Related papers: A note on intrinsic Conditional Autoregressive mod…
We introduce a nonparametric graphical model for discrete node variables based on additive conditional independence. Additive conditional independence is a three way statistical relation that shares similar properties with conditional…
This paper studies how to capture dependency graph structures from real data which may not be Gaussian. Starting from marginal loss functions not necessarily derived from probability distributions, we utilize an additive…
We propose a method for inferring the conditional independence graph (CIG) of a high-dimensional Gaussian vector time series (discrete-time process) from a finite-length observation. By contrast to existing approaches, we do not rely on a…
Conditions are obtained for a Gaussian vector autoregressive time series of order $k$, VAR($k$), to have univariate margins that are autoregressive of order $k$ or lower-dimensional margins that are also VAR($k$). This can lead to…
Theory of graphical models has matured over more than three decades to provide the backbone for several classes of models that are used in a myriad of applications such as genetic mapping of diseases, credit risk evaluation, reliability and…
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…
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…
We address the problem of learning graphical models which correspond to high dimensional autoregressive stationary stochastic processes. A graphical model describes the conditional dependence relations among the components of a stochastic…
Our concern is selecting the concentration matrix's nonzero coefficients for a sparse Gaussian graphical model in a high-dimensional setting. This corresponds to estimating the graph of conditional dependencies between the variables. We…
The paper considers the problem to estimate non-causal graphical models whose edges encode smoothing relations among the variables. We propose a new covariance extension problem and show that the solution minimizing the transportation…
Despite major methodological developments, Bayesian inference for Gaussian graphical models remains challenging in high dimension due to the tremendous size of the model space. This article proposes a method to infer the marginal and…
Conditional independence models in the Gaussian case are algebraic varieties in the cone of positive definite covariance matrices. We study these varieties in the case of Bayesian networks, with a view towards generalizing the recursive…
Decomposable dependency models and their graphical counterparts, i.e., chordal graphs, possess a number of interesting and useful properties. On the basis of two characterizations of decomposable models in terms of independence…
Causal graphs (CGs) are compact representations of the knowledge of the data generating processes behind the data distributions. When a CG is available, e.g., from the domain knowledge, we can infer the conditional independence (CI)…
We propose a method for inferring the conditional indepen- dence graph (CIG) of a high-dimensional discrete-time Gaus- sian vector random process from finite-length observations. Our approach does not rely on a parametric model (such as,…
A class of multivariate periodic autoregressive models is proposed where coupling between time series is achieved through linear mean functions. Various response distributions with quadratic mean-variance relationships fit into the…
We develop estimation for potentially high-dimensional additive structural equation models. A key component of our approach is to decouple order search among the variables from feature or edge selection in a directed acyclic graph encoding…
We present a graphical approach to deriving inequality constraints for directed acyclic graph (DAG) models, where some variables are unobserved. In particular we show that the observed distribution of a discrete model is always restricted…
Gaussian graphical models are parametric statistical models for jointly normal random variables whose dependence structure is determined by a graph. In previous work, we introduced trek separation, which gives a necessary and sufficient…
Graphical models have long been studied in statistics as a tool for inferring conditional independence relationships among a large set of random variables. The most existing works in graphical modeling focus on the cases that the data are…