Related papers: Lasso under Multi-way Clustering: Estimation and P…

In a polynomial regression model, the divisibility conditions implicit in polynomial hierarchy give way to a natural construction of constraints for the model parameters. We use this principle to derive versions of strong and weak hierarchy…

Choosing relevant predictors is central to the analysis of biomedical time-to-event data. Classical frequentist inference, however, presumes that the set of covariates is fixed in advance and does not account for data-driven variable…

The LASSO is a recent technique for variable selection in the regression model \bean y & = & X\beta + z, \eean where $X\in \R^{n\times p}$ and $z$ is a centered gaussian i.i.d. noise vector $\mathcal N(0,\sigma^2I)$. The LASSO has been…

High-dimensional time series datasets are becoming increasingly common in many areas of biological and social sciences. Some important applications include gene regulatory network reconstruction using time course gene expression data, brain…

In regression problems where covariates can be naturally grouped, the group Lasso is an attractive method for variable selection since it respects the grouping structure in the data. We study the selection and estimation properties of the…

In this paper, we introduce ``UniLasso'' -- a novel statistical method for sparse regression. This two-stage approach preserves the signs of the univariate coefficients and leverages their magnitude. Both of these properties are attractive…

Penalized regression methods, most notably the lasso, are a popular approach to analyzing high-dimensional data. An attractive property of the lasso is that it naturally performs variable selection. An important area of concern, however, is…

As data sets continue to grow in size and complexity, effective and efficient techniques are needed to target important features in the variable space. Many of the variable selection techniques that are commonly used alongside clustering…

Much theoretical and applied work has been devoted to high-dimensional regression with clean data. However, we often face corrupted data in many applications where missing data and measurement errors cannot be ignored. Loh and Wainwright…

Several new methods have been proposed for performing valid inference after model selection. An older method is sampling splitting: use part of the data for model selection and part for inference. In this paper we revisit sample splitting…

We propose a novel approach, Sequential Lasso, for feature selection in linear regression models with ultra-high dimensional feature spaces. We investigate in this article the asymptotic properties of Sequential Lasso and establish its…

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…

In this paper, we apply shrinkage strategies to estimate regression coefficients efficiently for the high-dimensional multiple regression model, where the number of samples is smaller than the number of predictors. We assume in the sparse…

In high dimensional regression, feature clustering by their effects on outcomes is often as important as feature selection. For that purpose, clustered Lasso and octagonal shrinkage and clustering algorithm for regression (OSCAR) are used…

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…

We propose a new approach for sparse regression and marginal testing, for data with correlated features. Our procedure first clusters the features, and then chooses as the cluster prototype the most informative feature in that cluster. Then…

The focus of modern biomedical studies has gradually shifted to explanation and estimation of joint effects of high dimensional predictors on disease risks. Quantifying uncertainty in these estimates may provide valuable insight into…

The least absolute shrinkage and selection operator (Lasso) is a popular method for high-dimensional statistics. However, it is known that the Lasso often has estimation bias and prediction error. To address such disadvantages, many…

We propose the Bayesian adaptive Lasso (BaLasso) for variable selection and coefficient estimation in linear regression. The BaLasso is adaptive to the signal level by adopting different shrinkage for different coefficients. Furthermore, we…

This article concerns the dimension reduction in regression for large data set. We introduce a new method based on the sliced inverse regression approach, called cluster-based regularized sliced inverse regression. Our method not only keeps…