Related papers: Local and Mixing-Based Algorithms for Gaussian Gra…
We provide a new approach to approximate emulation of large computer experiments. By focusing expressly on desirable properties of the predictive equations, we derive a family of local sequential design schemes that dynamically define the…
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…
Neighborhood selection is a widely used method used for estimating the support set of sparse precision matrices, which helps determine the conditional dependence structure in undirected graphical models. However, reporting only point…
We study the convergence properties of the Gibbs Sampler in the context of posterior distributions arising from Bayesian analysis of conditionally Gaussian hierarchical models. We develop a multigrid approach to derive analytic expressions…
Graphical model selection is a seemingly impossible task when many pairs of variables are never jointly observed; this requires inference of conditional dependencies with no observations of corresponding marginal dependencies. This…
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…
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…
A computational/analytics framework for assessing the value of drill-hole information in ore grade estimation is described using Gaussian Process and statistics. A distinguishing feature is that it presents both a near-term and long-term…
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 present a graph-regularized learning of Gaussian Mixture Models (GMMs) in distributed settings with heterogeneous and limited local data. The method exploits a provided similarity graph to guide parameter sharing among nodes, avoiding…
We study the mixing time of Glauber dynamics for Ising models in which the interaction matrix contains a single negative spectral outlier. This class includes the anti-ferromagnetic Curie-Weiss model, the anti-ferromagnetic Ising model on…
We consider the problem of estimating high-dimensional Gaussian graphical models corresponding to a single set of variables under several distinct conditions. This problem is motivated by the task of recovering transcriptional regulatory…
Variational inference with Gaussian mixture models (GMMs) enables learning of highly tractable yet multi-modal approximations of intractable target distributions with up to a few hundred dimensions. The two currently most effective methods…
Gaussian graphical models provide a powerful framework to reveal the conditional dependency structure between multivariate variables. The process of uncovering the conditional dependency network is known as structure learning. Bayesian…
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…
We study the local geometry of empirical risks in high dimensions via the spectral theory of their Hessian and information matrices. We focus on settings where the data, $(Y_\ell)_{\ell =1}^n \in \mathbb{R}^d$, are i.i.d. draws of a…
Self-supervised representation learning often relies on deterministic predictive architectures to align context and target views in latent space. While effective in many settings, such methods are limited in genuinely multi-modal inverse…
The semantic segmentation task aims at dense classification at the pixel-wise level. Deep models exhibited progress in tackling this task. However, one remaining problem with these approaches is the loss of spatial precision, often produced…
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…
Gaussian Graphical Models (GGM) are often used to describe the conditional correlations between the components of a random vector. In this article, we compare two families of GGM inference methods: nodewise edge selection and penalised…