Related papers: Sample-Efficient L0-L2 Constrained Structure Learn…
We consider the problem of learning the structure of ferromagnetic Ising models Markov on sparse Erdos-Renyi random graph. We propose simple local algorithms and analyze their performance in the regime of correlation decay. We prove that an…
Outstanding achievements of graph neural networks for spatiotemporal time series analysis show that relational constraints introduce an effective inductive bias into neural forecasting architectures. Often, however, the relational…
This paper considers a high-dimensional linear regression problem where there are complex correlation structures among predictors. We propose a graph-constrained regularization procedure, named Sparse Laplacian Shrinkage with the Graphical…
We study functional regression with random subgaussian design and real-valued response. The focus is on the problems in which the regression function can be well approximated by a functional linear model with the slope function being…
We study sparse linear regression over a network of agents, modeled as an undirected graph (with no centralized node). The estimation problem is formulated as the minimization of the sum of the local LASSO loss functions plus a quadratic…
We are motivated by problems that arise in a number of applications such as Online Marketing and explosives detection, where the observations are usually modeled using Poisson statistics. We model each observation as a Poisson random…
This paper investigates the problem of recovering missing samples using methods based on sparse representation adapted especially for image signals. Instead of $l_2$-norm or Mean Square Error (MSE), a new perceptual quality measure is used…
Graph learning problems are typically approached by focusing on learning the topology of a single graph when signals from all nodes are available. However, many contemporary setups involve multiple related networks and, moreover, it is…
Sparse Gaussian graphical models characterize sparse dependence relationships between random variables in a network. To estimate multiple related Gaussian graphical models on the same set of variables, we formulate a hierarchical model,…
For various applications, the relations between the dependent and independent variables are highly nonlinear. Consequently, for large scale complex problems, neural networks and regression trees are commonly preferred over linear models…
We propose a practical method for $L_0$ norm regularization for neural networks: pruning the network during training by encouraging weights to become exactly zero. Such regularization is interesting since (1) it can greatly speed up…
In numerous substitution models for the $\l_{0}$-norm minimization problem $(P_{0})$, the $\l_{p}$-norm minimization $(P_{p})$ with $0<p<1$ have been considered as the most natural choice. However, the non-convex optimization problem…
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…
We study sparse group Lasso for high-dimensional double sparse linear regression, where the parameter of interest is simultaneously element-wise and group-wise sparse. This problem is an important instance of the simultaneously structured…
Variable selection is a fundamental task in statistical data analysis. Sparsity-inducing regularization methods are a popular class of methods that simultaneously perform variable selection and model estimation. The central problem is a…
We compute approximate solutions to L0 regularized linear regression using L1 regularization, also known as the Lasso, as an initialization step. Our algorithm, the Lass-0 ("Lass-zero"), uses a computationally efficient stepwise search to…
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.…
In this paper we investigate the computational complexity of learning the graph structure underlying a discrete undirected graphical model from i.i.d. samples. We first observe that the notoriously difficult problem of learning parities…
Sparse estimation methods are aimed at using or obtaining parsimonious representations of data or models. They were first dedicated to linear variable selection but numerous extensions have now emerged such as structured sparsity or kernel…
We tackle the problem of recovering an unknown signal observed in an ill-posed inverse problem framework. More precisely, we study a procedure commonly used in numerical analysis or image deblurring: minimizing an empirical loss function…