Related papers: The Mismatch Principle: The Generalized Lasso Unde…
We consider the problem of subspace estimation in situations where the number of available snapshots and the observation dimension are comparable in magnitude. In this context, traditional subspace methods tend to fail because the…
Due to its low computational cost, Lasso is an attractive regularization method for high-dimensional statistical settings. In this paper, we consider multivariate counting processes depending on an unknown function parameter to be estimated…
This paper presents a comprehensive exploration of the theoretical properties inherent in the Adaptive Lasso and the Transfer Lasso. The Adaptive Lasso, a well-established method, employs regularization divided by initial estimators and is…
We study high-dimensional regression with missing entries in the covariates. A common strategy in practice is to \emph{impute} the missing entries with an appropriate substitute and then implement a standard statistical procedure acting as…
Sparse linear regression is a central problem in high-dimensional statistics. We study the correlated random design setting, where the covariates are drawn from a multivariate Gaussian $N(0,\Sigma)$, and we seek an estimator with small…
All models may be wrong -- but that is not necessarily a problem for inference. Consider the standard $t$-test for the significance of a variable $X$ for predicting response $Y$ whilst controlling for $p$ other covariates $Z$ in a random…
We propose a distributed method for simultaneous inference for datasets with sample size much larger than the number of covariates, i.e., N >> p, in the generalized linear models framework. When such datasets are too big to be analyzed…
Although the Lasso has been extensively studied, the relationship between its prediction performance and the correlations of the covariates is not fully understood. In this paper, we give new insights into this relationship in the context…
In many prediction problems, it is not uncommon that the number of variables used to construct a forecast is of the same order of magnitude as the sample size, if not larger. We then face the problem of constructing a prediction in the…
This paper studies well-posedness and parameter sensitivity of the Square Root LASSO (SR-LASSO), an optimization model for recovering sparse solutions to linear inverse problems in finite dimension. An advantage of the SR-LASSO (e.g., over…
Sparse linear regression is a vast field and there are many different algorithms available to build models. Two new papers published in Statistical Science study the comparative performance of several sparse regression methodologies,…
This paper is concerned with inference on the regression function of a high-dimensional linear model when outcomes are missing at random. We propose an estimator which combines a Lasso pilot estimate of the regression function with a bias…
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.…
In this paper, we introduce structured sparsity estimators in Generalized Linear Models. Structured sparsity estimators in the least squares loss are introduced by Stucky and van de Geer (2018) recently for fixed design and normal errors.…
The goal of compressed sensing is to estimate a vector from an underdetermined system of noisy linear measurements, by making use of prior knowledge on the structure of vectors in the relevant domain. For almost all results in this…
In high dimensional settings, sparse structures are crucial for efficiency, both in term of memory, computation and performance. It is customary to consider $\ell_1$ penalty to enforce sparsity in such scenarios. Sparsity enforcing methods,…
Although neural networks are powerful function approximators, the underlying modelling assumptions ultimately define the likelihood and thus the hypothesis class they are parameterizing. In classification, these assumptions are minimal as…
The Lasso is a popular statistical tool invented by Robert Tibshirani for linear regression when the number of covariates is greater than or comparable to the number of observations. The purpose of this note is to highlight the simple fact…
We compare alternative computing strategies for solving the constrained lasso problem. As its name suggests, the constrained lasso extends the widely-used lasso to handle linear constraints, which allow the user to incorporate prior…
In high-dimensional statistical inference, sparsity regularizations have shown advantages in consistency and convergence rates for coefficient estimation. We consider a generalized version of Sparse-Group Lasso which captures both…