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Conditional independence and graphical models are crucial concepts for sparsity and statistical modeling in higher dimensions. For L\'evy processes, a widely applied class of stochastic processes, these notions have not been studied. By the…

Statistics Theory · Mathematics 2024-11-13 Sebastian Engelke , Jevgenijs Ivanovs , Jakob D. Thøstesen

A graphical model encodes conditional independence relations via the Markov properties. For an undirected graph these conditional independence relations can be represented by a simple polytope known as the graph associahedron, which can be…

Statistics Theory · Mathematics 2017-12-08 Fatemeh Mohammadi , Caroline Uhler , Charles Wang , Josephine Yu

Graphical models encode conditional independence statements of a multivariate distribution via a graph. Traditionally, the marginal distributions in a graphical model are assumed to be Gaussian. In this paper, we propose a three-level…

Methodology · Statistics 2025-05-01 Luis E. Nieto-Barajas , Simón Lunagómez

Undirected graphical models have been successfully used to jointly model the spatial and the spectral dependencies in earth observing hyperspectral images. They produce less noisy, smooth, and spatially coherent land cover maps and give top…

Computer Vision and Pattern Recognition · Computer Science 2018-12-05 Utsav B. Gewali , Sildomar T. Monteiro

Knowing when a graphical model is perfect to a distribution is essential in order to relate separation in the graph to conditional independence in the distribution, and this is particularly important when performing inference from data.…

Statistics Theory · Mathematics 2019-09-06 Arash A. Amini , Bryon Aragam , Qing Zhou

In probability theory, the independence is a very fundamental concept, but with a little mystery. People can always easily manipulate it logistically but not geometrically, especially when it comes to the independence relationships among…

History and Overview · Mathematics 2021-07-22 Yan Zhang

We present a new family of models that is based on graphs that may have undirected, directed and bidirected edges. We name these new models marginal AMP (MAMP) chain graphs because each of them is Markov equivalent to some AMP chain graph…

Machine Learning · Statistics 2014-11-10 Jose M. Peña

We present a comprehensive study of graphical log-linear models for contingency tables. High dimensional contingency tables arise in many areas such as computational biology, collection of survey and census data and others. Analysis of…

Methodology · Statistics 2016-03-15 Niharika Gauraha

Graphs are important data representations for describing objects and their relationships, which appear in a wide diversity of real-world scenarios. As one of a critical problem in this area, graph generation considers learning the…

Machine Learning · Computer Science 2022-10-06 Xiaojie Guo , Liang Zhao

Graph-based modeling plays a fundamental role in many areas of computer science. In this paper, we introduce systems of graph formulas with variables for specifying graph properties; this notion generalizes the graph formulas introduced in…

Formal Languages and Automata Theory · Computer Science 2026-01-23 Frank Drewes , Berthold Hoffmann , Mark Minas

We consider a countable system of interacting (possibly non-Markovian) stochastic differential equations driven by independent Brownian motions and indexed by the vertices of a locally finite graph $G = (V,E)$. The drift of the process at…

Probability · Mathematics 2020-09-28 Daniel Lacker , Kavita Ramanan , Ruoyu Wu

Causal reasoning has gained great attention over the last half century as it allows (or at least intends) to answer questions which go above those within the capabilities of classical inferential statistics using just observational data. So…

Statistics Theory · Mathematics 2025-01-23 Ignacio González-Pérez

Graphical models are commonly used to represent conditional dependence relationships between variables. There are multiple methods available for exploring them from high-dimensional data, but almost all of them rely on the assumption that…

Machine Learning · Statistics 2020-04-22 Tianxi Li , Cheng Qian , Elizaveta Levina , Ji Zhu

Constraint-based causal discovery algorithms utilize many statistical tests for conditional independence to uncover networks of causal dependencies. These approaches to causal discovery rely on an assumed correspondence between the…

Machine Learning · Computer Science 2025-04-18 Bijan Mazaheri , Jiaqi Zhang , Caroline Uhler

Probabilistic graphical models, such as Markov random fields (MRF), exploit dependencies among random variables to model a rich family of joint probability distributions. Sophisticated inference algorithms, such as belief propagation (BP),…

Social and Information Networks · Computer Science 2020-04-22 Yifei Liu , Chao Chen , Xi Zhang , Sihong Xie

A new class of graphical models capturing the dependence structure of events that occur in time is proposed. The graphs represent so-called local independences, meaning that the intensities of certain types of events are independent of some…

Statistics Theory · Mathematics 2013-07-11 Vanessa Didelez

The invariance properties of interventional distributions relative to the observational distribution, and how these properties allow us to refine Markov equivalence classes (MECs) of DAGs, is central to causal DAG discovery algorithms that…

Statistics Theory · Mathematics 2020-06-09 Liam Solus

This paper reviews recent advances in missing data research using graphical models to represent multivariate dependencies. We first examine the limitations of traditional frameworks from three different perspectives: \textit{transparency,…

Methodology · Statistics 2019-11-15 Karthika Mohan , Judea Pearl

Graphical models in extremes have emerged as a diverse and quickly expanding research area in extremal dependence modeling. They allow for parsimonious statistical methodology and are particularly suited for enforcing sparsity in…

Methodology · Statistics 2024-02-06 Sebastian Engelke , Manuel Hentschel , Michaël Lalancette , Frank Röttger

We consider a Random Graph Model on $\mathbb{Z}^{d}$ that incorporates the interplay between the statistics of the graph and the underlying space where the vertices are located. Based on a graphical construction of the model as the…

Statistics Theory · Mathematics 2024-06-19 Andressa Cerqueira , Nancy L. Garcia