Related papers: Duality in Graphical Models
Bidirected graphs are a common generalisation of directed graphs where arcs can also be incoming to both their incident nodes, or outgoing from both their incident nodes. Such arcs allow a walk to change direction. Some algorithms can…
We introduce priors and algorithms to perform Bayesian inference in Gaussian models defined by acyclic directed mixed graphs. Such a class of graphs, composed of directed and bi-directed edges, is a representation of conditional…
Graphical models express conditional independence relationships among variables. Although methods for vector-valued data are well established, functional data graphical models remain underdeveloped. We introduce a notion of conditional…
In undirected graphical models, learning the graph structure and learning the functions that relate the predictive variables (features) to the responses given the structure are two topics that have been widely investigated in machine…
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…
In the process of building (structural learning) a probabilistic graphical model from a set of observed data, the directional, cyclic dependencies between the random variables of the model are often found. Existing graphical models such as…
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…
Directed acyclic graph models with hidden variables have been much studied, particularly in view of their computational efficiency and connection with causal methods. In this paper we provide the circumstances under which it is possible for…
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…
Mixed data refers to a type of data in which variables can be of multiple types, such as continuous, discrete, or categorical. This data is routinely collected in various fields, including healthcare and social sciences. A common goal in…
Directed graphs naturally model systems with asymmetric, ordered relationships, essential to applications in biology, transportation, social networks, and visual understanding. Generating such graphs enables tasks such as simulation, data…
A graphical model is a statistical model that is associated to a graph whose nodes correspond to variables of interest. The edges of the graph reflect allowed conditional dependencies among the variables. Graphical models admit…
Predicting the evolution of a large system of units using its structure of interaction is a fundamental problem in complex system theory. And so is the problem of reconstructing the structure of interaction from temporal observations. Here,…
A graphical design is a subset of graph vertices such that the weighted averages of certain graph eigenvectors over the design agree with their global averages. We use Gale duality to show that positively weighted graphical designs in…
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.…
Graphical models are used to describe the conditional independence relations in multivariate data. They have been used for a variety of problems, including log-linear models (Liu and Massam, 2006), network analysis (Holland and Leinhardt,…
Log-linear models are a classical tool for the analysis of contingency tables. In particular, the subclass of graphical log-linear models provides a general framework for modelling conditional independences. However, with the exception of…
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 introduce a general framework for undirected graphical models. It generalizes Gaussian graphical models to a wide range of continuous, discrete, and combinations of different types of data. The models in the framework, called exponential…
Graph translation is very promising research direction and has a wide range of potential real-world applications. Graph is a natural structure for representing relationship and interactions, and its translation can encode the intrinsic…