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Understanding and quantifying causal relationships between variables is essential for reasoning about the physical world. In this work, we develop a resource-theoretic framework to do so. Here, we focus on the simplest nontrivial setting --…

We investigate the conditions under which an uncontrollable background processes may be harnessed by an agent to perform a task that would otherwise be impossible within their operational framework. This situation can be understood from the…

Quantum Physics · Physics 2021-04-21 Graeme D. Berk , Andrew J. P. Garner , Benjamin Yadin , Kavan Modi , Felix A. Pollock

Two high-level "pictures" of probability theory have emerged: one that takes as central the notion of random variable, and one that focuses on distributions and probability channels (Markov kernels). While the channel-based picture has been…

Category Theory · Mathematics 2025-05-19 Dario Stein

We introduce resource graphs, a representation of linked ideas used when reasoning about specific contexts in physics. Our model is consistent with previous descriptions of resources and coordination classes. It can represent mesoscopic…

Physics Education · Physics 2009-11-11 Michael C. Wittmann

Machines that can replicate human intelligence with type 2 reasoning capabilities should be able to reason at multiple levels of spatio-temporal abstractions and scales using internal world models. Devising formalisms to develop such…

Artificial Intelligence · Computer Science 2025-07-01 Vaisakh Shaj

Identifying when observed statistics cannot be explained by any reasonable classical model is a central problem in quantum foundations. A principled and universally applicable approach to defining and identifying nonclassicality is given by…

Contextuality can be understood as the impossibility to construct a globally consistent description of a model even if there is local agreement. In particular, quantum models present this property. We can describe contextuality with the…

Quantum Physics · Physics 2024-07-04 Sidiney B. Montanhano

Traditionally categorical data analysis (e.g. generalized linear models) works with simple, flat datasets akin to a single table in a database with no notion of missing data or conflicting versions. In contrast, modern data analysis must…

Databases · Computer Science 2017-08-11 Jason Morton

In this work, we consider an extension of graphical models to random graphs, trees, and other objects. To do this, many fundamental concepts for multivariate random variables (e.g., marginal variables, Gibbs distribution, Markov properties)…

Machine Learning · Statistics 2017-05-08 Neil Hallonquist

Intensional computation derives concrete outputs from abstract function definitions; extensional computation defines functions through explicit input-output pairs. In formal semantics: intensional computation interprets expressions as…

Category Theory · Mathematics 2024-09-05 Daniel Quigley

Contextuality is a fundamental feature of quantum theory and is necessary for quantum computation and communication. Serious steps have therefore been taken towards a formal framework for contextuality as an operational resource. However,…

Quantum Physics · Physics 2018-04-26 Barbara Amaral , Adán Cabello , Marcelo Terra Cunha , Leandro Aolita

In this paper, we define a generalization of indexed categories and contextual categories which we call contextually indexed (contextual) categories. While contextual categories are models of ordinary type theories, contextually indexed…

Category Theory · Mathematics 2018-09-11 Valery Isaev

Contextuality provides a unifying paradigm for nonclassical aspects of quantum probabilities and resources of quantum information. Unfortunately, most forms of quantum contextuality remain experimentally unexplored due to the difficulty of…

Quantum Physics · Physics 2016-03-02 Adán Cabello

Marginal models involve restrictions on the conditional and marginal association structure of a set of categorical variables. They generalize log-linear models for contingency tables, which are the fundamental tools for modelling the…

Methodology · Statistics 2023-04-10 Tamas Rudas , Wicher Bergsma

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…

Machine Learning · Computer Science 2024-10-29 Martin Rabel , Wiebke Günther , Jakob Runge , Andreas Gerhardus

Ontological models are attempts to quantitatively describe the results of a probabilistic theory, such as Quantum Mechanics, in a framework exhibiting an explicit realism-based underpinning. Unlike either the well known quasi-probability…

Quantum Physics · Physics 2008-07-02 Nicholas Harrigan , Terry Rudolph , Scott Aaronson

Most behavioral and social experiments aimed at revealing contextuality are confined to cyclic systems with binary outcomes. In quantum physics, this broad class of systems includes as special cases Klyachko-Can-Binicioglu-Shumovsky-type,…

Neurons and Cognition · Quantitative Biology 2016-02-12 Ehtibar Dzhafarov , Ru Zhang , Janne Kujala

A large body of research in machine learning is concerned with supervised learning from examples. The examples are typically represented as vectors in a multi-dimensional feature space (also known as attribute-value descriptions). A teacher…

Machine Learning · Computer Science 2007-05-23 Peter D. Turney

A common framework is provided that comprises classical ordinal item response models as the cumulative, sequential and adjacent categories models as well as nominal response models and item response tree models. The taxonomy is based on the…

Methodology · Statistics 2020-10-06 Gerhard Tutz

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…

Machine Learning · Statistics 2021-08-06 Eigil F. Rischel , Sebastian Weichwald