Related papers: Graphical models in Macaulay2
An important task in data analysis is the discovery of causal relationships between observed variables. For continuous-valued data, linear acyclic causal models are commonly used to model the data-generating process, and the inference of…
We establish conditions under which latent causal graphs are nonparametrically identifiable and can be reconstructed from unknown interventions in the latent space. Our primary focus is the identification of the latent structure in…
We introduce efficient MCMC algorithms for Bayesian inference for single-factor models with correlated residuals where the residuals' distribution is a Gaussian graphical model. We call this family of models single-factor graphical models.…
This paper studies a class of binomial ideals associated to graphs with finite vertex sets. They generalize the binomial edge ideals, and they arise in the study of conditional independence ideals. A Gr\"obner basis can be computed by…
Undirected probabilistic graphical models represent the conditional dependencies, or Markov properties, of a collection of random variables. Knowing the sparsity of such a graphical model is valuable for modeling multivariate distributions…
Structure learning of Gaussian graphical models is an extensively studied problem in the classical multivariate setting where the sample size n is larger than the number of random variables p, as well as in the more challenging setting when…
Graphical models in probability and statistics are a core concept in the area of probabilistic reasoning and probabilistic programming-graphical models include Bayesian networks and factor graphs. In this paper we develop a new model of…
A classic application of description length is for model selection with the minimum description length (MDL) principle. The focus of this paper is to extend description length for data analysis beyond simple model selection and sequences of…
Motivated by extreme value theory, max-linear Bayesian networks have been recently introduced and studied as an alternative to linear structural equation models. However, for max-linear systems the classical independence results for…
Using the geometric vertex decomposition property first defined by Knutson, Miller, and Yong, a recursive definition for geometrically vertex decomposable ideals was given by Klein and Rajchgot. We introduce the Macaulay2 package…
Bayesian graphical models are a useful tool for understanding dependence relationships among many variables, particularly in situations with external prior information. In high-dimensional settings, the space of possible graphs becomes…
Gaussian graphical models with sparsity in the inverse covariance matrix are of significant interest in many modern applications. For the problem of recovering the graphical structure, information criteria provide useful optimization…
We present {\tt RandomPoints}, a package in \emph{Macaulay2} designed mainly to identify rational and geometric points in a variety over a finite field. We provide tools to estimate the dimension of a variety. We also present methods to…
In this note we discuss (Gaussian) intrinsic conditional autoregressive (CAR) models for disconnected graphs, with the aim of providing practical guidelines for how these models should be defined, scaled and implemented. We show how these…
Exploring missing data in attributed graphs introduces unique challenges beyond those found in tabular datasets. In this work, we extend the taxonomy for missing data mechanisms to attributed graphs by proposing GAMM (Graph Attributes…
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…
This paper is a multidisciplinary review of empirical, statistical learning from a graphical model perspective. Well-known examples of graphical models include Bayesian networks, directed graphs representing a Markov chain, and undirected…
Let $X = \{X_{u}\}_{u \in U}$ be a real-valued Gaussian process indexed by a set $U$. It can be thought of as an undirected graphical model with every random variable $X_{u}$ serving as a vertex. We characterize this graph in terms of the…
Geometric constraint systems underly popular Computer Aided Design soft- ware. Automated approaches for detecting dependencies in a design are critical for developing robust solvers and providing informative user feedback, and we provide…
The following article is an application of commutative algebra to the study of multiparameter persistent homology in topological data analysis. In particular, the theory of finite free resolutions of modules over polynomial rings is applied…