Related papers: Graphical Markov models for infinitely many variab…
The two most popular types of graphical model are directed models (Bayesian networks) and undirected models (Markov random fields, or MRFs). Directed and undirected models offer complementary properties in model construction, expressing…
We consider (annealed) large deviation principles for component empirical measures of several families of marked sparse random graphs, including (i) uniform graphs on $n$ vertices with a fixed degree distribution; (ii) uniform graphs on $n$…
We propose an extension of the Contextual Graph Markov Model, a deep and probabilistic machine learning model for graphs, to model the distribution of edge features. Our approach is architectural, as we introduce an additional Bayesian…
High-dimensional data analysis typically focuses on low-dimensional structure, often to aid interpretation and computational efficiency. Graphical models provide a powerful methodology for learning the conditional independence structure in…
Neural network design has utilized flexible nonlinear processes which can mimic biological systems, but has suffered from a lack of traceability in the resulting network. Graphical probabilistic models ground network design in probabilistic…
Inspired by "quantum graphity" models for spacetime, a statistical model of graphs is proposed to explore possible realizations of emergent manifolds. Graphs with given numbers of vertices and edges are considered, governed by a very…
In recent years, there has been considerable interest in estimating conditional independence graphs in the high-dimensional setting. Most prior work has assumed that the variables are multivariate Gaussian, or that the conditional means of…
In this paper, we introduce different concepts of Granger causality and contemporaneous correlation for multivariate stationary continuous-time processes to model different dependencies between the component processes. Several equivalent…
Markov random fields are known to be fully characterized by properties of their information diagrams, or I-diagrams. In particular, for Markov random fields, regions in the I-diagram corresponding to disconnected vertex sets in the graph…
We consider the problem of recovering conditional independence relationships between $p$ jointly distributed Hilbertian random elements given $n$ realizations thereof. We operate in the sparse high-dimensional regime, where $n \ll p$ and no…
Graphs are a powerful data structure to represent relational data and are widely used to describe complex real-world data structures. Probabilistic Graphical Models (PGMs) have been well-developed in the past years to mathematically model…
In recent years, a growing number of method and application works have adapted and applied the causal-graphical-model framework to time series data. Many of these works employ time-resolved causal graphs that extend infinitely into the past…
Generative models can be trained to emulate complex empirical data, but are they useful to make predictions in the context of previously unobserved environments? An intuitive idea to promote such extrapolation capabilities is to have the…
The problem of graphical model selection is to correctly estimate the graph structure of a Markov random field given samples from the underlying distribution. We analyze the information-theoretic limitations of the problem of graph…
We study the joint occurrence of large values of a Markov random field or undirected graphical model associated to a block graph. On such graphs, containing trees as special cases, we aim to generalize recent results for extremes of Markov…
Time-continuous dynamical systems defined on graphs are often used to model complex systems with many interacting components in a non-spatial context. In the reverse sense attaching meaningful dynamics to given 'interaction diagrams' is a…
We consider the problem of learning a conditional Gaussian graphical model in the presence of latent variables. Building on recent advances in this field, we suggest a method that decomposes the parameters of a conditional Markov random…
Markov networks are frequently used in sciences to represent conditional independence relationships underlying observed variables arising from a complex system. It is often of interest to understand how an underlying network differs between…
A set of independence statements may define the independence structure of interest in a family of joint probability distributions. This structure is often captured by a graph that consists of nodes representing the random variables and of…
We introduce a novel class of labeled directed acyclic graph (LDAG) models for finite sets of discrete variables. LDAGs generalize earlier proposals for allowing local structures in the conditional probability distribution of a node, such…