Related papers: Structured Variable Selection with Sparsity-Induci…

We introduce the localized Lasso, which is suited for learning models that are both interpretable and have a high predictive power in problems with high dimensionality $d$ and small sample size $n$. More specifically, we consider a function…

Sparse connectivity is a hallmark of the brain and a desired property of artificial neural networks. It promotes energy efficiency, simplifies training, and enhances the robustness of network function. Thus, a detailed understanding of how…

Prior knowledge on properties of a target model often come as discrete or combinatorial descriptions. This work provides a unified computational framework for defining norms that promote such structures. More specifically, we develop…

This paper begins with considering the identification of sparse linear time-invariant networks described by multivariable ARX models. Such models possess relatively simple structure thus used as a benchmark to promote further research. With…

Neural network pruning is widely used to reduce model size and computational cost. Yet, most existing methods treat sparsity as an externally imposed constraint, enforced through heuristic importance scores or training-time regularization.…

The lasso and related sparsity inducing algorithms have been the target of substantial theoretical and applied research. Correspondingly, many results are known about their behavior for a fixed or optimally chosen tuning parameter specified…

Our goal is to estimate causal interactions in multivariate time series. Using vector autoregressive (VAR) models, these can be defined based on non-vanishing coefficients belonging to respective time-lagged instances. As in most cases a…

Feature selection in learning to rank has recently emerged as a crucial issue. Whereas several preprocessing approaches have been proposed, only a few works have been focused on integrating the feature selection into the learning process.…

The success of compressed sensing relies essentially on the ability to efficiently find an approximately sparse solution to an under-determined linear system. In this paper, we developed an efficient algorithm for the sparsity promoting…

Sparsity promoting regularization is an important technique for signal reconstruction and several other ill-posed problems. Theoretical investigation typically bases on the assumption that the unknown solution has a sparse representation…

In high dimensional regression settings, sparsity enforcing penalties have proved useful to regularize the data-fitting term. A recently introduced technique called screening rules propose to ignore some variables in the optimization…

Using the $\ell_1$-norm to regularize the estimation of the parameter vector of a linear model leads to an unstable estimator when covariates are highly correlated. In this paper, we introduce a new penalty function which takes into account…

We study the problem of estimating multiple linear regression equations for the purpose of both prediction and variable selection. Following recent work on multi-task learning Argyriou et al. [2008], we assume that the regression vectors…

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…

Many statistical learning problems can be posed as minimization of a sum of two convex functions, one typically a composition of non-smooth and linear functions. Examples include regression under structured sparsity assumptions. Popular…

Assume that we observe a sample of size n composed of p-dimensional signals, each signal having independent entries drawn from a scaled Poisson distribution with an unknown intensity. We are interested in estimating the sum of the n unknown…

How to estimate heterogeneity, e.g. the effect of some variable differing across observations, is a key question in political science. Methods for doing so make simplifying assumptions about the underlying nature of the heterogeneity to…

Several learning applications require solving high-dimensional regression problems where the relevant features belong to a small number of (overlapping) groups. For very large datasets and under standard sparsity constraints, hard…

Sparse model selection is ubiquitous from linear regression to graphical models where regularization paths, as a family of estimators upon the regularization parameter varying, are computed when the regularization parameter is unknown or…

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…