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Building upon the Chatterjee correlation (2021: J. Am. Stat. Assoc. 116, p2009) for two real-valued variables, this study introduces a generalized measure of directed association between two vector variables, real or complex-valued, and of…

Differential equations are a ubiquitous tool to study dynamics, ranging from physical systems to complex systems, where a large number of agents interact through a graph with non-trivial topological features. Data-driven approximations of…

In statistical classification and machine learning, as well as in social and other sciences, a number of measures of association have been proposed for assessing and comparing individual classifiers, raters, as well as their groups. In this…

Measuring the dependence of data plays a central role in statistics and machine learning. In this work, we summarize and generalize the main idea of existing information-theoretic dependence measures into a higher-level perspective by the…

Before new clinical measurement methods are implemented in clinical practice, it must be confirmed whether their results are equivalent to those of existing methods. The agreement of the trend between these methods is evaluated using the…

This paper proposes a novel framework to test for slope heterogeneity between time-varying coefficients in panel data models. Our test not only allows us to detect whether the coefficient functions are the same across all units or not, but…

The concept of Entropy plays a key role in Information Theory, Statistics, and Machine Learning.This paper introduces a new entropy measure, called the t-entropy, which exploits the concavity of the inverse-tan function. We analytically…

Multivariate spatial field data are increasingly common and whose modeling typically relies on building cross-covariance functions to describe cross-process relationships. An alternative viewpoint is to model the matrix of spectral…

Recent research in causal inference under network interference has explored various experimental designs and estimation techniques to address this issue. However, existing methods, which typically rely on single experiments, often reach a…

We adapt Higher Criticism (HC) to the comparison of two frequency tables which may -- or may not -- exhibit moderate differences between the tables in some unknown, relatively small subset out of a large number of categories. Our analysis…

In this paper we study the integrals of fractional parts of given functions, and develop some new tools to understand the behaviour of prime differences. We demonstrate how simply some seemingly difficult conjectures related to prime…

Correlated data are ubiquitous in today's data-driven society. While regression models for analyzing means and variances of responses of interest are relatively well-developed, the development of these models for analyzing the correlations…

Heterogeneity is a hallmark of complex diseases. Regression-based heterogeneity analysis, which is directly concerned with outcome-feature relationships, has led to a deeper understanding of disease biology. Such an analysis identifies the…

Classic measures of graph centrality capture distinct aspects of node importance, from the local (e.g., degree) to the global (e.g., closeness). Here we exploit the connection between diffusion and geometry to introduce a multiscale…

Linear regression models depend directly on the design matrix and its properties. Techniques that efficiently estimate model coefficients by partitioning rows of the design matrix are increasingly popular for large-scale problems because…

Agreement coefficients provide a fundamental framework for quantifying the concordance between two or more measurement methods applied to the same continuous variable. Unlike correlation, which measures the strength of a linear…

Network analysis has emerged as a key technique in communication studies, economics, geography, history and sociology, among others. A fundamental issue is how to identify key nodes, for which purpose a number of centrality measures have…

Categorical data are common in educational and social science research; however, methods for its analysis are generally not covered in introductory statistics courses. This chapter overviews fundamental concepts and methods in categorical…

It is an important inferential problem to test no association between two binary variables based on data. Tests based on the sample odds ratio are commonly used. We bring in a competing test based on the Pearson correlation coefficient. In…

Through recognizing causal subgraphs, causal graph learning (CGL) has risen to be a promising approach for improving the generalizability of graph neural networks under out-of-distribution (OOD) scenarios. However, the empirical successes…