Related papers: Graphical Modelling in Genetics and Systems Biolog…

In this article, the notion of a mathematical model in science is attempted to be enlightened from several points of view. In particular, it is shown that mathematical models are introduced differently and used differently in different…

Graphs are widely used as a popular representation of the network structure of connected data. Graph data can be found in a broad spectrum of application domains such as social systems, ecosystems, biological networks, knowledge graphs, and…

In recent years, ideas from statistics and scientific computing have begun to interact in increasingly sophisticated and fruitful ways with ideas from computer science and the theory of algorithms to aid in the development of improved…

As data structures and mathematical objects used for complex systems modeling, hypergraphs sit nicely poised between on the one hand the world of network models, and on the other that of higher-order mathematical abstractions from algebra,…

Recent developments in Machine Learning approaches for modelling physical systems have begun to mirror the past development of numerical methods in the computational sciences. In this survey, we begin by providing an example of this with…

Geometric data analysis and learning has emerged as a distinct and rapidly developing research area, increasingly recognized for its effectiveness across diverse applications. At the heart of this field lies curvature, a powerful and…

The whole complex process to obtain a protein encoded by a gene is difficult to include in a mathematical model. There are many models for describing different aspects of a genetic network. Finding a better model is one of the most…

Graphs are commonly used in mathematics to represent some relationships between items. However, as simple objects, they sometimes fail to capture all relevant aspects of real-world data. To address this problem, we generalize them and model…

Graphs are a widely used paradigm for representing non-Euclidean data, with applications ranging from social network analysis to biomolecular prediction. While graph learning has achieved remarkable progress, real-world graph data presents…

This paper is a multidisciplinary review of empirical, statistical learning from a graphical model perspective. Well-known examples of graphical models include Bayesian networks, directed graphs representing a Markov chain, and undirected…

An emerging way of tackling the dimensionality issues arising in the modeling of a multivariate process is to assume that the inherent data structure can be captured by a graph. Nevertheless, though state-of-the-art graph-based methods have…

Machine learning methods can detect complex relationships between variables, but usually do not exploit domain knowledge. This is a limitation because in many scientific disciplines, such as systems biology, domain knowledge is available in…

Graph Neural Networks (GNN) have recently gained popularity in the forecasting domain due to their ability to model complex spatial and temporal patterns in tasks such as traffic forecasting and region-based demand forecasting. Most of…

Recent studies have shown great promise in applying graph neural networks for multivariate time series forecasting, where the interactions of time series are described as a graph structure and the variables are represented as the graph…

Graphical causal models are an important tool for knowledge discovery because they can represent both the causal relations between variables and the multivariate probability distributions over the data. Once learned, causal graphs can be…

Clustering multivariate data is a pervasive task in many applied problems, particularly in social studies and life science. Model-based approaches to clustering rely on mixture models, where each mixture component corresponds to the kernel…

Recently there has been increased interest in fitting generative graph models to real-world networks. In particular, Bl\"asius et al. have proposed a framework for systematic evaluation of the expressivity of random graph models. We extend…

Time series forecasting is an extensively studied subject in statistics, economics, and computer science. Exploration of the correlation and causation among the variables in a multivariate time series shows promise in enhancing the…

Causal processes in biomedicine may contain cycles, evolve over time or differ between populations. However, many graphical models cannot accommodate these conditions. We propose to model causation using a mixture of directed cyclic graphs…

Understanding the mechanisms of interactions within cells, tissues, and organisms is crucial to driving developments across biology and medicine. Mathematical modeling is an essential tool for simulating biological systems and revealing…