Related papers: Sparse Nonparametric Graphical Models
We revisit the probabilistic construction of sparse random matrices where each column has a fixed number of nonzeros whose row indices are drawn uniformly at random with replacement. These matrices have a one-to-one correspondence with the…
Dynamic networks models describe a growing number of important scientific processes, from cell biology and epidemiology to sociology and finance. There are many aspects of dynamical networks that require statistical considerations. In this…
Gaussian processes (GPs) are frequently used in machine learning and statistics to construct powerful models. However, when employing GPs in practice, important considerations must be made, regarding the high computational burden,…
Structure learning methods for covariance and concentration graphs are often validated on synthetic models, usually obtained by randomly generating: (i) an undirected graph, and (ii) a compatible symmetric positive definite (SPD) matrix. In…
We propose NonStGM, a general nonparametric graphical modeling framework for studying dynamic associations among the components of a nonstationary multivariate time series. It builds on the framework of Gaussian Graphical Models (GGM) and…
Bayesian nonparametric models offer a flexible and powerful framework for statistical model selection, enabling the adaptation of model complexity to the intricacies of diverse datasets. This survey intends to delve into the significance of…
We present a Bayesian formulation of weighted stochastic block models that can be used to infer the large-scale modular structure of weighted networks, including their hierarchical organization. Our method is nonparametric, and thus does…
The popular Lasso approach for sparse estimation can be derived via marginalization of a joint density associated with a particular stochastic model. A different marginalization of the same probabilistic model leads to a different…
A severe limitation of many nonparametric estimators for random coefficient models is the exponential increase of the number of parameters in the number of random coefficients included into the model. This property, known as the curse of…
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…
A multivariate distribution can be described by a triangular transport map from the target distribution to a simple reference distribution. We propose Bayesian nonparametric inference on the transport map by modeling its components using…
The literature on Gaussian graphical models (GGMs) contains two equally rich and equally significant domains of research efforts and interests. The first research domain relates to the problem of graph determination. That is, the underlying…
Estimating conditional independence graphs from high-dimensional Gaussian data is challenging because methods must detect relevant edges while rigorously controlling statistical errors. We propose a Bayesian framework based on a prior…
Graphical models have proven to be powerful tools for representing high-dimensional systems of random variables. One example of such a model is the undirected graph, in which lack of an edge represents conditional independence between two…
A flexible model for non-stationary Gaussian random fields on hypersurfaces is introduced.The class of random fields on curves and surfaces is characterized by an amplitude spectral density of a second order elliptic differential…
In this article, we discuss the composite likelihood estimation of sparse Gaussian graphical models. When there are symmetry constraints on the concentration matrix or partial correlation matrix, the likelihood estimation can be…
Gaussian Graphical Models (GGMs) are widely used in high-dimensional data analysis to synthesize the interaction between variables. In many applications, such as genomics or image analysis, graphical models rely on sparsity and clustering…
Randomising networks using a naive `accept-all' edge-swap algorithm is generally biased. Building on recent results for nondirected graphs, we construct an ergodic detailed balance Markov chain with non-trivial acceptance probabilities for…
We propose a semiparametric approach, named nonparanormal skeptic, for estimating high dimensional undirected graphical models. In terms of modeling, we consider the nonparanormal family proposed by Liu et al (2009). In terms of estimation,…
We consider the problem of learning a Gaussian variational approximation to the posterior distribution for a high-dimensional parameter, where we impose sparsity in the precision matrix to reflect appropriate conditional independence…