Related papers: Stratified Gaussian Graphical Models
We propose two types of Quantile Graphical Models (QGMs) --- Conditional Independence Quantile Graphical Models (CIQGMs) and Prediction Quantile Graphical Models (PQGMs). CIQGMs characterize the conditional independence of distributions by…
Gaussian graphical models are used for determining conditional relationships between variables. This is accomplished by identifying off-diagonal elements in the inverse-covariance matrix that are non-zero. When the ratio of variables (p) to…
We introduce Probabilistic Dependency Graphs (PDGs), a new class of directed graphical models. PDGs can capture inconsistent beliefs in a natural way and are more modular than Bayesian Networks (BNs), in that they make it easier to…
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…
For multivariate spatial Gaussian process (GP) models, customary specifications of cross-covariance functions do not exploit relational inter-variable graphs to ensure process-level conditional independence among the variables. This is…
We propose a novel Bayesian nonparametric method to learn translation-invariant relationships on non-Euclidean domains. The resulting graph convolutional Gaussian processes can be applied to problems in machine learning for which the input…
Gaussian Graphical Models provide a convenient framework for representing dependencies between variables. Recently, this tool has received a high interest for the discovery of biological networks. The literature focuses on the case where a…
Bayesian graphical models are powerful tools to infer complex relationships in high dimension, yet are often fraught with computational and statistical challenges. If exploited in a principled way, the increasing information collected…
Complex analyses involving multiple, dependent random quantities often lead to graphical models - a set of nodes denoting variables of interest, and corresponding edges denoting statistical interactions between nodes. To develop statistical…
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…
Dependency networks (Heckerman et al., 2000) provide a flexible framework for modeling complex systems with many variables by combining independently learned local conditional distributions through pseudo-Gibbs sampling. Despite their…
State-space models (SSM) are central to describe time-varying complex systems in countless signal processing applications such as remote sensing, networks, biomedicine, and finance to name a few. Inference and prediction in SSMs are…
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…
Learning the structure of dependence relations between variables is a pervasive issue in the statistical literature. A directed acyclic graph (DAG) can represent a set of conditional independences, but different DAGs may encode the same set…
Conditional independence in a multivariate normal (or Gaussian) distribution is characterized by the vanishing of subdeterminants of the distribution's covariance matrix. Gaussian conditional independence models thus correspond to algebraic…
Although there is much recent work developing flexible variational methods for Bayesian computation, Gaussian approximations with structured covariance matrices are often preferred computationally in high-dimensional settings. This paper…
Probabilistic graphical models that encode an underlying Markov random field are fundamental building blocks of generative modeling to learn latent representations in modern multivariate data sets with complex dependency structures. Among…
Many statistical models are algebraic in that they are defined by polynomial constraints or by parameterizations that are polynomial or rational maps. This opens the door for tools from computational algebraic geometry. These tools can be…
A conditional independence graph is a concise representation of pairwise conditional independence among many variables. Graphical Random Forests (GRaFo) are a novel method for estimating pairwise conditional independence relationships among…
Probabilistic Graphical Models are often used to understand dynamics of a system. They can model relationships between features (nodes) and the underlying distribution. Theoretically these models can represent very complex dependency…