Related papers: Categories of Empirical Models
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…
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…
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…
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…
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…
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…
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)…
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…
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,…
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…
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…
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…
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…
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…
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,…
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…
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…
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…