Related papers: Quantifying Non-linear Dependencies in Blind Sourc…
The dynamics of a power system with large penetration of renewable energy resources are becoming more nonlinear due to the intermittence of these resources and the switching of their power electronic devices. Therefore, it is crucial to…
Consider a time series of measurements of the state of an evolving system, x(t), where x has two or more components. This paper shows how to perform nonlinear blind source separation; i.e., how to determine if these signals are equal to…
We study the classical problem of recovering a multidimensional source signal from observations of nonlinear mixtures of this signal. We show that this recovery is possible (up to a permutation and monotone scaling of the source's original…
Multivariate datasets are common in various real-world applications. Recently, copulas have received significant attention for modeling dependencies among random variables. A copula-based information measure is required to quantify the…
This paper introduces a nonparametric copula-based index for detecting the strength and monotonicity structure of linear and nonlinear statistical dependence between pairs of random variables or stochastic signals. Our index, termed Copula…
Dependence strucuture estimation is one of the important problems in machine learning domain and has many applications in different scientific areas. In this paper, a theoretical framework for such estimation based on copula and copula…
A new index based on empirical copulas, termed the Copula Statistic (CoS), is introduced for assessing the strength of multivariate dependence and for testing statistical independence. New properties of the copulas are proved. They allow us…
Blind source separation (BSS) techniques aims at joint estimation of source signals and a mixing matrix from observations of mixtures. This paper addresses a doubly nonstationary BSS problem, where the mixing matrix is time dependent and…
A frequent task in exploratory data analysis consists in examining pairwise dependencies between data variables. Popular approaches include visualizing correlation or scatter plot matrices. However, both methods can be misleading. The…
This paper is concerned with modeling the dependence structure of two (or more) time-series in the presence of a (possible multivariate) covariate which may include past values of the time series. We assume that the covariate influences…
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…
Consider a time series of signal measurements $x(t)$, having components $x_k \mbox{ for } k = 1,2, \ldots ,N$. This paper shows how to determine if these signals are equal to linear or nonlinear mixtures of the state variables of two or…
Simultaneous recordings from many neurons hide important information and the connections characterizing the network remain generally undiscovered despite the progresses of statistical and machine learning techniques. Discerning the presence…
Given a time series of multicomponent measurements x(t), the usual objective of nonlinear blind source separation (BSS) is to find a "source" time series s(t), comprised of statistically independent combinations of the measured components.…
This paper proposes different methods to consistently detect multiple breaks in copula-based dependence measures, mainly focusing on Spearman's $\rho$. The leading model is a factor copula model due to its usefulness for analyzing data in…
We discuss the connection between information and copula theories by showing that a copula can be employed to decompose the information content of a multivariate distribution into marginal and dependence components, with the latter…
The paper presents a new copula based method for measuring dependence between random variables. Our approach extends the Maximum Mean Discrepancy to the copula of the joint distribution. We prove that this approach has several advantageous…
A framework named Copula Component Analysis (CCA) for blind source separation is proposed as a generalization of Independent Component Analysis (ICA). It differs from ICA which assumes independence of sources that the underlying components…
Frequency domain methods form a ubiquitous part of the statistical toolbox for time series analysis. In recent years, considerable interest has been given to the development of new spectral methodology and tools capturing dynamics in the…
In multivariate analysis, uncertainty arises from two sources: the marginal distributions of the variables and their dependence structure. Quantifying the dependence structure is crucial, as it provides valuable insights into the…