Related papers: Multiple Equivalent Solutions for the Lasso
This thesis investigates the use of problem-specific knowledge to enhance a genetic algorithm approach to multiple-choice optimisation problems.It shows that such information can significantly enhance performance, but that the choice of…
We consider the least-square linear regression problem with regularization by the $\ell^1$-norm, a problem usually referred to as the Lasso. In this paper, we first present a detailed asymptotic analysis of model consistency of the Lasso in…
In [1], we have explored the theoretical aspects of feature selection and evolutionary algorithms. In this chapter, we focus on optimization algorithms for enhancing data analytic process, i.e., we propose to explore applications of…
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…
Sparse learning techniques have been routinely used for feature selection as the resulting model usually has a small number of non-zero entries. Safe screening, which eliminates the features that are guaranteed to have zero coefficients for…
Sparse modeling is a powerful framework for data analysis and processing. Traditionally, encoding in this framework is done by solving an l_1-regularized linear regression problem, usually called Lasso. In this work we first combine the…
Feature selection plays an important role in the data mining process. It is needed to deal with the excessive number of features, which can become a computational burden on the learning algorithms. It is also necessary, even when…
Feature selection problems have been extensively studied for linear estimation, for instance, Lasso, but less emphasis has been placed on feature selection for non-linear functions. In this study, we propose a method for feature selection…
Sparse modelling or model selection with categorical data is challenging even for a moderate number of variables, because one parameter is roughly needed to encode one category or level. The Group Lasso is a well known efficient algorithm…
It is well-known that the statistical performance of Lasso can suffer significantly when the covariates of interest have strong correlations. In particular, the prediction error of Lasso becomes much worse than computationally inefficient…
Feature selection and instance selection are two important techniques of data processing. However, such selections have mostly been studied separately, while existing work towards the joint selection conducts feature/instance selection…
The network Lasso is a recently proposed convex optimization method for machine learning from massive network structured datasets, i.e., big data over networks. It is a variant of the well-known least absolute shrinkage and selection…
We propose a rescaled LASSO, by premultipying the LASSO with a matrix term, namely linear unified LASSO (LLASSO) for multicollinear situations. Our numerical study has shown that the LLASSO is comparable with other sparse modeling…
Stability selection (Meinshausen and Buhlmann, 2010) makes any feature selection method more stable by returning only those features that are consistently selected across many subsamples. We prove (in what is, to our knowledge, the first…
Feature selection is an important problem in high-dimensional data analysis and classification. Conventional feature selection approaches focus on detecting the features based on a redundancy criterion using learning and feature searching…
Best subset selection in linear regression is well known to be nonconvex and computationally challenging to solve, as the number of possible subsets grows rapidly with increasing dimensionality of the problem. As a result, finding the…
Feature selection is one of the most decisive tools in understanding data and machine learning models. Among other methods, sparsity induced by $L^{1}$ penalty is one of the simplest and best studied approaches to this problem. Although…
This paper studies high-dimensional regression models with lasso when data is sampled under multi-way clustering. First, we establish convergence rates for the lasso and post-lasso estimators. Second, we propose a novel inference method…
It is common to show the confidence intervals or $p$-values of selected features, or predictor variables in regression, but they often involve selection bias. The selective inference approach solves this bias by conditioning on the…
In this paper, we investigate the research problem of unsupervised multi-view feature selection. Conventional solutions first simply combine multiple pre-constructed view-specific similarity structures into a collaborative similarity…