Related papers: Structured Sparse Aggregation
We present an extension of sparse PCA, or sparse dictionary learning, where the sparsity patterns of all dictionary elements are structured and constrained to belong to a prespecified set of shapes. This \emph{structured sparse PCA} is…
The past few years have witnessed increasing research interest on covariance-based feature representation. A variety of methods have been proposed to boost its efficacy, with some recent ones resorting to nonlinear kernel technique. Noting…
We propose a new approach for metric learning by framing it as learning a sparse combination of locally discriminative metrics that are inexpensive to generate from the training data. This flexible framework allows us to naturally derive…
A structured variable selection problem is considered in which the covariates, divided into predefined groups, activate according to sparse patterns with few nonzero entries per group. Capitalizing on the concept of atomic norm, a composite…
We introduce a very general method for sparse and large-scale variable selection. The large-scale regression settings is such that both the number of parameters and the number of samples are extremely large. The proposed method is based on…
We offer a method to estimate a covariance matrix in the special case that \textit{both} the covariance matrix and the precision matrix are sparse --- a constraint we call double sparsity. The estimation method is maximum likelihood,…
This paper studies oracle properties of $\ell_1$-penalized least squares in nonparametric regression setting with random design. We show that the penalized least squares estimator satisfies sparsity oracle inequalities, i.e., bounds in…
Quantile regression is studied in combination with a penalty which promotes structured (or group) sparsity. A mixed $\ell_{1,\infty}$-norm on the parameter vector is used to impose structured sparsity on the traditional quantile regression…
The likelihood for the parameters of a generalized linear mixed model involves an integral which may be of very high dimension. Because of this intractability, many approximations to the likelihood have been proposed, but all can fail when…
In partially linear additive models the response variable is modelled with a linear component on a subset of covariates and an additive component in which the rest of the covariates enter to the model as a sum of univariate unknown…
Conformal predictors, introduced by Vovk et al. (2005), serve to build prediction intervals by exploiting a notion of conformity of the new data point with previously observed data. In the present paper, we propose a novel method for…
In this paper we consider estimation of sparse covariance matrices and propose a thresholding procedure which is adaptive to the variability of individual entries. The estimators are fully data driven and enjoy excellent performance both…
We provide finite sample properties of sparse multivariate ARCH processes, where the linear representation of ARCH models allows for an ordinary least squares estimation. Under the restricted strong convexity of the unpenalized loss…
We develop a constructive approach to estimating sparse, high-dimensional linear regression models. The approach is a computational algorithm motivated from the KKT conditions for the $\ell_0$-penalized least squares solutions. It generates…
In this thesis we discuss machine learning methods performing automated variable selection for learning sparse predictive models. There are multiple reasons for promoting sparsity in the predictive models. By relying on a limited set of…
Structured sparse optimization is an important and challenging problem for analyzing high-dimensional data in a variety of applications such as bioinformatics, medical imaging, social networks, and astronomy. Although a number of structured…
We study supervised learning problems using clustering constraints to impose structure on either features or samples, seeking to help both prediction and interpretation. The problem of clustering features arises naturally in text…
Sparse model estimation is a topic of high importance in modern data analysis due to the increasing availability of data sets with a large number of variables. Another common problem in applied statistics is the presence of outliers in the…
Composite likelihood has shown promise in settings where the number of parameters $p$ is large due to its ability to break down complex models into simpler components, thus enabling inference even when the full likelihood is not tractable.…
Joint sparsity offers powerful structural cues for feature selection, especially for variables that are expected to demonstrate a "grouped" behavior. Such behavior is commonly modeled via group-lasso, multitask lasso, and related methods…