Related papers: The Locally Gaussian Partial Correlation
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…
We propose a score test for dependence predictability in conditional copulas that is robust to temporal instabilities. Our semiparametric procedure accommodates flexible dynamics in the marginal processes and remains agnostic about the…
In this paper we propose and study a class of simple, nonparametric, yet interpretable measures of conditional dependence between two random variables $Y$ and $Z$ given a third variable $X$, all taking values in general topological spaces.…
The dependencies of the lagged (Pearson) correlation function on the coefficients of multivariate autoregressive models are interpreted in the framework of time series graphs. Time series graphs are related to the concept of Granger…
Distance correlation is a measure of dependence between two paired random vectors or matrices of arbitrary, not necessarily equal, dimensions. Unlike Pearson correlation, the population distance correlation coefficient is zero if and only…
Understanding and developing a correlation measure that can detect general dependencies is not only imperative to statistics and machine learning, but also crucial to general scientific discovery in the big data age. In this paper, we…
Detecting conditional independencies plays a key role in several statistical and machine learning tasks, especially in causal discovery algorithms. In this study, we introduce LCIT (Latent representation based Conditional Independence…
The statistical dependencies which independent component analysis (ICA) cannot remove often provide rich information beyond the linear independent components. It would thus be very useful to estimate the dependency structure from data.…
In this paper, we revisit the notion of partial copula, originally introduced to test conditional independence, highlighting its capability to represent the dependence between two random variables after removing their dependence with a…
Using the linear Gaussian latent variable model as a starting point we relax some of the constraints it imposes by deriving a nonparametric latent feature Gaussian variable model. This model introduces additional discrete latent variables…
This paper examines asymmetric and time-varying dependency structures between financial returns, using a novel approach consisting of a combination of regime-switching models and the local Gaussian correlation (LGC). We propose an LGC-based…
We describe various sets of conditional independence relationships, sufficient for qualitatively comparing non-vanishing squared partial correlations of a Gaussian random vector. These sufficient conditions are satisfied by several…
Local causal discovery is of great practical significance, as there are often situations where the discovery of the global causal structure is unnecessary, and the interest lies solely on a single target variable. Most existing local…
In Gaussian graphical models, conditional independence and partial correlations are natural inferential targets for understanding direct relationships in multivariate data. No comparable framework exists for spatial processes, where…
We propose new statistical tests, in high-dimensional settings, for testing the independence of two random vectors and their conditional independence given a third random vector. The key idea is simple, i.e., we first transform each…
Conditional local independence is an asymmetric independence relation among continuous time stochastic processes. It describes whether the evolution of one process is directly influenced by another process given the histories of additional…
It has been recently shown in Jaworski, P., Jelito, D. and Pitera, M. (2024), 'A note on the equivalence between the conditional uncorrelation and the independence of random variables', Electronic Journal of Statistics 18(1), that one can…
Measuring conditional dependence is an important topic in statistics with broad applications including graphical models. Under a factor model setting, a new conditional dependence measure based on projection is proposed. The corresponding…
Longitudinal and survival sub-models are two building blocks for joint modelling of longitudinal and time to event data. Extensive research indicates separate analysis of these two processes could result in biased outputs due to their…
We present a novel data-oriented statistical framework that assesses the presumed Gaussian dependence structure in a pairwise setting. This refers to both multivariate normality and normal copula goodness-of-fit testing. The proposed test…