相关论文: Sparsity oracle inequalities for the Lasso

We propose an $\ell_1$-penalized estimator for high-dimensional models of Expected Shortfall (ES). The estimator is obtained as the solution to a least-squares problem for an auxiliary dependent variable, which is defined as a…

We proposed a new penalized method in this paper to solve sparse Poisson Regression problems. Being different from $\ell_1$ penalized log-likelihood estimation, our new method can be viewed as penalized weighted score function method. We…

We study the absolute penalized maximum partial likelihood estimator in sparse, high-dimensional Cox proportional hazards regression models where the number of time-dependent covariates can be larger than the sample size. We establish…

We consider the problem of simultaneous variable selection and estimation in additive, partially linear models for longitudinal/clustered data. We propose an estimation procedure via polynomial splines to estimate the nonparametric…

Structured sparsity is an important part of the modern statistical toolkit. We say a set of model parameters has block diagonal sparsity up to permutations if its elements can be viewed as the edges of a graph that has multiple connected…

Modern statistical learning algorithms are capable of amazing flexibility, but struggle with interpretability. One possible solution is sparsity: making inference such that many of the parameters are estimated as being identically 0, which…

Consider a regression model with fixed design and Gaussian noise where the regression function can potentially be well approximated by a function that admits a sparse representation in a given dictionary. This paper resorts to exponential…

Given $n$ noisy samples with $p$ dimensions, where $n \ll p$, we show that the multi-step thresholding procedure based on the Lasso -- we call it the {\it Thresholded Lasso}, can accurately estimate a sparse vector $\beta \in \R^p$ in a…

This paper studies sparse linear regression analysis with outliers in the responses. A parameter vector for modeling outliers is added to the standard linear regression model and then the sparse estimation problem for both coefficients and…

We develop a constructive approach to estimating sparse, high-dimensional linear regression models. The approach is a computational algorithm motivated from the KKT conditions for the $\ell_0$-penalized least squares solutions. It generates…

The Lasso has attracted the attention of many authors these last years. While many efforts have been made to prove that the Lasso behaves like a variable selection procedure at the price of strong (though unavoidable) assumptions on the…

We consider high-dimensional generalized linear models with Lipschitz loss functions, and prove a nonasymptotic oracle inequality for the empirical risk minimizer with Lasso penalty. The penalty is based on the coefficients in the linear…

We derive oracle inequalities for the problems of isotonic and convex regression using the combination of $Q$-aggregation procedure and sparsity pattern aggregation. This improves upon the previous results including the oracle inequalities…

This paper investigates some theoretical properties of the Partial Least Square (PLS) method. We focus our attention on the single component case, that provides a useful framework to understand the underlying mechanism. We provide a…

We consider a general high-dimensional additive hazard model in a non-asymptotic setting, including regression for censored-data. In this context, we consider a Lasso estimator with a fully data-driven $\ell_1$ penalization, which is tuned…

This paper considers the problem of estimating a periodic function in a continuous time regression model with a general square integrable semimartingale noise. A model selection adaptive procedure is proposed. Sharp non-asymptotic oracle…

The Lasso is an attractive technique for regularization and variable selection for high-dimensional data, where the number of predictor variables $p_n$ is potentially much larger than the number of samples $n$. However, it was recently…

This paper aims to build an estimate of an unknown density of the data with measurement error as a linear combination of functions from a dictionary. Inspired by the penalization approach, we propose the weighted Elastic-net penalized…

In this paper, the high-dimensional sparse linear regression model is considered, where the overall number of variables is larger than the number of observations. We investigate the L1 penalized least absolute deviation method. Different…

In the context of a linear model with a sparse coefficient vector, exponential weights methods have been shown to be achieve oracle inequalities for prediction. We show that such methods also succeed at variable selection and estimation…