Related papers: Double shrunken selection operator
We propose a minimum distance estimation method for robust regression in sparse high-dimensional settings. The traditional likelihood-based estimators lack resilience against outliers, a critical issue when dealing with high-dimensional…
We present an estimation procedure of spatial and temporal effects in spatiotemporal autoregressive panel data models using the Least Absolute Shrinkage and Selection Operator, LASSO (Tibshirani, 1996). We assume that the spatiotemporal…
In high-dimensional statistics, the Lasso is a cornerstone method for simultaneous variable selection and parameter estimation. However, its reliance on the squared loss function renders it highly sensitive to outliers and heavy-tailed…
We address covariance estimation in the sense of minimum mean-squared error (MMSE) for Gaussian samples. Specifically, we consider shrinkage methods which are suitable for high dimensional problems with a small number of samples (large p…
This work is a re-examination of the sparse Bayesian learning (SBL) of linear regression models of Tipping (2001) in a high-dimensional setting. We propose a hard-thresholded version of the SBL estimator that achieves, for orthogonal design…
We revisit the problem of finding the shortest path between two selected vertices of a graph and formulate this as an $\ell_1$-regularized regression -- Least Absolute Shrinkage and Selection Operator (lasso). We draw connections between a…
Shuffled linear regression (SLR) seeks to estimate latent features through a linear transformation, complicated by unknown permutations in the measurement dimensions. This problem extends traditional least-squares (LS) and Least Absolute…
It is known that the Thresholded Lasso (TL), SCAD or MCP correct intrinsic estimation bias of the Lasso. In this paper we propose an alternative method of improving the Lasso for predictive models with general convex loss functions which…
We consider the problem of robustifying high-dimensional structured estimation. Robust techniques are key in real-world applications which often involve outliers and data corruption. We focus on trimmed versions of structurally regularized…
Scaled sparse linear regression jointly estimates the regression coefficients and noise level in a linear model. It chooses an equilibrium with a sparse regression method by iteratively estimating the noise level via the mean residual…
Penalized logistic regression is extremely useful for binary classification with large number of covariates (higher than the sample size), having several real life applications, including genomic disease classification. However, the…
In high-dimensional statistical inference in which the number of parameters to be estimated is larger than that of the holding data, regularized linear estimation techniques are widely used. These techniques have, however, some drawbacks.…
In this paper, we propose a triple (or double-debiased) Lasso estimator for inference on a low-dimensional parameter in high-dimensional linear regression models. The estimator is based on a moment function that satisfies not only first-…
This paper considers the problem of estimating a high-dimensional vector of parameters $\boldsymbol{\theta} \in \mathbb{R}^n$ from a noisy observation. The noise vector is i.i.d. Gaussian with known variance. For a squared-error loss…
Sparse reduced rank regression is an essential statistical learning method. In the contemporary literature, estimation is typically formulated as a nonconvex optimization that often yields to a local optimum in numerical computation. Yet,…
Model averaging (MA), a technique for combining estimators from a set of candidate models, has attracted increasing attention in machine learning and statistics. In the existing literature, there is an implicit understanding that MA can be…
Modern variable selection procedures make use of penalization methods to execute simultaneous model selection and estimation. A popular method is the LASSO (least absolute shrinkage and selection operator), the use of which requires…
Detecting influential features in non-linear and/or high-dimensional data is a challenging and increasingly important task in machine learning. Variable selection methods have thus been gaining much attention as well as post-selection…
In this paper, we consider a compressed sensing problem of reconstructing a sparse signal from an undersampled set of noisy linear measurements. The regularized least squares or least absolute shrinkage and selection operator (LASSO)…
This note develops a simple two-stage least squares (2SLS) procedure to estimate the causal effect of some endogenous regressors on a randomly right censored outcome in the linear model. The proposal replaces the usual ordinary least…