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Distributed parameter estimation for large-scale systems is an active research problem. The goal is to derive a distributed algorithm in which each agent obtains a local estimate of its own subset of the global parameter vector, based on…

Graph Self-Supervised Learning (GSSL) has emerged as a powerful paradigm for generating high-quality representations for graph-structured data. While multi-scale graph contrastive learning has received increasing attention, many existing…

We consider the problem of maximum likelihood estimation in linear models represented by factor graphs and solved via the Gaussian belief propagation algorithm. Motivated by massive internet of things (IoT) networks and edge computing, we…

Sparse graphs built by sparse representation has been demonstrated to be effective in clustering high-dimensional data. Albeit the compelling empirical performance, the vanilla sparse graph ignores the geometric information of the data by…

Feature selection remains a major challenge in medical prediction, where existing approaches such as LASSO often lack robustness and interpretability. We introduce GRASP, a novel framework that couples Shapley value driven attribution with…

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…

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 study a set of regularization methods for high-dimensional linear regression models. These penalized estimators have the square root of the residual sum of squared errors as loss function, and any weakly decomposable norm as penalty…

Classical least squares estimators are well-known to be robust with respect to moment assumptions concerning the error distribution in a wide variety of finite-dimensional statistical problems; generally only a second moment assumption is…

We consider a general class of regression models with normally distributed covariates, and the associated nonconvex problem of fitting these models from data. We develop a general recipe for analyzing the convergence of iterative algorithms…

Clustering data into meaningful subsets is a major task in scientific data analysis. To date, various strategies ranging from model-based approaches to data-driven schemes, have been devised for efficient and accurate clustering. One…

This paper shows that graph spectral embedding using the random walk Laplacian produces vector representations which are completely corrected for node degree. Under a generalised random dot product graph, the embedding provides uniformly…

Despite a large corpus of recent work on scaling up Gaussian processes, a stubborn trade-off between computational speed, prediction and uncertainty quantification accuracy, and customizability persists. This is because the vast majority of…

Gaussian Graphical Models (GGMs) are popular tools for studying network structures. However, many modern applications such as gene network discovery and social interactions analysis often involve high-dimensional noisy data with outliers or…

Recognizing the successes of treed Gaussian process (TGP) models as an interpretable and thrifty model for nonparametric regression, we seek to extend the model to classification. Both treed models and Gaussian processes (GPs) have,…

Gaussian mixtures are commonly used for modeling heavy-tailed error distributions in robust linear regression. Combining the likelihood of a multivariate robust linear regression model with a standard improper prior distribution yields an…

Motivated by recent work on stochastic gradient descent methods, we develop two stochastic variants of greedy algorithms for possibly non-convex optimization problems with sparsity constraints. We prove linear convergence in expectation to…

High-dimensional graphical models are often estimated using regularization that is aimed at reducing the number of edges in a network. In this work, we show how even simpler networks can be produced by aggregating the nodes of the graphical…

Excessive computational cost for learning large data and streaming data can be alleviated by using stochastic algorithms, such as stochastic gradient descent and its variants. Recent advances improve stochastic algorithms on convergence…

Graphical Lasso (GL) is a popular method for learning the structure of an undirected graphical model, which is based on an $l_1$ regularization technique. The objective of this paper is to compare the computationally-heavy GL technique with…