Related papers: LASSO Methods for Gaussian Instrumental Variables …
State-space models have been successfully used for more than fifty years in different areas of science and engineering. We present a procedure for efficient variational Bayesian learning of nonlinear state-space models based on sparse…
In the context of multiple regression model, suppose that the vector parameter of interest \beta is subjected to lie in the subspace hypothesis H\beta = h, where this restriction is based on either additional information or prior knowledge.…
Confidence intervals based on penalized maximum likelihood estimators such as the LASSO, adaptive LASSO, and hard-thresholding are analyzed. In the known-variance case, the finite-sample coverage properties of such intervals are determined…
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…
An empirical Bayes approach to the estimation of possibly sparse sequences observed in Gaussian white noise is set out and investigated. The prior considered is a mixture of an atom of probability at zero and a heavy-tailed density \gamma,…
We introduce a novel Bayesian approach for both covariate selection and sparse precision matrix estimation in the context of high-dimensional Gaussian graphical models involving multiple responses. Our approach provides a sparse estimation…
We present a new methodology for simultaneous variable selection and parameter estimation in function-on-scalar regression with an ultra-high dimensional predictor vector. We extend the LASSO to functional data in both the $\textit{dense}$…
We consider the sparse regression model where the number of parameters $p$ is larger than the sample size $n$. The difficulty when considering high-dimensional problems is to propose estimators achieving a good compromise between…
We analyze lensless imaging systems with estimation-theoretic techniques based on Fisher information. Our analysis evaluates multiple optical encoder designs on objects with varying sparsity, in the context of both Gaussian and Poisson…
Quantifying uncertainty in high-dimensional sparse linear regression is a fundamental task in statistics that arises in various applications. One of the most successful methods for quantifying uncertainty is the debiased LASSO, which has a…
We consider a linear regression problem in a high dimensional setting where the number of covariates $p$ can be much larger than the sample size $n$. In such a situation, one often assumes sparsity of the regression vector, \textit i.e.,…
We consider the problem of estimating sparse graphs by a lasso penalty applied to the inverse covariance matrix. Using a coordinate descent procedure for the lasso, we develop a simple algorithm that is remarkably fast: in the worst cases,…
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…
Experts classifying data are often imprecise. Recently, several models have been proposed to train classifiers using the noisy labels generated by these experts. How to choose between these models? In such situations, the true labels are…
Granger causality is among the widely used data-driven approaches for causal analysis of time series data with applications in various areas including economics, molecular biology, and neuroscience. Two of the main challenges of this…
Inverse probability weighted estimators are the oldest and potentially most commonly used class of procedures for the estimation of causal effects. By adjusting for selection biases via a weighting mechanism, these procedures estimate an…
This paper study sparse classification problems. We show that under single-index models, vanilla Lasso could give good estimate of unknown parameters. With this result, we see that even if the model is not linear, and even if the response…
The aim of this paper is to provide a comprehensive introduction for the study of L1-penalized estimators in the context of dependent observations. We define a general $\ell_{1}$-penalized estimator for solving problems of stochastic…
We propose a general adaptive LASSO method for a quantile regression model. Our method is very interesting when we know nothing about the first two moments of the model error. We first prove that the obtained estimators satisfy the oracle…
We consider the problem of fitting the parameters of a high-dimensional linear regression model. In the regime where the number of parameters $p$ is comparable to or exceeds the sample size $n$, a successful approach uses an…