Related papers: Decomposable context-specific models
Recently semantic parsing in context has received considerable attention, which is challenging since there are complex contextual phenomena. Previous works verified their proposed methods in limited scenarios, which motivates us to conduct…
Graphical Markov models combine conditional independence constraints with graphical representations of stepwise data generating processes.The models started to be formulated about 40 years ago and vigorous development is ongoing.…
Classical finite association schemes lead to a finite-dimensional algebras which are generated by finitely many stochastic matrices. Moreover, there exist associated finite hypergroups. The notion of classical discrete association schemes…
A notion of morphism that is suitable for the sheaf-theoretic approach to contextuality is developed, resulting in a resource theory for contextuality. The key features involve using an underlying relation rather than a function between…
The visual world around us can be described as a structured set of objects and their associated relations. An image of a room may be conjured given only the description of the underlying objects and their associated relations. While there…
We study varieties associated to hypergraphs from the point of view of projective geometry and matroid theory. We describe their decompositions into matroid varieties, which may be reducible and can have arbitrary singularities by the…
The variability of structure in a finite Markov equivalence class of causally sufficient models represented by directed acyclic graphs has been fully characterized. Without causal sufficiency, an infinite semi-Markov equivalence class of…
Bayesian networks provide a language for qualitatively representing the conditional independence properties of a distribution. This allows a natural and compact representation of the distribution, eases knowledge acquisition, and supports…
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…
We introduce Clique Matrices as an alternative representation of undirected graphs, being a generalisation of the incidence matrix representation. Here we use clique matrices to decompose a graph into a set of possibly overlapping clusters,…
In designing generative models, it is commonly believed that in order to learn useful latent structure, we face a fundamental tension between expressivity and structure. In this paper we challenge this view by proposing a new approach to…
Markov networks are models for compactly representing complex probability distributions. They are composed by a structure and a set of numerical weights. The structure qualitatively describes independences in the distribution, which can be…
In this paper, we apply the machinery developed in arXiv:2401.06641(2) to study the behavior of computable categoricity relativized to non-c.e. degrees. In particular, we show that we can build a computable structure which is not computably…
In this paper we investigate the use of staged tree models for discrete longitudinal data. Staged trees are a type of probabilistic graphical model for finite sample space processes. They are a natural fit for longitudinal data because a…
Let G be a semisimple affine algebraic group of inner type over a field F. We write C for the class of all finite direct products of projective G-homogeneous F-varieties. We determine the structure of the Chow motives with coefficients in a…
This paper explores the role of Directed Acyclic Graphs (DAGs) as a representation of conditional independence relationships. We show that DAGs offer polynomially sound and complete inference mechanisms for inferring conditional…
The study presents an exploratory graphical modeling approach for evaluating local item dependency within cognitively diagnostic classification models (DCMs). Current approaches to modeling local dependence require known item structure and…
Denoising diffusion models enable conditional generation and density modeling of complex relationships like images and text. However, the nature of the learned relationships is opaque making it difficult to understand precisely what…
Inspired by rational canonical forms, we introduce and analyze two decompositions of dynamic programming (DP) problems for systems with linear dynamics. Specifically, we consider both finite and infinite horizon DP problems in which the…
Causal representation learning promises to extend causal models to hidden causal variables from raw entangled measurements. However, most progress has focused on proving identifiability results in different settings, and we are not aware of…