random embeddings has been intensively studied in applied and theoretical computer science. Despite that vast body of literature, we still lack of complete understanding of statistical…
In this paper, we consider probability measures $\mu$ and $\nu$ on a $d$--dimensional sphere in $\Rd, d \geq 1,$ and cost functions of the form $c(\x,\y)=l(\frac{|\x-\y|^2}{2})$ that generalize those arising in geometric optics where…
Despite being widely used as a performance measure for visual detection tasks, Average Precision (AP) is limited in (i) reflecting localisation quality, (ii) interpretability and (iii) robustness to the design choices regarding its…
In this article, we study the approximate solutions set $\Lambda_b$ of an inconsistent system of $\max-\min$ fuzzy relational equations $(S): A \Box_{\min}^{\max}x =b$. Using the $L_\infty$ norm, we compute by an explicit analytical formula…
We propose a framework for modeling and solving low-rank optimization problems to certifiable optimality. We introduce symmetric projection matrices that satisfy $Y^2=Y$, the matrix analog of binary variables that satisfy $z^2=z$, to model…
This paper is concerned with low-rank matrix optimization, which has found a wide range of applications in machine learning. This problem in the special case of matrix sensing has been studied extensively through the notion of Restricted…
Many statistical and machine learning approaches rely on pairwise distances between data points. The choice of distance metric has a fundamental impact on performance of these procedures, raising questions about how to appropriately…
The limits of standard cosmography are here revised addressing the problem of error propagation during statistical analyses. To do so, we propose the use of Chebyshev polynomials to parameterize cosmic distances. In particular, we…
This paper presents a novel method for qualitative mapping of large scale spaces. The proposed framework makes use of a graphical representation of the world in order to build a map consisting of qualitative constraints on the geometric…
We adopt and expand McDonald's (2011) regression framework for measurement precision, integrating two key perspectives: (a) reliability of observed scores and (b) optimal prediction of latent scores. Reliability arises from a measurement…
The Earth movers distance (EMD) is a measure of distance between probability distributions which is at the heart of mass transportation theory. Recent research has shown that the EMD plays a crucial role in studying the potential impact of…
This paper focuses on optimal unimodal transformation of the score outputs of a univariate learning model under linear loss functions. We demonstrate that the optimal mapping between score values and the target region is a rectangular…
The problem of recovering the configuration of points from their partial pairwise distances, referred to as the Euclidean Distance Matrix Completion (EDMC) problem, arises in a broad range of applications, including sensor network…
The method of stable random projections is popular for efficiently computing the Lp distances in high dimension (where 0<p<=2), using small space. Because it adopts nonadaptive linear projections, this method is naturally suitable when the…
The most important aspect of any classifier is its error rate, because this quantifies its predictive capacity. Thus, the accuracy of error estimation is critical. Error estimation is problematic in small-sample classifier design because…
In this study, we present a low-cost and unified framework for vectorized road mapping leveraging enhanced inverse perspective mapping (IPM). In this framework, Catmull-Rom splines are utilized to characterize lane lines, and all the other…
The constrained mock-Chebyshev least squares operator is a linear approximation operator based on an equispaced grid of points. Like other polynomial or rational approximation methods, it was recently introduced in order to defeat the Runge…
This paper introduces a new simulation-based inference procedure to model and sample from multi-dimensional probability distributions given access to i.i.d.\ samples, circumventing the usual approaches of explicitly modeling the density…