Related papers: Error Bounds for Generalized Group Sparsity

Demanding sparsity in estimated models has become a routine practice in statistics. In many situations, we wish to require that the sparsity patterns attained honor certain problem-specific constraints. Hierarchical sparse modeling (HSM)…

We study a localized notion of uniform convergence known as an "optimistic rate" (Panchenko 2002; Srebro et al. 2010) for linear regression with Gaussian data. Our refined analysis avoids the hidden constant and logarithmic factor in…

This paper investigates the theoretical guarantees of L1-analysis regularization when solving linear inverse problems. Most of previous works in the literature have mainly focused on the sparse synthesis prior where the sparsity is measured…

Inverse problems arise in a wide spectrum of applications in fields ranging from engineering to scientific computation. Connected with the rise of interest in inverse problems is the development and analysis of regularization methods, such…

It has been observed that the performances of many high-dimensional estimation problems are universal with respect to underlying sensing (or design) matrices. Specifically, matrices with markedly different constructions seem to achieve…

Selecting appropriate regularization coefficients is critical to performance with respect to regularized empirical risk minimization problems. Existing theoretical approaches attempt to determine the coefficients in order for regularized…

We consider the problem of estimating a sparse linear regression vector $\beta^*$ under a gaussian noise model, for the purpose of both prediction and model selection. We assume that prior knowledge is available on the sparsity pattern,…

In this manuscript we consider the problem of generalized linear estimation on Gaussian mixture data with labels given by a single-index model. Our first result is a sharp asymptotic expression for the test and training errors in the…

The Lasso is an attractive technique for regularization and variable selection for high-dimensional data, where the number of predictor variables $p_n$ is potentially much larger than the number of samples $n$. However, it was recently…

Exponential generalization bounds with near-tight rates have recently been established for uniformly stable learning algorithms. The notion of uniform stability, however, is stringent in the sense that it is invariant to the data-generating…

The problem of consistently estimating the sparsity pattern of a vector $\betastar \in \real^\mdim$ based on observations contaminated by noise arises in various contexts, including subset selection in regression, structure estimation in…

This paper proposes a general framework to design a sparse sensing matrix $\ensuremath{\mathbf{A}}\in \mathbb{R}^{m\times n}$, in a linear measurement system $\ensuremath{\mathbf{y}} = \ensuremath{\mathbf{Ax}}^{\natural} +…

In this paper, we are concerned with regression problems where covariates can be grouped in nonoverlapping blocks, and where only a few of them are assumed to be active. In such a situation, the group Lasso is an at- tractive method for…

We present a unified framework for estimation and analysis of generalized additive models in high dimensions. The framework defines a large class of penalized regression estimators, encompassing many existing methods. An efficient…

Sparse estimation methods are aimed at using or obtaining parsimonious representations of data or models. While naturally cast as a combinatorial optimization problem, variable or feature selection admits a convex relaxation through the…

Measurement error is a pervasive issue which renders the results of an analysis unreliable. The measurement error literature contains numerous correction techniques, which can be broadly divided into those which aim to produce exactly…

We consider the problem of minimizing an objective function that is the sum of a convex function and a group sparsity-inducing regularizer. Problems that integrate such regularizers arise in modern machine learning applications, often for…

Doubly stochastic learning algorithms are scalable kernel methods that perform very well in practice. However, their generalization properties are not well understood and their analysis is challenging since the corresponding learning…

Convex sparsity-promoting regularizations are ubiquitous in modern statistical learning. By construction, they yield solutions with few non-zero coefficients, which correspond to saturated constraints in the dual optimization formulation.…

Recently, distributed dual averaging has received increasing attention due to its superiority in handling constraints and dynamic networks in multiagent optimization. However, all distributed dual averaging methods reported so far…