Related papers: Measuring correlations between non-stationary seri…
The maximal correlation coefficient is a well-established generalization of the Pearson correlation coefficient for measuring non-linear dependence between random variables. It is appealing from a theoretical standpoint, satisfying…
Information criteria (IC) have been widely used in factor models to estimate an unknown number of latent factors. It has recently been shown that IC perform well in Common Correlated Effects (CCE) and related setups in selecting a set of…
We develop a method for the multifractal characterization of nonstationary time series, which is based on a generalization of the detrended fluctuation analysis (DFA). We relate our multifractal DFA method to the standard partition…
We introduce the Randomized Dependence Coefficient (RDC), a measure of non-linear dependence between random variables of arbitrary dimension based on the Hirschfeld-Gebelein-R\'enyi Maximum Correlation Coefficient. RDC is defined in terms…
We derive an analytical expression for a novel large-scale structure observable: the line correlation function. The line correlation function, which is constructed from the three-point correlation function of the phase of the density field,…
We describe two families of statistical tests to detect partial correlation in vectorial timeseries. The tests measure whether an observed timeseries Y can be predicted from a second series X, even after accounting for a third series Z…
Quantification of relations between measured variables of interest by statistical measures of dependence is a common step in analysis of climate data. The term "connectivity" is used in the network context including the study of complex…
Distance correlation is a recent extension of Pearson's correlation, that characterises general statistical independence between Euclidean-space-valued random variables, not only linear relations. This review delves into how and when…
In high-throughput data, dynamic correlation between genes, i.e. changing correlation patterns under different biological conditions, can reveal important regulatory mechanisms. Given the complex nature of dynamic correlation, and the…
Canonical correlation analysis (CCA) is a multivariate statistical method which describes the associations between two sets of variables. The objective is to find linear combinations of the variables in each data set having maximal…
The partial correlation coefficient is a commonly used measure to assess the conditional dependence between two random variables. We provide a thorough explanation of the partial copula, which is a natural generalization of the partial…
This article presents several alternatives to Pearson's correlation coefficient and many examples. In the samples where the rank in a discrete variable counts more than the variable values, the mixtures that we propose of Pearson's and…
In this paper, we propose a novel framework for non-stationary time-series analysis that replaces conventional correlation-based statistics with direct estimation of statistical dependence in the normalized joint density of input and target…
Modern regression analysis often involves responses and predictors taking values in the same or distinct metric spaces. To rank non-Euclidean heterogeneous predictors in regression by explanatory strength, analogous to the classical $R^2$,…
We show that the codifference is a useful tool in studying the ergodicity breaking and non-Gaussianity properties of stochastic time series. While the codifference is a measure of dependence that was previously studied mainly in the context…
This paper presents Deep Dynamic Probabilistic Canonical Correlation Analysis (D2PCCA), a model that integrates deep learning with probabilistic modeling to analyze nonlinear dynamical systems. Building on the probabilistic extensions of…
Recent work has sought to understand the behavior of neural networks by comparing representations between layers and between different trained models. We examine methods for comparing neural network representations based on canonical…
The sample correlation coefficient $R$ plays an important role in many statistical analyses. We study the moments of $R$ under the bivariate Gaussian model assumption, provide a novel approximation for its finite sample mean and connect it…
In this paper, we propose a novel Euclidean-distance-based coefficient, named differential distance correlation, to measure the strength of dependence between a random variable $ Y \in \mathbb{R} $ and a random vector $ \boldsymbol{X} \in…
The Pearson correlation coefficient is commonly used for quantifying the global level of degree-degree association in complex networks. Here, we use a probabilistic representation of the underlying network structure for assessing the…