相关论文: Model distances for vine copulas in high dimension…
We present a new model-independent method to determine the spatial curvature and to mitigate the circularity problem affecting the use of quasars as distance indicators. The cosmic-chronometer measurements are used to construct the…
We investigate the problem of detecting dependencies between the components of a high-dimensional vector. Our approach advances the existing literature in two important respects. First, we consider the problem under privacy constraints.…
Measuring a strength of dependence of random variables is an important problem in statistical practice. In this paper, we propose a new function valued measure of dependence of two random variables. It allows one to study and visualize…
This paper provides a detailed investigation of using the Kullback-Leibler (KL) Divergence as a way to compare and analyse game-levels, and hence to use the measure as the objective function of an evolutionary algorithm to evolve new…
Cosmological distances are fundamental observables in cosmology. The luminosity ($D_L$), angular diameter ($D_A$) and gravitational wave ($D_{\rm GW}$) distances are all trivially related in General Relativity assuming no significant…
This paper presents a new similarity measure to be used for general tasks including supervised learning, which is represented by the K-nearest neighbor classifier (KNN). The proposed similarity measure is invariant to large differences in…
Selecting an appropriate divergence measure is a critical aspect of machine learning, as it directly impacts model performance. Among the most widely used, we find the Kullback-Leibler (KL) divergence, originally introduced in kinetic…
We consider problems of estimation of structured covariance matrices, and in particular of matrices with a Toeplitz structure. We follow a geometric viewpoint that is based on some suitable notion of distance. To this end, we overview and…
A distance measure is presented between two unitary propagators of quantum systems of differing dimensions along with a corresponding method of computation. A typical application is to compare the propagator of the actual (real) process…
Quantifying similarity between data objects is an important part of modern data science. Deciding what similarity measure to use is very application dependent. In this paper, we combine insights from systems theory and machine learning, and…
We show that, for vector spaces in which distance measurement is performed using a gauge, the existence of best coapproximations in $1$-codimensional closed linear subspaces implies in dimensions $\geq 2$ that the gauge is a norm, and in…
We propose a new method with $\mathcal{L}_2$ distance that maps one $N$-dimensional distribution to another, taking into account available information about correspondences. We solve the high-dimensional problem in 1D space using an…
The class of index-mixed copulas is introduced and its properties are investigated. Index-mixed copulas are constructed from given base copulas and a random index vector, and show a rather remarkable degree of analytical tractability. The…
This paper presents a new methodology for clustering multivariate time series leveraging optimal transport between copulas. Copulas are used to encode both (i) intra-dependence of a multivariate time series, and (ii) inter-dependence…
Uncertain information on input parameters of reliability models is usually modeled by considering these parameters as random, and described by marginal distributions and a dependence structure of these variables. In numerous real-world…
Robotic pruning of dormant grapevines is an area of active research in order to promote vine balance and grape quality, but so far robotic efforts have largely focused on planar, simplified vines not representative of commercial vineyards.…
Identifying statistical dependence between the features and the label is a fundamental problem in supervised learning. This paper presents a framework for estimating dependence between numerical features and a categorical label using…
Implicit copulas are the most common copula choice for modeling dependence in high dimensions. This broad class of copulas is introduced and surveyed, including elliptical copulas, skew $t$ copulas, factor copulas, time series copulas and…
Sliced Wasserstein distances preserve properties of classic Wasserstein distances while being more scalable for computation and estimation in high dimensions. The goal of this work is to quantify this scalability from three key aspects: (i)…
Starting from the characterization of extreme-value copulas based on max-stability, large-sample tests of extreme-value dependence for multivariate copulas are studied. The two key ingredients of the proposed tests are the empirical copula…