Related papers: Consistent selection via the Lasso for high dimens…

We compute approximate solutions to L0 regularized linear regression using L1 regularization, also known as the Lasso, as an initialization step. Our algorithm, the Lass-0 ("Lass-zero"), uses a computationally efficient stepwise search to…

We consider the problem of simultaneous variable selection and constant coefficient identification in high-dimensional varying coefficient models based on B-spline basis expansion. Both objectives can be considered as some type of model…

With growing applications of Machine Learning (ML) techniques in the real world, it is highly important to ensure that these models work in an equitable manner. One main step in ensuring fairness is to effectively measure fairness, and to…

High-dimensional statistical inference deals with models in which the the number of parameters p is comparable to or larger than the sample size n. Since it is usually impossible to obtain consistent procedures unless $p/n\rightarrow0$, a…

The Graphical Lasso (GLasso) algorithm is fast and widely used for estimating sparse precision matrices (Friedman et al., 2008). Its central role in the literature of high-dimensional covariance estimation rivals that of Lasso regression…

This paper studies model selection consistency for high dimensional sparse regression when data exhibits both cross-sectional and serial dependency. Most commonly-used model selection methods fail to consistently recover the true model when…

In a polynomial regression model, the divisibility conditions implicit in polynomial hierarchy give way to a natural construction of constraints for the model parameters. We use this principle to derive versions of strong and weak hierarchy…

We introduce a statistical physics inspired supervised machine learning algorithm for classification and regression problems. The method is based on the invariances or stability of predicted results when known data is represented as…

Linear mixed models (LMMs) are suitable for clustered data and are common in biometrics, medicine, survey statistics and many other fields. In those applications, it is essential to carry out valid inference after selecting a subset of the…

We consider the least-square regression problem with regularization by a block 1-norm, i.e., a sum of Euclidean norms over spaces of dimensions larger than one. This problem, referred to as the group Lasso, extends the usual regularization…

The LASSO estimator is an $\ell_1$-norm penalized least-squares estimator, which was introduced for variable selection in the linear model. When the design matrix satisfies, e.g. the Restricted Isometry Property, or has a small coherence…

The graphical lasso is a widely used algorithm for fitting undirected Gaussian graphical models. However, for inference on functionals of edge values in the learned graph, standard tools lack formal statistical guarantees, such as control…

In this paper, we present a novel and effective inference approach to conduct both finite- and large-sample inference for high-dimensional linear regression models. This approach is developed under the so-called repro samples framework, in…

The high-dimensional rank lasso (hdr lasso) model is an efficient approach to deal with high-dimensional data analysis. It was proposed as a tuning-free robust approach for the high-dimensional regression and was demonstrated to enjoy…

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,…

Supervised learning by extreme learning machines resp. neural networks with random weights is studied under a non-stationary spatial-temporal sampling design which especially addresses settings where an autonomous object moving in a…

Estimation of a precision matrix (i.e., inverse covariance matrix) is widely used to exploit conditional independence among continuous variables. The influence of abnormal observations is exacerbated in a high dimensional setting as the…

This thesis studies two problems in modern statistics. First, we study selective inference, or inference for hypothesis that are chosen after looking at the data. The motiving application is inference for regression coefficients selected by…

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…

This paper provides a statistical analysis of high-dimensional batch Reinforcement Learning (RL) using sparse linear function approximation. When there is a large number of candidate features, our result sheds light on the fact that…