Related papers: Interaction Measures, Partition Lattices and Kerne…

Kernel-based hypothesis tests offer a flexible, non-parametric tool to detect high-order interactions in multivariate data, beyond pairwise relationships. Yet the scalability of such tests is limited by the computationally demanding…

Traditional measures based solely on pairwise associations often fail to capture the complex statistical structure of multivariate data. Existing approaches for identifying information shared among $d>3$ variables are frequently…

Dynamic graphs are rife with higher-order interactions, such as co-authorship relationships and protein-protein interactions in biological networks, that naturally arise between more than two nodes at once. In spite of the ubiquitous…

Pairwise interactions between perturbations to a system can provide evidence for the causal dependencies of the underlying underlying mechanisms of a system. When observations are low dimensional, hand crafted measurements, detecting…

Dynamical systems across many disciplines are modeled as interacting particles or agents, with interaction rules that depend on a very small number of variables (e.g. pairwise distances, pairwise differences of phases, etc...), functions of…

To date, testing interactions in high dimensions has been a challenging task. Existing methods often have issues with sensitivity to modeling assumptions and heavily asymptotic nominal p-values. To help alleviate these issues, we propose a…

We consider stochastic systems of interacting particles or agents, with dynamics determined by an interaction kernel which only depends on pairwise distances. We study the problem of inferring this interaction kernel from observations of…

The network representation is becoming increasingly popular for the description of cardiovascular interactions based on the analysis of multiple simultaneously collected variables. However, the traditional methods to assess network links…

Multivariate time series data that capture the temporal evolution of interconnected systems are ubiquitous in diverse areas. Understanding the complex relationships and potential dependencies among co-observed variables is crucial for the…

Complex systems, such as economic, social, biological, and ecological systems, usually feature interactions not only between pairwise entities but also among three or more entities. These multi-entity interactions are known as higher-order…

Modeling the complex interactions of systems of particles or agents is a fundamental scientific and mathematical problem that is studied in diverse fields, ranging from physics and biology, to economics and machine learning. In this work,…

We introduce a method for learning pairwise interactions in a manner that satisfies strong hierarchy: whenever an interaction is estimated to be nonzero, both its associated main effects are also included in the model. We motivate our…

Identifying how dependence relationships vary across different conditions plays a significant role in many scientific investigations. For example, it is important for the comparison of biological systems to see if relationships between…

In recent years, networks with higher-order interactions have emerged as a powerful tool to model complex systems. Comparing these higher-order systems remains however a challenge. Traditional similarity measures designed for pairwise…

In this study, we tested the interaction effect of multimodal datasets using a novel method called the kernel method for detecting higher order interactions among biologically relevant mulit-view data. Using a semiparametric method on a…

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…

Many complex systems often contain interactions between more than two nodes, known as higher-order interactions, which can change the structure of these systems in significant ways. Researchers often assume that all interactions paint a…

A wide variety of complex systems are characterized by interactions of different types involving varying numbers of units. Multiplex hypergraphs serve as a tool to describe such structures, capturing distinct types of higher-order…

Systems of interacting particles or agents have wide applications in many disciplines such as Physics, Chemistry, Biology and Economics. These systems are governed by interaction laws, which are often unknown: estimating them from…

Logistic Regression (LR) is a widely used statistical method in empirical binary classification studies. However, real-life scenarios oftentimes share complexities that prevent from the use of the as-is LR model, and instead highlight the…