Related papers: A Pliable Lasso
Varying coefficient models are useful in applications where the effect of the covariate might depend on some other covariate such as time or location. Various applications of these models often give rise to case-specific prior distributions…
This paper studies a very flexible model that can be used widely to analyze the relation between a response and multiple covariates. The model is nonparametric, yet renders easy interpretation for the effects of the covariates. The model…
Modern statistical learning algorithms are capable of amazing flexibility, but struggle with interpretability. One possible solution is sparsity: making inference such that many of the parameters are estimated as being identically 0, which…
We develop a model-based empirical Bayes approach to variable selection problems in which the number of predictors is very large, possibly much larger than the number of responses (the so-called 'large p, small n' problem). We consider the…
We consider the problem of identifying significant predictors in large data bases, where the response variable depends on the linear combination of explanatory variables through an unknown link function, corrupted with the noise from the…
In machine learning one of the strategic tasks is the selection of only significant variables as predictors for the response(s). In this paper an approach is proposed which consists in the application of permutation tests on the candidate…
In linear models it is common to have situations where several regression coefficients are zero. In these situations a common tool to perform regression is a variable selection operator. One of the most common such operators is the LASSO…
Varying coefficient regression is a flexible technique for modeling data where the coefficients are functions of some effect-modifying parameter, often time or location in a certain domain. While there are a number of methods for variable…
In a multivariate linear regression model with $p>1$ covariates, implementation of penalization techniques often implies a preliminary univariate standardization step. Although this prevents scale effects on the covariates selection…
In high-dimensional survival analysis, effective variable selection is crucial for both model interpretation and predictive performance. This paper investigates Cox regression with lasso and adaptive lasso penalties in genomic datasets…
There are proposals that extend the classical generalized additive models (GAMs) to accommodate high-dimensional data ($p>>n$) using group sparse regularization. However, the sparse regularization may induce excess shrinkage when estimating…
Sparse regularization such as $\ell_1$ regularization is a quite powerful and widely used strategy for high dimensional learning problems. The effectiveness of sparse regularization has been supported practically and theoretically by…
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…
Selective inference methods are developed for group lasso estimators for use with a wide class of distributions and loss functions. The method includes the use of exponential family distributions, as well as quasi-likelihood modeling for…
We consider the estimation of regression models on strata defined using a categorical covariate, in order to identify interactions between this categorical covariate and the other predictors. A basic approach requires the choice of a…
The choice of the tuning parameter in the Lasso is central to its statistical performance in high-dimensional linear regression. In this work, we study tuning regimes under which the Lasso exhibits suboptimal prediction performance, in the…
Pretraining is a popular and powerful paradigm in machine learning to pass information from one model to another. As an example, suppose one has a modest-sized dataset of images of cats and dogs, and plans to fit a deep neural network to…
We propose a generalized debiased Lasso estimator based on a stability principle. When a single column of the design matrix is perturbed, the estimator admits a simple update formula that can be computed from the original solution. Under…
We study the limitations of the well known LASSO regression as a variable selector when there exists dependence structures among covariates. We analyze both the classic situation with $n\geq p$ and the high dimensional framework with $p>n$.…
We propose a general adaptive LASSO method for a quantile regression model. Our method is very interesting when we know nothing about the first two moments of the model error. We first prove that the obtained estimators satisfy the oracle…