Related papers: A simple measure of conditional dependence
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…
The maximal information coefficient (MIC), which measures the amount of dependence between two variables, is able to detect both linear and non-linear associations. However, computational cost grows rapidly as a function of the dataset…
Motivated by applications in biological science, we propose a novel test to assess the conditional mean dependence of a response variable on a large number of covariates. Our procedure is built on the martingale difference divergence…
Following our previous work on copula-based nonsymmetric dependence measures, we introduce similar measures for discrete random variables. The measures cover the range between two extremes: independence and complete dependence, which take…
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…
Independence screening is a powerful method for variable selection for `Big Data' when the number of variables is massive. Commonly used independence screening methods are based on marginal correlations or variations of it. In many…
This paper proposes new tests of conditional independence of two random variables given a single-index involving an unknown finite-dimensional parameter. The tests employ Rosenblatt transforms and are shown to be distribution-free while…
Measuring and quantifying dependencies between random variables (RV's) can give critical insights into a data-set. Typical questions are: `Do underlying relationships exist?', `Are some variables redundant?', and `Is some target variable…
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…
A central goal of probabilistic programming languages (PPLs) is to separate modelling from inference. However, this goal is hard to achieve in practice. Users are often forced to re-write their models in order to improve efficiency of…
This paper develops a conditional independence (CI) test from a conditional density ratio (CDR) for weakly dependent data. The main contribution is presenting a closed-form expression for the estimated conditional density ratio function…
One of the common obstacles for learning causal models from data is that high-order conditional independence (CI) relationships between random variables are difficult to estimate. Since CI tests with conditioning sets of low order can be…
This article deals with the problem of testing conditional independence between two random vectors ${\bf X}$ and ${\bf Y}$ given a confounding random vector ${\bf Z}$. Several authors have considered this problem for multivariate data.…
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…
We formulate and analyze a graphical model selection method for inferring the conditional independence graph of a high-dimensional nonstationary Gaussian random process (time series) from a finite-length observation. The observed process…
We propose a method for inferring the conditional independence graph (CIG) of a high-dimensional Gaussian vector time series (discrete-time process) from a finite-length observation. By contrast to existing approaches, we do not rely on a…
Consider a random sample $X_1 , X_2 , ..., X_n$ drawn independently and identically distributed from some known sampling distribution $P_X$. Let $X_{(1)} \le X_{(2)} \le ... \le X_{(n)}$ represent the order statistics of the sample. The…
Conditional independence testing is an important problem, especially in Bayesian network learning and causal discovery. Due to the curse of dimensionality, testing for conditional independence of continuous variables is particularly…
Independence and Conditional Independence (CI) are two fundamental concepts in probability and statistics, which can be applied to solve many central problems of statistical inference. There are many existing independence and CI measures…
A seminal result in the ICA literature states that for $AY = \varepsilon$, if the components of $\varepsilon$ are independent and at most one is Gaussian, then $A$ is identified up to sign and permutation of its rows (Comon, 1994). In this…