Related papers: Bad estimation, good prediction: the Lasso in dens…
We consider estimation in a high-dimensional linear model with strongly correlated variables. We propose to cluster the variables first and do subsequent sparse estimation such as the Lasso for cluster-representatives or the group Lasso…
In this article we investigate consistency of selection in regression models via the popular Lasso method. Here we depart from the traditional linear regression assumption and consider approximations of the regression function $f$ with…
In this paper we develop inference for high dimensional linear models, with serially correlated errors. We examine Lasso under the assumption of strong mixing in the covariates and error process, allowing for fatter tails in their…
We consider selection of random predictors for high-dimensional regression problem with binary response for a general loss function. Important special case is when the binary model is semiparametric and the response function is misspecified…
Penalized regression methods, most notably the lasso, are a popular approach to analyzing high-dimensional data. An attractive property of the lasso is that it naturally performs variable selection. An important area of concern, however, is…
As a popular tool for producing meaningful and interpretable models, large-scale sparse learning works efficiently when the underlying structures are indeed or close to sparse. However, naively applying the existing regularization methods…
This paper studies the properties of linear regression on centrality measures when network data is sparse and observed with error. We make three contributions in this setting. First, we show that OLS estimators can become inconsistent under…
While Weighted Lasso sparse regression has appealing statistical guarantees that would entail a major real-world impact in finance, genomics, and brain imaging applications, it is typically scarcely adopted due to its complex…
Regularization is a common tool in variational inverse problems to impose assumptions on the parameters of the problem. One such assumption is sparsity, which is commonly promoted using lasso and total variation-like regularization.…
In this work, we consider learning sparse models in large scale settings, where the number of samples and the feature dimension can grow as large as millions or billions. Two immediate issues occur under such challenging scenario: (i)…
In high-dimensional statistical inference, sparsity regularizations have shown advantages in consistency and convergence rates for coefficient estimation. We consider a generalized version of Sparse-Group Lasso which captures both…
Using a multiplicative reparametrization, I show that a subclass of $L_q$ penalties with $q\leq 1$ can be expressed as sums of $L_2$ penalties. It follows that the lasso and other norm-penalized regression estimates may be obtained using a…
In this paper we revisit the risk bounds of the lasso estimator in the context of transductive and semi-supervised learning. In other terms, the setting under consideration is that of regression with random design under partial labeling.…
We study the finite sample behavior of Lasso-based inference methods such as post double Lasso and debiased Lasso. We show that these methods can exhibit substantial omitted variable biases (OVBs) due to Lasso not selecting relevant…
Popular regularizers with non-differentiable penalties, such as Lasso, Elastic Net, Generalized Lasso, or SLOPE, reduce the dimension of the parameter space by inducing sparsity or clustering in the estimators' coordinates. In this paper,…
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…
In a polynomial regression model, the divisibility conditions implicit in polynomial hierarchy give way to a natural construction of constraints for the model parameters. We use this principle to derive versions of strong and weak hierarchy…
The Bayesian Lasso is constructed in the linear regression framework and applies the Gibbs sampling to estimate the regression parameters. This paper develops a new sparse learning model, named the Bayesian Lasso Sparse (BLS) model, that…
High-dimensional data sets are often analyzed and explored via the construction of a latent low-dimensional space which enables convenient visualization and efficient predictive modeling or clustering. For complex data structures, linear…
We examine the linear regression problem in a challenging high-dimensional setting with correlated predictors where the vector of coefficients can vary from sparse to dense. In this setting, we propose a combination of probabilistic…