Related papers: Interaction Measures, Partition Lattices and Kerne…

Understanding what kinds of cooperative structures deep neural networks (DNNs) can represent remains a fundamental yet insufficiently understood problem. In this work, we treat interactions as the fundamental units of such structure and…

Measuring and testing dependence between complex objects is of great importance in modern statistics. Most existing work relied on the distance between random variables, which inevitably required the moment conditions to guarantee the…

We propose a general framework to extract microscopic interactions from raw configurations with deep neural networks. The approach replaces the modeling Hamiltonian by the neural networks, in which the interaction is encoded. It can be…

Information diffusion on networks is an important concept in network science observed in many situations such as information spreading and rumor controlling in social networks, disease contagion between individuals, cascading failures in…

Species interactions (ranging from direct predator prey relationships to indirect effects mediated by the environment) are central to ecosystem balance and biodiversity. While empirical methods for measuring these interactions exist, their…

Qualitative interactions occur when a treatment effect or measure of association varies in sign by sub-population. Of particular interest in many biomedical settings are absence/presence qualitative interactions, which occur when an effect…

We consider the testing of all pairwise interactions in a two-class problem with many features. We devise a hierarchical testing framework that considers an interaction only when one or more of its constituent features has a nonzero main…

The effective residual interaction for a system of hadrons has a long tradition in theoretical physics. It has been mostly addressed in terms of boson exchange models. The aim of this review is to describe approaches based on lattice field…

Measurements of systems taken along a continuous functional dimension, such as time or space, are ubiquitous in many fields, from the physical and biological sciences to economics and engineering.Such measurements can be viewed as…

Sequential measurements of non-commuting observables produce order effects that are well-known in quantum physics. But their conceptual basis, a significant measurement interaction, is relevant for far more general situations. We argue that…

We introduce a family of random matrices where correlations between matrix elements are induced via interaction-derived Boltzmann factors. Varying these yields access to different ensembles. We find a universal scaling behavior of the…

The hysteresis curves of systems composed of small interacting magnetic particles, regularly placed on stacked layers, are obtained with Monte Carlo simulations. The remanence as a function of temperature, in interacting systems, presents a…

Finding interactions between variables in large and high-dimensional datasets is often a serious computational challenge. Most approaches build up interaction sets incrementally, adding variables in a greedy fashion. The drawback is that…

Finding statistically significant high-order interaction features in predictive modeling is important but challenging task. The difficulty lies in the fact that, for a recent applications with high-dimensional covariates, the number of…

In this paper, we tackle a critical issue in nonparametric inference for systems of interacting particles on Riemannian manifolds: the identifiability of the interaction functions. Specifically, we define the function spaces on which the…

Interacting systems are ubiquitous in nature and engineering, ranging from particle dynamics in physics to functionally connected brain regions. These interacting systems can be modeled by graphs where edges correspond to the interactions…

In this paper, we consider the statistical analysis of a protein interaction network. We propose a Bayesian model that uses a hierarchy of probabilistic assumptions about the way proteins interact with one another in order to: (i) identify…

In many contexts it is extremely costly to perform enough high quality experimental measurements to accurately parameterize a predictive quantitative model. However, it is often much easier to carry out large numbers of experiments that…

While including pairwise interactions in a regression model can better approximate response surface, fitting such an interaction model is a well-known difficult problem. In particular, analyzing contemporary high-dimensional datasets often…

Interacting agent and particle systems are extensively used to model complex phenomena in science and engineering. We consider the problem of learning interaction kernels in these dynamical systems constrained to evolve on Riemannian…