Related papers: Pac-bayesian bounds for sparse regression estimati…

We propose a new approach to mixed-frequency regressions in a high-dimensional environment that resorts to Group Lasso penalization and Bayesian techniques for estimation and inference. In particular, to improve the prediction properties of…

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…

This paper introduces an efficient sparse recovery approach for Polynomial Chaos (PC) expansions, which promotes the sparsity by breaking the dimensionality of the problem. The proposed algorithm incrementally explores sub-dimensional…

This paper presents a general theoretical framework of penalized quasi-maximum likelihood (PQML) estimation in stationary multiple time series models when the number of parameters possibly diverges. We show the oracle property of the PQML…

Implicit sampling is a weighted sampling method that is used in data assimilation, where one sequentially updates estimates of the state of a stochastic model based on a stream of noisy or incomplete data. Here we describe how to use…

This paper provides the relevant literature with a complete toolkit for conducting robust estimation and inference about the parameters of interest involved in a high-dimensional panel data framework. Specifically, (1) we allow for…

In all areas of human knowledge, datasets are increasing in both size and complexity, creating the need for richer statistical models. This trend is also true for economic data, where high-dimensional and nonlinear/nonparametric inference…

We consider high-dimensional inference for potentially misspecified Cox proportional hazard models based on low dimensional results by Lin and Wei [1989]. A de-sparsified Lasso estimator is proposed based on the log partial likelihood…

Sparse linear regression is a fundamental problem in high-dimensional statistics, but strikingly little is known about how to efficiently solve it without restrictive conditions on the design matrix. We consider the (correlated) random…

The paper revisits the Bayesian group lasso and uses spike and slab priors for group variable selection. In the process, the connection of our model with penalized regression is demonstrated, and the role of posterior median for…

Zou [J. Amer. Statist. Assoc. 101 (2006) 1418-1429] proposed the Adaptive LASSO (ALASSO) method for simultaneous variable selection and estimation of the regression parameters, and established its oracle property. In this paper, we…

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…

Variable selection is one of the most important tasks in statistics and machine learning. To incorporate more prior information about the regression coefficients, the constrained Lasso model has been proposed in the literature. In this…

We study a sparse negative binomial regression (NBR) for count data by showing the non-asymptotic advantages of using the elastic-net estimator. Two types of oracle inequalities are derived for the NBR's elastic-net estimates by using the…

This paper studies sparse linear regression analysis with outliers in the responses. A parameter vector for modeling outliers is added to the standard linear regression model and then the sparse estimation problem for both coefficients and…

We develop a technique to design efficiently computable estimators for sparse linear regression in the simultaneous presence of two adversaries: oblivious and adaptive. We design several robust algorithms that outperform the state of the…

For multiple index models, it has recently been shown that the sliced inverse regression (SIR) is consistent for estimating the sufficient dimension reduction (SDR) space if and only if $\rho=\lim\frac{p}{n}=0$, where $p$ is the dimension…

The sparse inverse covariance estimation problem is commonly solved using an $\ell_{1}$-regularized Gaussian maximum likelihood estimator known as "graphical lasso", but its computational cost becomes prohibitive for large data sets. A…

In this paper, we study the system identification problem for sparse linear time-invariant systems. We propose a sparsity promoting block-regularized estimator to identify the dynamics of the system with only a limited number of input-state…

High-dimensional learning problems, where the number of features exceeds the sample size, often require sparse regularization for effective prediction and variable selection. While established for fully supervised data, these techniques…