Related papers: Distance-based Chatterjee correlation: a new gener…
Recently established, directed dependence measures for pairs $(X,Y)$ of random variables build upon the natural idea of comparing the conditional distributions of $Y$ given $X=x$ with the marginal distribution of $Y$. They assign pairs…
This paper tackles the challenge of estimating correlations between higher-level biological variables (e.g., proteins and gene pathways) when only lower-level measurements are directly observed (e.g., peptides and individual genes).…
While researchers commonly use the bootstrap for statistical inference, many of us have realized that the standard bootstrap, in general, does not work for Chatterjee's rank correlation. In this paper, we provide proof of this issue under…
The marginal correlation between two variables is a measure of their linear dependence. The two original variables need not interact directly, because marginal correlation may arise from the mediation of other variables in the system. The…
We consider a classical problem in choice theory -- vote aggregation -- using novel distance measures between permutations that arise in several practical applications. The distance measures are derived through an axiomatic approach, taking…
The magnitude of Pearson correlation between two scalar random variables can be visually judged from the two-dimensional scatter plot of an independent and identically distributed sample drawn from the joint distribution of the two…
Generalized dimensions of multifractal measures are usually seen as static objects, related to the scaling properties of suitable partition functions, or moments of measures of cells. When these measures are invariant for the flow of a…
The intraclass correlation coefficient (ICC) is a classical index of measurement reliability. With the advent of new and complex types of data for which the ICC is not defined, there is a need for new ways to assess reliability. To meet…
Inferring linear relationships lies at the heart of many empirical investigations. A measure of linear dependence should correctly evaluate the strength of the relationship as well as qualify whether it is meaningful for the population.…
Not a matter of serious contention, Pearson's correlation coefficient is still the most important statistical association measure. Restricted to just two variables, this measure sometimes doesn't live up to users' needs and expectations.…
Comparing the functional behavior of neural network models, whether it is a single network over time or two (or more networks) during or post-training, is an essential step in understanding what they are learning (and what they are not),…
Analyzing correlation between variables is often both the tool and the goal of modern science. A crucial question is whether the correlation between two variables is a direct correlation or only an indirect correlation through a confounder.…
Distributional regression is extended to Gaussian response vectors of dimension greater than two by parameterizing the covariance matrix $\Sigma$ of the response distribution using the entries of its Cholesky decomposition. The more common…
Sensitivity analysis is an important tool used in many domains of computational science to either gain insight into the mathematical model and interaction of its parameters or study the uncertainty propagation through the input-output…
We prove that a suitably de-biased version of Chatterjee's rank correlation based on i.i.d. copies of a random vector $(X,Y)$ is asymptotically normal whenever $Y$ is not almost surely constant. No further conditions on the joint…
Explainable artificial intelligence promises to yield insights into relevant features, thereby enabling humans to examine and scrutinize machine learning models or even facilitating scientific discovery. Considering the widespread technique…
This paper derives new results for the analysis of nonlinear systems by extending contraction theory in the framework of vector distances. A new tool, vector contraction analysis utilizing a notion of the vector-valued norm which evidently…
In this paper, we deal with the problem of inferring causal directions when the data is on discrete domain. By considering the distribution of the cause $P(X)$ and the conditional distribution mapping cause to effect $P(Y|X)$ as independent…
The discovery of causal relationships is a fundamental problem in science and medicine. In recent years, many elegant approaches to discovering causal relationships between two variables from observational data have been proposed. However,…
The use of empirical characteristic functions for inference problems, including estimation in some special parametric settings and testing for goodness of fit, has a long history dating back to the 70s (see for example, Feuerverger and…