Related papers: LASSO, Iterative Feature Selection and the Correla…
This paper proposes a Lasso-based estimator which uses information embedded in the Moran statistic to develop a selection procedure called Moran's I Lasso (Mi-Lasso) to solve the Eigenvector Spatial Filtering (ESF) eigenvector selection…
An Orthogonal Least Squares (OLS) based feature selection method is proposed for both binomial and multinomial classification. The novel Squared Orthogonal Correlation Coefficient (SOCC) is defined based on Error Reduction Ratio (ERR) in…
We consider a high-dimensional linear regression problem. Unlike many papers on the topic, we do not require sparsity of the regression coefficients; instead, our main structural assumption is a decay of eigenvalues of the covariance matrix…
Lasso is a celebrated method for variable selection in linear models, but it faces challenges when the variables are moderately or strongly correlated. This motivates alternative approaches such as using a non-convex penalty, adding a ridge…
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…
The LASSO-Patternsearch algorithm is proposed to efficiently identify patterns of multiple dichotomous risk factors for outcomes of interest in demographic and genomic studies. The patterns considered are those that arise naturally from the…
In this paper, we investigate seemingly unrelated regression (SUR) models that allow the number of equations (N) to be large, and to be comparable to the number of the observations in each equation (T). It is well known in the literature…
In a previous article, a least square regression estimation procedure was proposed: first, we condiser a family of functions and study the properties of an estimator in every unidimensionnal model defined by one of these functions; we then…
The problem of adaptive multivariate function estimation in the single-index regression model with random design and weak assumptions on the noise is investigated. A novel estimation procedure that adapts simultaneously to the unknown index…
The Graphical Lasso (GLasso) algorithm is fast and widely used for estimating sparse precision matrices (Friedman et al., 2008). Its central role in the literature of high-dimensional covariance estimation rivals that of Lasso regression…
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…
Many applications that use empirically estimated functions face a curse of dimensionality, because the integrals over most function classes must be approximated by sampling. This paper introduces a novel regression-algorithm that learns…
We study an $\ell_{1}$-regularized generalized least-squares (GLS) estimator for high-dimensional regressions with autocorrelated errors. Specifically, we consider the case where errors are assumed to follow an autoregressive process,…
Classification with a sparsity constraint on the solution plays a central role in many high dimensional machine learning applications. In some cases, the features can be grouped together so that entire subsets of features can be selected or…
Sparse linear regression is a central problem in high-dimensional statistics. We study the correlated random design setting, where the covariates are drawn from a multivariate Gaussian $N(0,\Sigma)$, and we seek an estimator with small…
We propose an algorithm to select parameter subset combinations that can be estimated using an ordinary least-squares (OLS) inverse problem formulation with a given data set. First, the algorithm selects the parameter combinations that…
Sparse feature selection has been demonstrated to be effective in handling high-dimensional data. While promising, most of the existing works use convex methods, which may be suboptimal in terms of the accuracy of feature selection and…
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…
When we are interested in high-dimensional system and focus on classification performance, the $\ell_{1}$-penalized logistic regression is becoming important and popular. However, the Lasso estimates could be problematic when penalties of…
We establish rates of convergences in time series forecasting using the statistical learning approach based on oracle inequalities. A series of papers extends the oracle inequalities obtained for iid observations to time series under weak…