Related papers: An algorithm for the multivariate group lasso with…
This paper tackles the problem of robust covariance matrix estimation when the data is incomplete. Classical statistical estimation methodologies are usually built upon the Gaussian assumption, whereas existing robust estimation ones assume…
We consider the linear regression problem. We propose the S-Lasso procedure to estimate the unknown regression parameters. This estimator enjoys sparsity of the representation while taking into account correlation between successive…
The Lasso (Least Absolute Shrinkage and Selection Operator) has been a popular technique for simultaneous linear regression estimation and variable selection. In this paper, we propose a new novel approach for robust Lasso that follows the…
This paper deals with the grouped variable selection problem. A widely used strategy is to augment the negative log-likelihood function with a sparsity-promoting penalty. Existing methods include the group Lasso, group SCAD, and group MCP.…
The Lasso has become a benchmark data analysis procedure, and numerous variants have been proposed in the literature. Although the Lasso formulations are stated so that overall prediction error is optimized, no full control over the…
Researchers in the behavioral and social sciences use linear discriminant analysis (LDA) for predictions of group membership (classification) and for identifying the variables most relevant to group separation among a set of continuous…
In this paper, we present an algorithm for learning time-correlated measurement covariances for application in batch state estimation. We parameterize the inverse measurement covariance matrix to be block-banded, which conveniently…
Causal effect estimation is a critical task in statistical learning that aims to find the causal effect on subjects by identifying causal links between a number of predictor (or, explanatory) variables and the outcome of a treatment. In a…
Reduced-rank regression estimates regression coefficients by imposing a low-rank constraint on the matrix of regression coefficients, thereby accounting for correlations among response variables. To further improve predictive accuracy and…
The central problem we address in this work is estimation of the parameter support set S, the set of indices corresponding to nonzero parameters, in the context of a sparse parametric likelihood model for discrete multivariate time series.…
In this paper, a linear model with grouped explanatory variables is considered. The idea is to perform an automatic detection of different successive groups of the unknown coefficients under the assumption that the number of groups is of…
We present a novel method for variable selection in regression models when covariates are measured with error. The iterative algorithm we propose, MEBoost, follows a path defined by estimating equations that correct for covariate…
Increasing effort is put into the development of methods for learning mechanistic models from data. This task entails not only the accurate estimation of parameters but also a suitable model structure. Recent work on the discovery of…
Linear optimization problems are investigated whose parameters are uncertain. We apply coherent distortion risk measures to capture the possible violation of a restriction. Each risk constraint induces an uncertainty set of coefficients,…
The Lasso regression is a popular regularization method for feature selection in statistics. Prior to computing the Lasso estimator in both linear and generalized linear models, it is common to conduct a preliminary rescaling of the feature…
We consider ``one-at-a-time'' coordinate-wise descent algorithms for a class of convex optimization problems. An algorithm of this kind has been proposed for the $L_1$-penalized regression (lasso) in the literature, but it seems to have…
Although the Lasso has been extensively studied, the relationship between its prediction performance and the correlations of the covariates is not fully understood. In this paper, we give new insights into this relationship in the context…
Estimation of large covariance matrices has drawn considerable recent attention, and the theoretical focus so far has mainly been on developing a minimax theory over a fixed parameter space. In this paper, we consider adaptive covariance…
This work concerns estimation of multidimensional nonlinear regression models using multilayer perceptron (MLP). The main problem with such model is that we have to know the covariance matrix of the noise to get optimal estimator. however…
We present two sets of theoretical results on the grouped lasso with overlap of Jacob, Obozinski and Vert (2009) in the linear regression setting. This method allows for joint selection of predictors in sparse regression, allowing for…