Related papers: Variance estimation in graphs with the fused lasso
Consider estimating a structured signal $\mathbf{x}_0$ from linear, underdetermined and noisy measurements $\mathbf{y}=\mathbf{A}\mathbf{x}_0+\mathbf{z}$, via solving a variant of the lasso algorithm: $\hat{\mathbf{x}}=\arg\min_\mathbf{x}\{…
The pattern of zero entries in the inverse covariance matrix of a multivariate normal distribution corresponds to conditional independence restrictions between variables. Covariance selection aims at estimating those structural zeros from…
We study the problem of robust estimation under heterogeneous corruption rates, where each sample may be independently corrupted with a known but non-identical probability. This setting arises naturally in distributed and federated…
The main result of this article is that we obtain an elementwise error bound for the Fused Lasso estimator for any general convex loss function $\rho$. We then focus on the special cases when either $\rho$ is the square loss function (for…
Given a graph with a subset of labeled nodes, we are interested in the quality of the averaging estimator which for an unlabeled node predicts the average of the observations of its labeled neighbors. We rigorously study concentration…
It is of particular interest to reconstruct or estimate bandlimited graph signals, which are smoothly varying signals defined over graphs, from partial noisy measurements. However, choosing an optimal subset of nodes to sample is NP-hard.…
We propose a desigining method of a flexible sampling operator for graph signals via a difference-of-convex (DC) optimization algorithm. A fundamental challenge in graph signal processing is sampling, especially for graph signals that are…
In this paper we introduce and study fused lasso nearly-isotonic signal approximation, which is a combination of fused lasso and generalized nearly-isotonic regression. We show how these three estimators relate to each other, derive…
Debiasing group graphical lasso estimates enables statistical inference when multiple Gaussian graphical models share a common sparsity pattern. We analyze the estimation properties of group graphical lasso, establishing convergence rates…
We consider the problem of estimating multiple related but distinct graphical models on the basis of a high-dimensional data set with observations that belong to distinct classes. A motivating example occurs in the analysis of gene…
Learning distributed representations for nodes in graphs is a crucial primitive in network analysis with a wide spectrum of applications. Linear graph embedding methods learn such representations by optimizing the likelihood of both…
In many applied fields, such as genomics, different types of data are collected on the same system, and it is not uncommon that some of these datasets are subject to censoring as a result of the measurement technologies used, such as data…
Large-sample Bayesian analogs exist for many frequentist methods, but are less well-known for the widely-used 'sandwich' or 'robust' variance estimates. We review existing approaches to Bayesian analogs of sandwich variance estimates and…
In this manuscript a unified framework for conducting inference on complex aggregated data in high dimensional settings is proposed. The data are assumed to be a collection of multiple non-Gaussian realizations with underlying undirected…
Many Machine Learning algorithms are formulated as regularized optimization problems, but their performance hinges on a regularization parameter that needs to be calibrated to each application at hand. In this paper, we propose a general…
In neuroscience, researchers seek to uncover the connectivity of neurons from large-scale neural recordings or imaging; often people employ graphical model selection and estimation techniques for this purpose. But, existing technologies can…
Dyadic data are common in the social sciences, although inference for such settings involves accounting for a complex clustering structure. Many analyses in the social sciences fail to account for the fact that multiple dyads share a…
We describe a protocol for the average consensus problem on any fixed undirected graph whose convergence time scales linearly in the total number nodes $n$. The protocol is completely distributed, with the exception of requiring all nodes…
We apply classical and Bayesian lasso regularizations to a family of models with the presence of mixture and process variables. We analyse the performance of these estimates with respect to ordinary least squares estimators by a simulation…
Despite numerous years of research into the merits and trade-offs of various model selection criteria, obtaining robust results that elucidate the behavior of cross-validation remains a challenging endeavor. In this paper, we highlight the…