Related papers: Measuring dependence in metric abstract elementary…
We take a different look at the problem of testing the independence of two metric-space-valued random variables using the distance correlation. Instead of testing if the distance correlation vanishes exactly, we are interested in the…
We consider the problem of bounding large deviations for non-i.i.d. random variables that are allowed to have arbitrary dependencies. Previous works typically assumed a specific dependence structure, namely the existence of independent…
In this note, we describe how the study of backgrounds for general quantum systems can be formulated in terms of the representation theory of abstract $C^*$ algebras. We illustrate our general framework through two example systems:…
We study elementary submodels of a stable homogeneous structure. We improve the independence relation defined in [T. Hyttinen, On nonstructure of elementary submodels of a stable homogeneous structure, Fundamenta Mathematicae, 156(1998):…
Distance correlation is a new measure of dependence between random vectors. Distance covariance and distance correlation are analogous to product-moment covariance and correlation, but unlike the classical definition of correlation,…
In this paper we introduce several natural definitions of asymptotic independence of two sequences of random elements. We discuss their basic properties, some simple connections between them and connections with properties of weak…
It follows from a theorem of Rosenthal that a compact space is $ccc$ if and only if every Eberlein continuous image is metrizable. Motivated by this result, for a class of compact spaces $\mathcal{C}$ we define its orthogonal…
Besides the classical distinction of correlation and dependence, many dependence measures bear further pitfalls in their application and interpretation. The aim of this paper is to raise and recall awareness of some of these limitations by…
We propose a test of independence of two multivariate random vectors, given a sample from the underlying population. Our approach, which we call MINT, is based on the estimation of mutual information, whose decomposition into joint and…
The main result of this paper is a generalization of Popa's free independence result for subalgebras of ultraproduct ${\rm II_1}$ factors [Po95] to the framework of ultraproduct von Neumann algebras $(M^\omega, \varphi^\omega)$ where $(M,…
We study the spectrum of limit models assuming the existence of a nicely behaved independence notion. Under reasonable assumptions, we show that all `long' limit models are isomorphic, and all `short' limit models are non-isomorphic.…
We develop a unified framework for testing independence and quantifying association between random objects that are located in general metric spaces. Special cases include functional and high-dimensional data as well as networks, covariance…
The (e,n)-complexity functions describe total instability of trajectories in dynamical systems. They reflect an ability of trajectories going through a Borel set to diverge on the distance $\epsilon$ during the time interval n. Behavior of…
We propose a new multivariate dependency measure. It is obtained by considering a Gaussian kernel based distance between the copula transform of the given d-dimensional distribution and the uniform copula and then appropriately normalizing…
We impose rank one constraints on marginalizations of a tensor, given by a simplicial complex. Following work of Kirkup and Sullivant, such marginal independence models can be made toric by a linear change of coordinates. We study their…
We propose a novel method for testing serial independence of object-valued time series in metric spaces, which is more general than Euclidean or Hilbert spaces. The proposed method is fully nonparametric, free of tuning parameters, and can…
We develop a new notion of independence suggested by Scanlon (th-independence). We prove that in a large class of theories (which includes all simple theories) this notion has many of the properties needed for an adequate geometric…
A dependence measure for arbitrary type pairs of random variables is proposed and analyzed, which in the particular case where both random variables are continuous turns out to be a concordance measure. Also, a sample version of the…
We propose new concepts in order to analyze and model the dependence structure between two time series. Our methods rely exclusively on the order structure of the data points. Hence, the methods are stable under monotone transformations of…
The notion of a tensor product with projections or with inclusions is defined. It is shown that the definition of stochastic independence relies on such a structure and that independence can be defined in an arbitrary category with a tensor…