Related papers: Safe Feature Elimination for the LASSO and Sparse …
L1 -penalized regression methods such as the Lasso (Tibshirani 1996) that achieve both variable selection and shrinkage have been very popular. An extension of this method is the Fused Lasso (Tibshirani and Wang 2007), which allows for the…
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…
In several applications, input samples are more naturally represented in terms of similarities between each other, rather than in terms of feature vectors. In these settings, machine-learning algorithms can become very computationally…
Solving l1 regularized optimization problems is common in the fields of computational biology, signal processing and machine learning. Such l1 regularization is utilized to find sparse minimizers of convex functions. A well-known example is…
In this paper, we propose a novel sparse learning based feature selection method that directly optimizes a large margin linear classification model sparsity with l_(2,p)-norm (0 < p < 1)subject to data-fitting constraints, rather than using…
In high-dimensional model selection problems, penalized simple least-square approaches have been extensively used. This paper addresses the question of both robustness and efficiency of penalized model selection methods, and proposes a…
The problem of finding the maximum likelihood estimates for the regression coefficients in generalised linear models with an L1 sparsity penalty is shown to be equivalent to minimising the unpenalised maximum log-likelihood function over a…
We propose a Multi-step Screening Procedure (MSP) for the recovery of sparse linear models in high-dimensional data. This method is based on a repeated small penalty strategy that quickly converges to an estimate within a few iterations.…
In many high dimensional classification or regression problems set in a biological context, the complete identification of the set of informative features is often as important as predictive accuracy, since this can provide mechanistic…
We propose Robust Lasso-Zero, an extension of the Lasso-Zero methodology, initially introduced for sparse linear models, to the sparse corruptions problem. We give theoretical guarantees on the sign recovery of the parameters for a slightly…
We study the problem of estimating high-dimensional regression models regularized by a structured sparsity-inducing penalty that encodes prior structural information on either the input or output variables. We consider two widely adopted…
Inferring network structures remains an interesting question for its importance on the understanding and controlling collective dynamics of complex systems. The existing shrinking methods such as Lasso-type estimation can not suitably…
This paper presents new algorithms to solve the feature-sparsity constrained PCA problem (FSPCA), which performs feature selection and PCA simultaneously. Existing optimization methods for FSPCA require data distribution assumptions and are…
We propose a new prediction method for multivariate linear regression problems where the number of features is less than the sample size but the number of outcomes is extremely large. Many popular procedures, such as penalized regression…
We propose a new algorithm for recovery of sparse signals from their compressively sensed samples. The proposed algorithm benefits from the strategy of gradual movement to estimate the positions of non-zero samples of sparse signal. We…
The Lasso is a very well known penalized regression model, which adds an $L_{1}$ penalty with parameter $\lambda_{1}$ on the coefficients to the squared error loss function. The Fused Lasso extends this model by also putting an $L_{1}$…
We develop an approach for feature elimination in statistical learning with kernel machines, based on recursive elimination of features.We present theoretical properties of this method and show that it is uniformly consistent in finding the…
We consider the least angle regression and forward stagewise algorithms for solving penalized least squares regression problems. In Efron, Hastie, Johnstone & Tibshirani (2004) it is proved that the least angle regression algorithm, with a…
Despite widespread adoption in practice, guarantees for the LASSO and Group LASSO are strikingly lacking in settings beyond statistical problems, and these algorithms are usually considered to be a heuristic in the context of sparse convex…
The performance of penalized likelihood approaches depends profoundly on the selection of the tuning parameter; however, there is no commonly agreed-upon criterion for choosing the tuning parameter. Moreover, penalized likelihood estimation…