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

Maximum likelihood estimation of large Markov-switching vector autoregressions (MS-VARs) can be challenging or infeasible due to parameter proliferation. To accommodate situations where dimensionality may be of comparable order to or…

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…

The popular Lasso approach for sparse estimation can be derived via marginalization of a joint density associated with a particular stochastic model. A different marginalization of the same probabilistic model leads to a different…

We consider a novel Bayesian approach to estimation, uncertainty quantification, and variable selection for a high-dimensional linear regression model under sparsity. The number of predictors can be nearly exponentially large relative to…

In this article we study post-model selection estimators that apply ordinary least squares (OLS) to the model selected by first-step penalized estimators, typically Lasso. It is well known that Lasso can estimate the nonparametric…

In statistical learning theory, determining the sample complexity of realizable binary classification for VC classes was a long-standing open problem. The results of Simon and Hanneke established sharp upper bounds in this setting. However,…

We propose a very fast approximate Markov Chain Monte Carlo (MCMC) sampling framework that is applicable to a large class of sparse Bayesian inference problems, where the computational cost per iteration in several models is of order…

Aggregation methods have emerged as a powerful and flexible framework in statistical learning, providing unified solutions across diverse problems such as regression, classification, and density estimation. In the context of generalized…

The abundance of high-dimensional data in the modern sciences has generated tremendous interest in penalized estimators such as the lasso, scaled lasso, square-root lasso, elastic net, and many others. In this paper, we establish a general…

Considering the increasing size of available data, the need for statistical methods that control the finite sample bias is growing. This is mainly due to the frequent settings where the number of variables is large and allowed to increase…

There has been an intense development on the estimation of a sparse regression coefficient vector in statistics, machine learning and related fields. In this paper, we focus on the Bayesian approach to this problem, where sparsity is…

Recent results have proven the minimax optimality of LASSO and related algorithms for noisy linear regression. However, these results tend to rely on variance estimators that are inefficient or optimizations that are slower than LASSO…

The $\ell_1$-penalized method, or the Lasso, has emerged as an important tool for the analysis of large data sets. Many important results have been obtained for the Lasso in linear regression which have led to a deeper understanding of…

This paper addresses the problem of model selection in the sequence model $Y=\theta+\varepsilon\xi$, when $\xi$ is sub-Gaussian, for non-euclidian loss-functions. In this model, the Penalized Comparison to Overfitting procedure is studied…

Large-scale sequential data is often exposed to some degree of inhomogeneity in the form of sudden changes in the parameters of the data-generating process. We consider the problem of detecting such structural changes in a high-dimensional…

This paper is concerned with inference on the regression function of a high-dimensional linear model when outcomes are missing at random. We propose an estimator which combines a Lasso pilot estimate of the regression function with a bias…

A robust and sparse estimator for multinomial regression is proposed for high dimensional data. Robustness of the estimator is achieved by trimming the observations, and sparsity of the estimator is obtained by the elastic net penalty,…

We show that two polynomial time methods, a Lasso estimator with adaptively chosen tuning parameter and a Slope estimator, adaptively achieve the exact minimax prediction and $\ell_2$ estimation rate $(s/n)\log (p/s)$ in high-dimensional…

We consider the problem of estimating the parameters of a Gaussian or binary distribution in such a way that the resulting undirected graphical model is sparse. Our approach is to solve a maximum likelihood problem with an added l_1-norm…

We consider machine learning techniques to develop low-latency approximate solutions to a class of inverse problems. More precisely, we use a probabilistic approach for the problem of recovering sparse stochastic signals that are members of…