Related papers: Learning High-dimensional Gaussian Graphical Model…
Recent work has shown the ability to learn generative models for 3D shapes from only unstructured 2D images. However, training such models requires differentiating through the rasterization step of the rendering process, therefore past work…
Graphical models are commonly used tools for modeling multivariate random variables. While there exist many convenient multivariate distributions such as Gaussian distribution for continuous data, mixed data with the presence of discrete…
We propose a new method of estimation in high-dimensional linear regression model. It allows for very weak distributional assumptions including heteroscedasticity, and does not require the knowledge of the variance of random errors. The…
We consider covariance estimation in the multivariate generalized Gaussian distribution (MGGD) and elliptically symmetric (ES) distribution. The maximum likelihood optimization associated with this problem is non-convex, yet it has been…
In Gaussian graphical model selection, noise-corrupted samples present significant challenges. It is known that even minimal amounts of noise can obscure the underlying structure, leading to fundamental identifiability issues. A recent line…
We propose an active learning method for discovering low-dimensional structure in high-dimensional Gaussian process (GP) tasks. Such problems are increasingly frequent and important, but have hitherto presented severe practical…
Analyzing multi-layered graphical models provides insight into understanding the conditional relationships among nodes within layers after adjusting for and quantifying the effects of nodes from other layers. We obtain the penalized maximum…
We consider distributed estimation of the inverse covariance matrix, also called the concentration or precision matrix, in Gaussian graphical models. Traditional centralized estimation often requires global inference of the covariance…
In Gaussian graphical models, the likelihood equations must typically be solved iteratively. We investigate two algorithms: A version of iterative proportional scaling which avoids inversion of large matrices, and an algorithm based on…
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…
We study the problem of learning a directed acyclic graph from data generated according to an additive, non-linear structural equation model with Gaussian noise. We express each non-linear function through a basis expansion, and derive a…
The concept of Gaussian process tomography along with nonnegative constraints is applied in the context of high-resolution image reconstruction using segmented planar detectors with few readout channels.Expanding on the concept of 2-D…
Graphical models are commonly used to discover associations within gene or protein networks for complex diseases such as cancer. Most existing methods estimate a single graph for a population, while in many cases, researchers are interested…
We consider the problem of estimating differences in two Gaussian graphical models (GGMs) which are known to have similar structure. The GGM structure is encoded in its precision (inverse covariance) matrix. In many applications one is…
We present a stepwise approach to estimate high dimensional Gaussian graphical models. We exploit the relation between the partial correlation coefficients and the distribution of the prediction errors, and parametrize the model in terms of…
Computational image reconstruction algorithms generally produce a single image without any measure of uncertainty or confidence. Regularized Maximum Likelihood (RML) and feed-forward deep learning approaches for inverse problems typically…
Devising augmentations for graph contrastive learning is challenging due to their irregular structure, drastic distribution shifts, and nonequivalent feature spaces across datasets. We introduce LG2AR, Learning Graph Augmentations to Learn…
Gaussian graphical modeling has been widely used to explore various network structures, such as gene regulatory networks and social networks. We often use a penalized maximum likelihood approach with the $L_1$ penalty for learning a…
In this paper, we study a 2D tomography problem for point source models with random unknown view angles. Rather than recovering the projection angles, we reconstruct the model through a set of rotation-invariant features that are estimated…
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…