Related papers: Graphical models in Macaulay2
Graphical models are ubiquitous tools to describe the interdependence between variables measured simultaneously such as large-scale gene or protein expression data. Gaussian graphical models (GGMs) are well-established tools for…
In Gaussian graphical models, conditional independence and partial correlations are natural inferential targets for understanding direct relationships in multivariate data. No comparable framework exists for spatial processes, where…
The problem of identifying statistically significant inferences about the structure of the graphical model is considered, along with the related task of constructing a confidence set for a graphical model. It has been proven that the…
This short expository paper outlines applications of computer algebra to the implication problem of conditional independence for Gaussian random variables. We touch on certificates for validity and invalidity of inference rules from the…
For a directed acyclic graph, there are two known criteria to decide whether any specific conditional independence statement is implied for all distributions factorized according to the given graph. Both criteria are based on special types…
We present a nonparametric graphical model. Our model uses an undirected graph that represents conditional independence for general random variables defined by the conditional dependence coefficient (Azadkia and Chatterjee (2021)). The set…
This thesis studies two problems in modern statistics. First, we study selective inference, or inference for hypothesis that are chosen after looking at the data. The motiving application is inference for regression coefficients selected by…
The use of directed acyclic graphs (DAGs) to represent conditional independence relations among random variables has proved fruitful in a variety of ways. Recursive structural equation models are one kind of DAG model. However,…
The Gaussian graphical model (GGM) incorporates an undirected graph to represent the conditional dependence between variables, with the precision matrix encoding partial correlation between pair of variables given the others. To achieve…
Graphical model has been widely used to investigate the complex dependence structure of high-dimensional data, and it is common to assume that observed data follow a homogeneous graphical model. However, observations usually come from…
While graphical models for continuous data (Gaussian graphical models) and discrete data (Ising models) have been extensively studied, there is little work on graphical models linking both continuous and discrete variables (mixed data),…
Graphical models are commonly used tools for modeling multivariate random variables. While there exist many convenient multivariate distributions such as Gaussian distribution for continuous data, mixed data with the presence of discrete…
This paper describes the RationalMaps package for Macaulay2. This package provides functionality for computing several aspects of rational maps such as whether a map is birational, or a closed embedding.
We introduce the Multiple Quantile Graphical Model (MQGM), which extends the neighborhood selection approach of Meinshausen and Buhlmann for learning sparse graphical models. The latter is defined by the basic subproblem of modeling the…
Despite the growing interest in causal and statistical inference for settings with data dependence, few methods currently exist to account for missing data in dependent data settings; most classical missing data methods in statistics and…
We define Gaussian graphical models on directed acyclic graphs with coloured vertices and edges, calling them RDAG (restricted directed acyclic graph) models. If two vertices or edges have the same colour, their parameters in the model must…
We consider the problem of estimating an undirected Gaussian graphical model when the underlying distribution is multivariate totally positive of order 2 (MTP2), a strong form of positive dependence. Such distributions are relevant for…
We study the zero sets of the independence polynomial on recursive sequences of graphs. We prove that for a maximally independent starting graph and a stable and expanding recursion algorithm, the zeros of the independence polynomial are…
Bayesian methods for learning Gaussian graphical models offer a principled framework for quantifying model uncertainty and incorporating prior knowledge. However, their scalability is constrained by the computational cost of jointly…
Gaussian graphical models have become a well-recognized tool for the analysis of conditional independencies within a set of continuous random variables. From an inferential point of view, it is important to realize that they are composite…