Related papers: Scaled Sparse Linear Regression
Sparse linear regression is one of the classic problems in the field of statistics, which has deep connections and high intersections with optimization, computation, and machine learning. To address the effective handling of…
We present the framework of slowly varying regression under sparsity, allowing sparse regression models to exhibit slow and sparse variations. The problem of parameter estimation is formulated as a mixed-integer optimization problem. We…
We introduce and study the Group Square-Root Lasso (GSRL) method for estimation in high dimensional sparse regression models with group structure. The new estimator minimizes the square root of the residual sum of squares plus a penalty…
We propose a novel sparse sliced inverse regression method based on random projections in a large $p$ small $n$ setting. Embedded in a generalized eigenvalue framework, the proposed approach finally reduces to parallel execution of…
Forward stagewise regression follows a very simple strategy for constructing a sequence of sparse regression estimates: it starts with all coefficients equal to zero, and iteratively updates the coefficient (by a small amount $\epsilon$) of…
We consider model selection and estimation for partial spline models and propose a new regularization method in the context of smoothing splines. The regularization method has a simple yet elegant form, consisting of roughness penalty on…
We consider the problem of mixed sparse linear regression with two components, where two real $k$-sparse signals $\beta_1, \beta_2$ are to be recovered from $n$ unlabelled noisy linear measurements. The sparsity is allowed to be sublinear…
We consider the high-dimensional linear regression model and assume that a fraction of the measurements are altered by an adversary with complete knowledge of the data and the underlying distribution. We are interested in a scenario where…
There has been much recent work on inference after model selection when the noise level is known, however, $\sigma$ is rarely known in practice and its estimation is difficult in high-dimensional settings. In this work we propose using the…
We investigate the signal reconstruction performance of sparse linear regression in the presence of noise when piecewise continuous nonconvex penalties are used. Among such penalties, we focus on the SCAD penalty. The contributions of this…
The Bayesian Lasso is constructed in the linear regression framework and applies the Gibbs sampling to estimate the regression parameters. This paper develops a new sparse learning model, named the Bayesian Lasso Sparse (BLS) model, that…
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…
This paper studies the problem of estimating a large coefficient matrix in a multiple response linear regression model when the coefficient matrix could be both of low rank and sparse in the sense that most nonzero entries concentrate on a…
Sparse linear regression is one of the most basic questions in machine learning and statistics. Here, we are given as input a design matrix $X \in \mathbb{R}^{N \times d}$ and measurements or labels ${y} \in \mathbb{R}^N$ where ${y} = {X}…
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…
In this manuscript, we study quantile regression in partial functional linear model where response is scalar and predictors include both scalars and multiple functions. Wavelet basis are adopted to better approximate functional slopes while…
In this paper, we discuss application of iterative Stochastic Optimization routines to the problem of sparse signal recovery from noisy observation. Using Stochastic Mirror Descent algorithm as a building block, we develop a multistage…
We explore algorithms and limitations for sparse optimization problems such as sparse linear regression and robust linear regression. The goal of the sparse linear regression problem is to identify a small number of key features, while the…
Corrupted data sets containing noisy or missing observations are prevalent in various contemporary applications such as economics, finance and bioinformatics. Despite the recent methodological and algorithmic advances in high-dimensional…
The SparseStep algorithm is presented for the estimation of a sparse parameter vector in the linear regression problem. The algorithm works by adding an approximation of the exact counting norm as a constraint on the model parameters and…