Related papers: Manifold Properties from Causal Sets using Chains

Learning the dynamic causal structure of time series is a challenging problem. Most existing approaches rely on distributional or structural invariance to uncover underlying causal dynamics, assuming stationary or partially stationary…

The aim of this paper is to discuss a recent result which shows that probabilistic inference in the presence of (unknown) causal mechanisms can be tractable for models that have traditionally been viewed as intractable. This result was…

Feature selection is a crucial preprocessing step in data analytics and machine learning. Classical feature selection algorithms select features based on the correlations between predictive features and the class variable and do not attempt…

Causal discovery is the subfield of causal inference concerned with estimating the structure of cause-and-effect relationships in a system of interrelated variables, as opposed to quantifying the strength or describing the form of causal…

Casual structure can take the form of cone bundles on a manifold, more general local preorders on a topological space, or simplicial orientations implicit in a simplicial set. This note takes a triangulation of a conal manifold M to mean an…

Area metric manifolds emerge as a refinement of symplectic and metric geometry in four dimensions, where in numerous situations of physical interest they feature as effective matter backgrounds. In this article, this prompts us to identify…

We look more carefully at the modeling of causality using structural equations. It is clear that the structural equations can have a major impact on the conclusions we draw about causality. In particular, the choice of variables and their…

This paper considers inference of causal structure in a class of graphical models called "conditional DAGs". These are directed acyclic graph (DAG) models with two kinds of variables, primary and secondary. The secondary variables are used…

Contextuality is a non-classical behaviour that can be exhibited by quantum systems. It is increasingly studied for its relationship to quantum-over-classical advantages in informatic tasks. To date, it has largely been studied in…

We prove metric rigidity for complete manifolds supporting solutions of certain second order differential systems, thus extending classical works on a characterization of space-forms. In the route, we also discover new characterizations of…

Causality is one of the fundamental structures of spacetimes, determining the possible behaviour and propagation of physical information. Causal structure can be analysed through the various modal logics it induces. The modal logics for the…

The connection between contextuality and graph theory has led to many developments in the field. In particular, the sets of probability distributions in many contextuality scenarios can be described using well known convex sets from graph…

We define a new type of transformation for Lorentzian manifolds characterized by mapping every causal future-directed vector onto a causal future-directed vector. The set of all such transformations, which we call causal symmetries, has the…

In general relativity, the causal structure between events is dynamical, but it is definite and observer-independent; events are point-like and the membership of an event A in the future or past light-cone of an event B is an…

Causal graphs are widely used in software engineering to document and explore causal relationships. Though widely used, they may also be wildly misleading. Causal structures generated from SE data can be highly variable. This instability is…

We give a short historical review of early Kaluza-Klein theories. We study various causal structures on manifolds, especially those which cannot be described by a metric tensor with signature (+---). The smooth structure (atlas) on a…

We apply our earlier work on the higher-dimensional analogue of the Mumford conjecture to two questions. Inspired by work of Ebert we prove non-triviality of certain characteristic classes of bundles of smooth closed manifolds. Inspired by…

Scientists often use directed acyclic graphs (days) to model the qualitative structure of causal theories, allowing the parameters to be estimated from observational data. Two causal models are equivalent if there is no experiment which…

We discuss promising recent contributions on quantifying feature relevance using Shapley values, where we observed some confusion on which probability distribution is the right one for dropped features. We argue that the confusion is based…

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…