Related papers: A manifestly covariant framework for causal set dy…

A key challenge in causal inference from observational studies is the identification and estimation of causal effects in the presence of unmeasured confounding. In this paper, we introduce a novel approach for causal inference that…

This note considers the maximal positively invariant set for polynomial discrete time dynamics subject to constraints specified by a basic semialgebraic set. The note utilizes a relatively direct, but apparently overlooked, fact stating…

Causal set theory is a discrete model of spacetime that retains a notion of causal structure. We understand how to construct causal sets that approximate a given spacetime, but most causal sets are not at all manifold-like, and must be…

This paper investigates the structure of generic motives and their implications for the motivic cohomology of fields. Originating in Voevodsky's theory of motives and related to Beilinson's vision of a motivic $t$-structure, generic motives…

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.…

Real-world learning tasks often encounter uncertainty due to covariate shift and noisy or inconsistent labels. However, existing robust learning methods merge these effects into a single distributional uncertainty set. In this work, we…

In this short note we provide an analytical formula for the conditional covariance matrices of the elliptically distributed random vectors, when the conditioning is based on the values of any linear combination of the marginal random…

Causal discovery procedures aim to deduce causal relationships among variables in a multivariate dataset. While various methods have been proposed for estimating a single causal model or a single equivalence class of models, less attention…

We introduce a persistence-type invariant for finite weighted graphs based on combinatorial multivector dynamics. For each threshold parameter, a relation matrix determines a graph multivector field, whose induced directed dynamics admits a…

We fully develop the concept of causal symmetry introduced in Class. Quant. Grav. 20 (2003) L139. A causal symmetry is a transformation of a Lorentzian manifold (V,g) which maps every future-directed vector onto a future-directed vector. We…

We present groupoid morphisms as an algebraic structure for nonautonomous dynamics, as well as a generalization of group morphisms, which describe classic dynamical systems. We introduce the structure of cotranslations, as a specific kind…

In many applications involving binary variables, only pairwise dependence measures, such as correlations, are available. However, for multi-way tables involving more than two variables, these quantities do not uniquely determine the joint…

Classical correlations without predefined causal order arise from processes where parties manipulate random variables, and where the order of these interactions is not predefined. No assumption on the causal order of the parties is made,…

Rank-based dependence measures such as Spearman's footrule are robust and invariant, but they often fail to capture directional or asymmetric dependence in multivariate settings. This paper introduces a new family of directional Spearman's…

Within the field of causal inference, it is desirable to learn the structure of causal relationships holding between a system of variables from the correlations that these variables exhibit; a sub-problem of which is to certify whether or…

For two causal structures with the same set of visible variables, one is said to observationally dominate the other if the set of distributions over the visible variables realizable by the first contains the set of distributions over the…

We explore the relationship between causality, symmetry, and compression. We build on and generalize the known connection between learning and compression to a setting where causal models are not identifiable. We propose a framework where…

We demonstrate when and how an entire left-infinite orbit of an underlying dynamical system or observations from such left-infinite orbits can be uniquely represented by a pair of elements in a different space, a phenomenon which we call…

Causal inference, a critical tool for informing business decisions, traditionally relies heavily on structured data. However, in many real-world scenarios, such data can be incomplete or unavailable. This paper presents a framework that…

This is the first of a series of papers in which a new formulation of quantum theory is developed for totally constrained systems, that is, canonical systems in which the hamiltonian is written as a linear combination of constraints…