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We analyze the statistical consistency of robust estimators for precision matrices in high dimensions. We focus on a contamination mechanism acting cellwise on the data matrix. The estimators we analyze are formed by plugging appropriately…
Penalized estimation methods for diffusion processes and dependent data have recently gained significant attention due to their effectiveness in handling high-dimensional stochastic systems. In this work, we introduce an adaptive…
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…
Finite Gaussian mixture models provide a powerful and widely employed probabilistic approach for clustering multivariate continuous data. However, the practical usefulness of these models is jeopardized in high-dimensional spaces, where…
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…
In linear regression, SLOPE is a new convex analysis method that generalizes the Lasso via the sorted L1 penalty: larger fitted coefficients are penalized more heavily. This magnitude-dependent regularization requires an input of penalty…
We consider the problem of estimating log-determinants of large, sparse, positive definite matrices. A key focus of our algorithm is to reduce computational cost, and it is based on sparse approximate inverses. The algorithm can be…
For some special data in reality, such as the genetic data, adjacent genes may have the similar function. Thus ensuring the smoothness between adjacent genes is highly necessary. But, in this case, the standard lasso penalty just doesn't…
We offer a method to estimate a covariance matrix in the special case that \textit{both} the covariance matrix and the precision matrix are sparse --- a constraint we call double sparsity. The estimation method is maximum likelihood,…
We provide a selected overview of methodology and theory for estimation and inference on the edge weights in high-dimensional directed and undirected Gaussian graphical models. For undirected graphical models, two main explicit…
We propose an L1-penalized algorithm for fitting high-dimensional generalized linear mixed models. Generalized linear mixed models (GLMMs) can be viewed as an extension of generalized linear models for clustered observations. This…
Graph matching is a challenging problem with very important applications in a wide range of fields, from image and video analysis to biological and biomedical problems. We propose a robust graph matching algorithm inspired in…
Bayesian estimation of Gaussian graphical models has proven to be challenging because the conjugate prior distribution on the Gaussian precision matrix, the G-Wishart distribution, has a doubly intractable partition function. Recent…
Differential graphical models are designed to represent the difference between the conditional dependence structures of two groups, thus are of particular interest for scientific investigation. Motivated by modern applications, this…
One of the fundamental tasks of science is to find explainable relationships between observed phenomena. One approach to this task that has received attention in recent years is based on probabilistic graphical modelling with sparsity…
Variable selection plays an important role in the high-dimensional data analysis. However the high-dimensional data often induces the strongly correlated variables problem. In this paper, we propose Elastic Net procedure for partially…
We consider a framework for determining and estimating the conditional pairwise relationships of variables when the observed samples are contaminated with measurement error in high dimensional settings. Assuming the true underlying…
We propose a scalable, efficient and statistically motivated computational framework for Graphical Lasso (Friedman et al., 2007b) - a covariance regularization framework that has received significant attention in the statistics community…
In this paper, we consider the Graphical Lasso (GL), a popular optimization problem for learning the sparse representations of high-dimensional datasets, which is well-known to be computationally expensive for large-scale problems.…
Covariance regression offers an effective way to model the large covariance matrix with the auxiliary similarity matrices. In this work, we propose a sparse covariance regression (SCR) approach to handle the potentially high-dimensional…