Related papers: Manifold Properties from Causal Sets using Chains

Dataflow computing was shown to bring significant benefits to multiple niches of systems engineering and has the potential to become a general-purpose paradigm of choice for data-driven application development. One of the characteristic…

We investigate the behavior of small subsets of causal sets that approximate Minkowski space in three, four, and five dimensions, and show that their effective dimension decreases smoothly at small distances. The details of the short…

Structural-equations models (SEMs) are perhaps the most commonly used framework for modeling causality. However, as we show, naively extending this framework to infinitely many variables, which is necessary, for example, to model dynamical…

Bayesian networks can be used to extract explanations about the observed state of a subset of variables. In this paper, we explicate the desiderata of an explanation and confront them with the concept of explanation proposed by existing…

Causal set theory provides a model of discrete spacetime in which spacetime events are represented by elements of a causal set---a locally finite, partially ordered set in which the partial order represents the causal relationships between…

Causal reasoning provides a language to ask important interventional and counterfactual questions beyond purely statistical association. In medical imaging, for example, we may want to study the causal effect of genetic, environmental, or…

Causal understanding is important in many disciplines of science and engineering, where we seek to understand how different factors in the system causally affect an experiment or situation and pave a pathway towards creating effective or…

Causal structures give us a way to understand the origin of observed correlations. These were developed for classical scenarios, but quantum mechanical experiments necessitate their generalisation. Here we study causal structures in a broad…

The framework of causal models provides a principled approach to causal reasoning, applied today across many scientific domains. Here we present this framework in the language of string diagrams, interpreted formally using category theory.…

We explore to what extent one may hope to preserve geometric properties of three dimensional manifolds with lower scalar curvature bounds under Gromov-Hausdorff and Intrinsic Flat limits. We introduce a new construction, called sewing, of…

We investigate the curves in the complex plane which are generated by sequences of real numbers being the lifts of the points on the orbit of an orientation preserving circle homeomorphism. Geometrical properties of these curves such as…

We study identifiability in continuous-time linear stationary stochastic differential equations with known causal structure. Unlike existing approaches, we relax the assumption of a known diffusion matrix, thereby respecting the model's…

The rules in a shape grammar apply in terms of embedding to take advantage of the parts that emerge visually in the appearance of shapes. While the shapes are kept unanalyzed as a computation moves forward, part-structures for shapes can be…

Structured prediction provides a general framework to deal with supervised problems where the outputs have semantically rich structure. While classical approaches consider finite, albeit potentially huge, output spaces, in this paper we…

Foundations of the formal series $*$ -- calculus in deformation quantisation are discussed. Several classes of continuous linear functionals over algebras applied in classical and quantum physics are introduced. The notion of nonnegativity…

Causality defines the relationship between cause and effect. In multivariate time series field, this notion allows to characterize the links between several time series considering temporal lags. These phenomena are particularly important…

We propose Universal Causality, an overarching framework based on category theory that defines the universal property that underlies causal inference independent of the underlying representational formalism used. More formally, universal…

Causal inference is a science with multi-disciplinary evolution and applications. On the one hand, it measures effects of treatments in observational data based on experimental designs and rigorous statistical inference to draw causal…

We review several competing chaining methods to estimate the supremum, the diameter of the range or the modulus of continuity of a stochastic process in terms of tail bounds of their two-dimensional distributions. Then we show how they can…

Classical machine learning techniques often struggle with overfitting and unreliable predictions when exposed to novel conditions. Introducing causality into the modelling process offers a promising way to mitigate these challenges by…