Related papers: Information-Theoretic Measures on Lattices for Hig…
Networks can describe the structure of a wide variety of complex systems by specifying which pairs of entities in the system are connected. While such pairwise representations are flexible, they are not necessarily appropriate when the…
This paper revisits building machine learning algorithms that involve interactions between entities, such as those between financial assets in an actively managed portfolio, or interactions between users in a social network. Our goal is to…
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…
The information that two random variables $Y$, $Z$ contain about a third random variable $X$ can have aspects of shared information (contained in both $Y$ and $Z$), of complementary information (only available from $(Y,Z)$ together) and of…
Information Theory provides a fundamental basis for analysis, and for a variety of subsequent methodological approaches, in relation to uncertainty quantification. The transversal character of concepts and derived results justifies its…
Experts do not always feel very, comfortable when they have to give precise numerical estimations of certainty degrees. In this paper we present a qualitative approach which allows for attaching partially ordered symbolic grades to logical…
One of the fundamental steps toward understanding a complex system is identifying variation at the scale of the system's components that is most relevant to behavior on a macroscopic scale. Mutual information provides a natural means of…
Many scientific applications involve mixed spatially indexed outcomes of heterogeneous types that are driven by shared latent mechanisms. Modeling such data is challenging due to complex, nonlinear, and potentially nonstationary spatial…
Inferring and comparing complex, multivariable probability density functions is fundamental to problems in several fields, including probabilistic learning, network theory, and data analysis. Classification and prediction are the two faces…
We present a new method to describe the kinetics of driven lattice gases with particle-particle interactions beyond hard-core exclusions. The method is based on the time-dependent density functional theory for lattice systems and allows one…
Human actions often involve complex interactions across several inter-related objects in the scene. However, existing approaches to fine-grained video understanding or visual relationship detection often rely on single object representation…
Williams and Beer (2010) proposed a nonnegative mutual information decomposition, based on the construction of redundancy lattices, which allows separating the information that a set of variables contains about a target variable into…
The knowledge of transitions between regular, laminar or chaotic behavior is essential to understand the underlying mechanisms behind complex systems. While several linear approaches are often insufficient to describe such processes, there…
This paper is concerned with the joint analysis of multivariate mixed-type spatial data, where some components are point processes and some are of lattice-type by nature. After a survey of statistical methods for marked spatial point and…
In many machine learning systems that jointly learn from multiple modalities, a core research question is to understand the nature of multimodal interactions: how modalities combine to provide new task-relevant information that was not…
Outcome labeling ambiguity and subjectivity are ubiquitous in real-world datasets. While practitioners commonly combine ambiguous outcome labels for all data points (instances) in an ad hoc way to improve the accuracy of multi-class…
Inferring the laws of interaction between particles and agents in complex dynamical systems from observational data is a fundamental challenge in a wide variety of disciplines. We propose a non-parametric statistical learning approach to…
The machine learning of lattice operators has three possible bottlenecks. From a statistical standpoint, it is necessary to design a constrained class of operators based on prior information with low bias, and low complexity relative to the…
Lattices are a popular field of study in mathematical research, but also in more practical areas like cryptology or multiple-input/multiple-output (MIMO) transmission. In mathematical theory, most often lattices over real numbers are…
Data generated from a system of interest typically consists of measurements from an ensemble of subjects across multiple response and covariate features, and is naturally represented by one response-matrix against one covariate-matrix.…