Related papers: Bayesian Variable Selection in Multivariate Nonlin…
This research proposes a flexible Bayesian extension of the composite Gaussian process (CGP) model of Ba and Joseph (2012) for predicting (stationary or) non-stationary $y(\mathbf{x})$. The CGP generalizes the regression plus stationary…
Bayesian networks provide a method of representing conditional independence between random variables and computing the probability distributions associated with these random variables. In this paper, we extend Bayesian network structures to…
Gaussian process state-space models (GPSSMs) provide a principled and flexible approach to modeling the dynamics of a latent state, which is observed at discrete-time points via a likelihood model. However, inference in GPSSMs is…
Selecting interpretable feature sets in underdetermined ($n \ll p$) and highly correlated regimes constitutes a fundamental challenge in data science, particularly when analyzing physical measurements. In such settings, multiple distinct…
This paper develops a Bayesian graphical model for fusing disparate types of count data. The motivating application is the study of bacterial communities from diverse high dimensional features, in this case transcripts, collected from…
Gaussian process regression is a powerful Bayesian nonlinear regression method. Recent research has enabled the capture of many types of observations using non-Gaussian likelihoods. To deal with various tasks in spatial modeling, we benefit…
An important task in microbiome studies is to test the existence of and give characterization to differences in the microbiome composition across groups of samples. Important challenges of this problem include the large within-group…
A graphical model is a statistical model that is associated to a graph whose nodes correspond to variables of interest. The edges of the graph reflect allowed conditional dependencies among the variables. Graphical models admit…
We consider the problem of estimating the marginal independence structure of a Bayesian network from observational data, learning an undirected graph we call the unconditional dependence graph. We show that unconditional dependence graphs…
We study the convergence properties of a collapsed Gibbs sampler for Bayesian vector autoregressions with predictors, or exogenous variables. The Markov chain generated by our algorithm is shown to be geometrically ergodic regardless of…
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…
Finite Gaussian mixture models are widely used for model-based clustering of continuous data. Nevertheless, since the number of model parameters scales quadratically with the number of variables, these models can be easily…
Graphical network inference is used in many fields such as genomics or ecology to infer the conditional independence structure between variables, from measurements of gene expression or species abundances for instance. In many practical…
In high-dimensional graph learning problems, some topological properties of the graph, such as bounded node degree or tree structure, are typically assumed to hold so that the sample complexity of recovering the graph structure can be…
Gaussian graphical model is one of the powerful tools to analyze conditional independence between two variables for multivariate Gaussian-distributed observations. When the dimension of data is moderate or high, penalized likelihood methods…
We consider the problem of estimating the conditional mean of a real Gaussian variable $\nolinebreak Y=\sum_{i=1}^p\nolinebreak\theta_iX_i+\nolinebreak \epsilon$ where the vector of the covariates $(X_i)_{1\leq i\leq p}$ follows a joint…
Bayesian nonparametric mixtures and random partition models are powerful tools for probabilistic clustering. However, standard independent mixture models can be restrictive in some applications such as inference on cell lineage due to the…
Generalized linear models (GLMs) using a regression procedure to fit relationships between predictor and target variables are widely used in automobile insurance data. Here, in the process of ratemaking and in order to compute the premiums…
The cumulative shrinkage process is an increasing shrinkage prior that can be employed within models in which additional terms are supposed to play a progressively negligible role. A natural application is to Gaussian factor models, where…
Bayesian regression remains a simple but effective tool based on Bayesian inference techniques. For large-scale applications, with complicated posterior distributions, Markov Chain Monte Carlo methods are applied. To improve the well-known…