Related papers: Inference for feature selection using the Lasso wi…
Beta regression is commonly employed when the outcome variable is a proportion. Since its conception, the approach has been widely used in applications spanning various scientific fields. A series of extensions have been proposed over time,…
Variable selection, also known as feature selection in machine learning, plays an important role in modeling high dimensional data and is key to data-driven scientific discoveries. We consider here the problem of detecting influential…
We present a new method for post-selection inference for L1 (lasso)-penalized likelihood models, including generalized regression models. Our approach generalizes the post-selection framework presented in Lee et al (2014). The method…
We consider the problem of fitting the parameters of a high-dimensional linear regression model. In the regime where the number of parameters $p$ is comparable to or exceeds the sample size $n$, a successful approach uses an…
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…
It is known that the Thresholded Lasso (TL), SCAD or MCP correct intrinsic estimation bias of the Lasso. In this paper we propose an alternative method of improving the Lasso for predictive models with general convex loss functions which…
Penalized likelihood approaches are widely used for high-dimensional regression. Although many methods have been proposed and the associated theory is now well-developed, the relative efficacy of different approaches in finite-sample…
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…
We propose a new measure of variable importance in high-dimensional regression based on the change in the LASSO solution path when one covariate is left out. The proposed procedure provides a novel way to calculate variable importance and…
We propose new inference tools for forward stepwise regression, least angle regression, and the lasso. Assuming a Gaussian model for the observation vector y, we first describe a general scheme to perform valid inference after any selection…
In this article we investigate consistency of selection in regression models via the popular Lasso method. Here we depart from the traditional linear regression assumption and consider approximations of the regression function $f$ with…
This paper examines LASSO, a widely-used $L_{1}$-penalized regression method, in high dimensional linear predictive regressions, particularly when the number of potential predictors exceeds the sample size and numerous unit root regressors…
We add a set of convex constraints to the lasso to produce sparse interaction models that honor the hierarchy restriction that an interaction only be included in a model if one or both variables are marginally important. We give a precise…
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…
Shrinkage estimators that possess the ability to produce sparse solutions have become increasingly important to the analysis of today's complex datasets. Examples include the LASSO, the Elastic-Net and their adaptive counterparts.…
Estimating the importance of variables is an essential task in modern machine learning. This help to evaluate the goodness of a feature in a given model. Several techniques for estimating the importance of variables have been developed…
The Lasso is one of the most important approaches for parameter estimation and variable selection in high dimensional linear regression. At the heart of its success is the attractive rate of convergence result even when $p$, the dimension…
We propose the variable selection procedure incorporating prior constraint information into lasso. The proposed procedure combines the sample and prior information, and selects significant variables for responses in a narrower region where…
Variable selection for regression models plays a key role in the analysis of biomedical data. However, inference after selection is not covered by classical statistical frequentist theory which assumes a fixed set of covariates in the…
Selective Inference (SI) has been actively studied in the past few years for conducting inference on the features of linear models that are adaptively selected by feature selection methods such as Lasso. The basic idea of SI is to make…