Related papers: Estimating the Lasso's Effective Noise

The application of the lasso is espoused in high-dimensional settings where only a small number of the regression coefficients are believed to be nonzero. Moreover, statistical properties of high-dimensional lasso estimators are often…

Regression methods assume that accurate labels are available for training. However, in certain scenarios, obtaining accurate labels may not be feasible, and relying on multiple specialists with differing opinions becomes necessary. Existing…

The least absolute shrinkage and selection operator (LASSO) is a popular technique for simultaneous estimation and model selection. There have been a lot of studies on the large sample asymptotic distributional properties of the LASSO…

Suppose that we observe $y \in \mathbb{R}^n$ and $X \in \mathbb{R}^{n \times m}$ in the following errors-in-variables model: \begin{eqnarray*} y & = & X_0 \beta^* +\epsilon \\ X & = & X_0 + W, \end{eqnarray*} where $X_0$ is an $n \times m$…

We consider in this paper the problem of estimating a parameter matrix from observations which are affected by two types of noise components: (i) a sparse noise sequence which, whenever nonzero can have arbitrarily large amplitude (ii) and…

We consider the problem of identifying significant predictors in large data bases, where the response variable depends on the linear combination of explanatory variables through an unknown link function, corrupted with the noise from the…

Quantile regression is a statistical method for estimating conditional quantiles of a response variable. In addition, for mean estimation, it is well known that quantile regression is more robust to outliers than $l_2$-based methods. By…

While the performance of machine learning systems has experienced significant improvement in recent years, relatively little attention has been paid to the fundamental question: to what extent can we improve our models? This paper provides…

We consider the problem of learning a coefficient vector x_0\in R^N from noisy linear observation y=Ax_0+w \in R^n. In many contexts (ranging from model selection to image processing) it is desirable to construct a sparse estimator x'. In…

Linear regression studies the problem of estimating a model parameter $\beta^* \in \mathbb{R}^p$, from $n$ observations $\{(y_i,\mathbf{x}_i)\}_{i=1}^n$ from linear model $y_i = \langle \mathbf{x}_i,\beta^* \rangle + \epsilon_i$. We…

We derive new theoretical results on the properties of the adaptive least absolute shrinkage and selection operator (adaptive lasso) for time series regression models. In particular, we investigate the question of how to conduct finite…

Label noise widely exists in large-scale datasets and significantly degenerates the performances of deep learning algorithms. Due to the non-identifiability of the instance-dependent noise transition matrix, most existing algorithms address…

While considerable advances have been made in estimating high-dimensional structured models from independent data using Lasso-type models, limited progress has been made for settings when the samples are dependent. We consider estimating…

A classical problem that arises in numerous signal processing applications asks for the reconstruction of an unknown, $k$-sparse signal $x_0\in R^n$ from underdetermined, noisy, linear measurements $y=Ax_0+z\in R^m$. One standard approach…

Label noise is frequently observed in real-world large-scale datasets. The noise is introduced due to a variety of reasons; it is heterogeneous and feature-dependent. Most existing approaches to handling noisy labels fall into two…

We propose a novel iterative algorithm for estimating a deterministic but unknown parameter vector in the presence of model uncertainties. This iterative algorithm is based on a system model where an overall noise term describes both, the…

We develop a new approach for estimating the risk of an arbitrary estimator of the mean vector in the classical normal means problem. The key idea is to generate two auxiliary data vectors, by adding carefully constructed normal noise…

This paper considers the problem of inference in a linear regression model with outliers where the number of outliers can grow with sample size but their proportion goes to 0. We apply the square-root lasso estimator penalizing the l1-norm…

The precision matrix that encodes conditional linear dependency relations among a set of variables forms an important object of interest in multivariate analysis. Sparse estimation procedures for precision matrices such as the graphical…

We consider the problem of noisy Bayesian active learning, where we are given a finite set of functions $\mathcal{H}$, a sample space $\mathcal{X}$, and a label set $\mathcal{L}$. One of the functions in $\mathcal{H}$ assigns labels to…