Related papers: Asymptotic Theory for Graphical SLOPE: Precision E…
This paper considers the problem of estimating multiple related Gaussian graphical models from a $p$-dimensional dataset consisting of different classes. Our work is based upon the formulation of this problem as group graphical lasso. This…
Gaussian processes (GPs) provide a probabilistic nonparametric representation of functions in regression, classification, and other problems. Unfortunately, exact learning with GPs is intractable for large datasets. A variety of approximate…
Sparse structure learning in high-dimensional Gaussian graphical models is an important problem in multivariate statistical signal processing; since the sparsity pattern naturally encodes the conditional independence relationship among…
In this article, we discuss the composite likelihood estimation of sparse Gaussian graphical models. When there are symmetry constraints on the concentration matrix or partial correlation matrix, the likelihood estimation can be…
Graphical Gaussian models with edge and vertex symmetries were introduced by \citet{HojLaur:2008} who also gave an algorithm to compute the maximum likelihood estimate of the precision matrix for such models. In this paper, we take a…
This paper considers a canonical clustering problem where one receives unlabeled samples drawn from a balanced mixture of two elliptical distributions and aims for a classifier to estimate the labels. Many popular methods including PCA and…
Gaussian belief propagation (GBP) is a recursive computation method that is widely used in inference for computing marginal distributions efficiently. Depending on how the factorization of the underlying joint Gaussian distribution is…
Gradient compression is of growing interests for solving constrained optimization problems including compressed sensing, noisy recovery and matrix completion under limited communication resources and storage costs. Convergence analysis of…
The graphical lasso is a widely used algorithm for fitting undirected Gaussian graphical models. However, for inference on functionals of edge values in the learned graph, standard tools lack formal statistical guarantees, such as control…
The Collective Graphical Model (CGM) models a population of independent and identically distributed individuals when only collective statistics (i.e., counts of individuals) are observed. Exact inference in CGMs is intractable, and previous…
We formulate the sparse classification problem of $n$ samples with $p$ features as a binary convex optimization problem and propose a cutting-plane algorithm to solve it exactly. For sparse logistic regression and sparse SVM, our algorithm…
Training neural networks with high certified accuracy against adversarial examples remains an open challenge despite significant efforts. While certification methods can effectively leverage tight convex relaxations for bound computation,…
Obtaining high certainty in predictive models is crucial for making informed and trustworthy decisions in many scientific and engineering domains. However, extensive experimentation required for model accuracy can be both costly and…
We study sparse linear regression over a network of agents, modeled as an undirected graph and no server node. The estimation of the $s$-sparse parameter is formulated as a constrained LASSO problem wherein each agent owns a subset of the…
Convex optimization is an essential tool for modern data analysis, as it provides a framework to formulate and solve many problems in machine learning and data mining. However, general convex optimization solvers do not scale well, and…
The quality of graph-structured data is fundamental to the success of modern graph analysis techniques such as Graph Neural Networks (GNNs). However, real-world graph data is often suboptimal, suffering from issues such as noise and…
Tensor network contraction on arbitrary graphs is a fundamental computational challenge with applications ranging from quantum simulation to error correction. While belief propagation (BP) provides a powerful approximation algorithm for…
We consider linear regression in the high-dimensional regime where the number of observations $n$ is smaller than the number of parameters $p$. A very successful approach in this setting uses $\ell_1$-penalized least squares (a.k.a. the…
The multivariate generalized Gaussian distribution (MGGD), also known as the multivariate exponential power (MEP) distribution, is widely used in signal and image processing. However, estimating MGGD parameters, which is required in…
Spectral clustering refers to a family of unsupervised learning algorithms that compute a spectral embedding of the original data based on the eigenvectors of a similarity graph. This non-linear transformation of the data is both the key of…