Related papers: Conditional Independence, Conditional Mean Indepen…
We consider two variables that are related to each other by an invertible function. While it has previously been shown that the dependence structure of the noise can provide hints to determine which of the two variables is the cause, we…
We consider settings in which the data of interest correspond to pairs of ordered times, e.g, the birth times of the first and second child, the times at which a new user creates an account and makes the first purchase on a website, and the…
A prescription is presented for a new and practical correlation coefficient, $\phi_K$, based on several refinements to Pearson's hypothesis test of independence of two variables. The combined features of $\phi_K$ form an advantage over…
Given observations from a stationary time series, permutation tests allow one to construct exactly level $\alpha$ tests under the null hypothesis of an i.i.d. (or, more generally, exchangeable) distribution. On the other hand, when the null…
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…
Bell-type criteria of contextuality/nonlocality can be derived without any falsifiable assumptions, such as context-independent mapping (or local causality), free choice, or no-fine-tuning. This is achieved by deriving Bell-type criteria…
In dynamical systems composed of interacting parts, conditional exponents, conditional exponent entropies and cylindrical entropies are shown to be well defined ergodic invariants which characterize the dynamical selforganization and…
In this paper an autoregressive time series model with conditional heteroscedasticity is considered, where both conditional mean and conditional variance function are modeled nonparametrically. A test for the model assumption of…
This study demonstrates the existence of a testable condition for the identification of the causal effect of a treatment on an outcome in observational data, which relies on two sets of variables: observed covariates to be controlled for…
The goal of this paper is to integrate the notions of stochastic conditional independence and variation conditional independence under a more general notion of extended conditional independence. We show that under appropriate assumptions…
We provide a set of copulas that can be interpreted as having the negative extreme dependence. This set of copulas is interesting because it coincides with countermonotonic copula for a bivariate case, and more importantly, is shown to be…
Concerning bivariate least squares linear regression, the classical approach pursued for functional models in earlier attempts is reviewed using a new formalism in terms of deviation (matrix) traces. Within the framework of classical error…
In data analysis problems where we are not able to rely on distributional assumptions, what types of inference guarantees can still be obtained? Many popular methods, such as holdout methods, cross-validation methods, and conformal…
In spatio-temporal analysis, we often record data at specific time intervals but with varying spatial locations between these timepoints. We propose a conditional model to analyze such spatio-temporal data that accommodates the dependencies…
Conditional probabilities are a core concept in machine learning. For example, optimal prediction of a label $Y$ given an input $X$ corresponds to maximizing the conditional probability of $Y$ given $X$. A common approach to inference tasks…
Independence testing plays a central role in statistical and causal inference from observational data. Standard independence tests assume that the data samples are independent and identically distributed (i.i.d.) but that assumption is…
We introduce a nonresponse mechanism for multivariate missing data in which each study variable and its nonresponse indicator are conditionally independent given the remaining variables and their nonresponse indicators. This is a…
It has been postulated that a good representation is one that disentangles the underlying explanatory factors of variation. However, it remains an open question what kind of training framework could potentially achieve that. Whereas most…
Is it possible to define a coefficient of correlation which is (a) as simple as the classical coefficients like Pearson's correlation or Spearman's correlation, and yet (b) consistently estimates some simple and interpretable measure of the…
Consider a stationary real-valued time series $\{X_n\}_{n=0}^{\infty}$ with a priori unknown distribution. The goal is to estimate the conditional expectation $E(X_{n+1}|X_0,..., X_n)$ based on the observations $(X_0,..., X_n)$ in a…