Related papers: Intrinsic Universality of Causal Graph Dynamics

In this thesis we investigate the importance of causality in non-perturbative approaches to quantum gravity. Firstly, causal sets are introduced as a simple kinematical model for causal geometry. It is shown how causal sets could account…

Causal discovery is a fundamental problem with applications spanning various areas in science and engineering. It is well understood that solely using observational data, one can only orient the causal graph up to its Markov equivalence…

Causal structure learning with data from multiple contexts carries both opportunities and challenges. Opportunities arise from considering shared and context-specific causal graphs enabling to generalize and transfer causal knowledge across…

Causal discovery, the task of inferring causal structure from data, has the potential to uncover mechanistic insights from biological experiments, especially those involving perturbations. However, causal discovery algorithms over larger…

Based on a recent development in the area of error control coding, we introduce the notion of convolutional factor graphs (CFGs) as a new class of probabilistic graphical models. In this context, the conventional factor graphs are referred…

Understanding causal relationships among the variables of a system is paramount to explain and control its behavior. For many real-world systems, however, the true causal graph is not readily available and one must resort to predictions…

This paper builds on the connection between graph neural networks and traditional dynamical systems. We propose continuous graph neural networks (CGNN), which generalise existing graph neural networks with discrete dynamics in that they can…

Graphs are fundamental data structures which concisely capture the relational structure in many important real-world domains, such as knowledge graphs, physical and social interactions, language, and chemistry. Here we introduce a powerful…

Starting from certain causality conditions and a discrete form of general covariance, we derive a very general family of classically stochastic, sequential growth dynamics for causal sets. The resulting theories provide a relatively…

Symbolic dynamics is partly the study of walks in a directed graph. By a walk, here we mean a morphism to the graph from the Cayley graph of the monoid of non-negative integers. Sets of these walks are also important in other areas, such as…

In many problems, the measured variables (e.g., image pixels) are just mathematical functions of the latent causal variables (e.g., the underlying concepts or objects). For the purpose of making predictions in changing environments or…

The method of four-dimensional Causal Dynamical Triangulations provides a background-independent definition of the sum over geometries in quantum gravity, in the presence of a positive cosmological constant. We present the evidence…

We present a categorical framework for relating causal models that represent the same system at different levels of abstraction. We define a causal abstraction as natural transformations between appropriate Markov functors, which concisely…

Graph rewrite formalisms are a powerful approach to modeling complex molecular systems. They capture the intrinsic concurrency of molecular interactions, thereby enabling a formal notion of mechanism (a partially ordered set of events) that…

Causal Bayesian networks are 'causal' models since they make predictions about interventional distributions. To connect such causal model predictions to real-world outcomes, we must determine which actions in the world correspond to which…

Understanding causal mechanisms across different populations is essential for designing effective public health interventions. Recently, difference graphs have been introduced as a tool to visually represent causal variations between two…

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…

The formalism of Causal Dynamical Triangulations (CDT) attempts to provide a non-perturbative regularization of quantum gravity, viewed as an ordinary quantum field theory. In two dimensions one can solve the lattice theory analytically and…

Parametric causal modelling techniques rarely provide functionality for counterfactual estimation, often at the expense of modelling complexity. Since causal estimations depend on the family of functions used to model the data, simplistic…

Graphs are common mathematical structures that are visual and intuitive. They constitute a natural and seamless way for system modelling in science, engineering and beyond, including computer science, biology, business process modelling,…