相关论文: Products, Abstractions and Inclusions of Causal Sp…

We describe the interface between measure theoretic probability and causal inference by constructing causal models on probability spaces within the potential outcomes framework. We find that measure theory provides a precise and instructive…

The notion of causal effect is fundamental across many scientific disciplines. Traditionally, quantitative researchers have studied causal effects at the level of variables; for example, how a certain drug dose (W) causally affects a…

Causality is a central concept in a wide range of research areas, yet there is still no universally agreed axiomatisation of causality. We view causality both as an extension of probability theory and as a study of \textit{what happens when…

We mathematically axiomatise the stochastics of counterfactuals, by introducing two related frameworks, called counterfactual probability spaces and counterfactual causal spaces, which we collectively term counterfactual spaces. They are,…

We introduce a class of variational principles on measure spaces which are causal in the sense that they generate a relation on pairs of points, giving rise to a distinction between spacelike and timelike separation. General existence…

Causality plays an important role in understanding intelligent behavior, and there is a wealth of literature on mathematical models for causality, most of which is focused on causal graphs. Causal graphs are a powerful tool for a wide range…

Causality among events is widely recognized as a most fundamental structure of spacetime, and causal sets have been proposed as discrete models of the latter in the context of quantum gravity theories, notably in the Causal Set Programme.…

Causality is a non-obvious concept that is often considered to be related to temporality. In this paper we present a number of past and present approaches to the definition of temporality and causality from philosophical, physical, and…

Over the past two decades, the rapid surge in data-intensive computational techniques for statistical modeling may have had the effect of diminishing the use of applied mathematics in causal scientific inquiry. In this paper, co-authored by…

We provide a unified operational framework for the study of causality, non-locality and contextuality, in a fully device-independent and theory-independent setting. We define causaltopes, our chosen portmanteau of "causal polytopes", for…

The moments of random variables are fundamental statistical measures for characterizing the shape of a probability distribution, encompassing metrics such as mean, variance, skewness, and kurtosis. Additionally, the product moments,…

Interventional causal models describe several joint distributions over some variables used to describe a system, one for each intervention setting. They provide a formal recipe for how to move between the different joint distributions and…

The possibility of non-causal signal propagation is examined for various theories of dense matter. This investigation requires a discussion of definitions of causality, together with interpretations of spacetime position. Specific examples…

We introduce and explore the notion of "spaces of input histories", a broad family of combinatorial objects which can be used to model input-dependent, dynamical causal order. We motivate our definition with reference to traditional partial…

Discussions on causal relations in real life often consider variables for which the definition of causality is unclear since the notion of interventions on the respective variables is obscure. Asking 'what qualifies an action for being an…

Statistical science (as opposed to mathematical statistics) involves far more than probability theory, for it requires realistic causal models of data generators - even for purely descriptive goals. Statistical decision theory requires more…

We analyze a definition of product of Banach spaces that is naturally associated by duality with an abstract notion of space of multiplication operators. This dual relation allows to understand several constructions coming from different…

Perhaps the most prominent current definition of (actual) causality is due to Halpern and Pearl. It is defined using causal models (also known as structural equations models). We abstract the definition, extracting its key features, so that…

We provide a unified operational framework for the study of causality, non-locality and contextuality, in a fully device-independent and theory-independent setting. Our work has its roots in the sheaf-theoretic framework for contextuality…

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…