Related papers: Post-Selection Inference for Sparse Estimation
As datasets grow larger, they are often distributed across multiple machines that compute in parallel and communicate with a central machine through short messages. In this paper, we focus on sparse regression and propose a new procedure…
This note studies a method for the efficient estimation of a finite number of unknown parameters from linear equations, which are perturbed by Gaussian noise. In case the unknown parameters have only few nonzero entries, the proposed…
We consider the least-square linear regression problem with regularization by the $\ell^1$-norm, a problem usually referred to as the Lasso. In this paper, we first present a detailed asymptotic analysis of model consistency of the Lasso in…
In high-dimensional linear models, the sparsity assumption is typically made, stating that most of the parameters are equal to zero. Under the sparsity assumption, estimation and, recently, inference have been well studied. However, in…
We study sparse group Lasso for high-dimensional double sparse linear regression, where the parameter of interest is simultaneously element-wise and group-wise sparse. This problem is an important instance of the simultaneously structured…
A multiple interval-valued linear regression model considering all the cross-relationships between the mids and spreads of the intervals has been introduced recently. A least-squares estimation of the regression parameters has been carried…
The $\ell_1$-penalized method, or the Lasso, has emerged as an important tool for the analysis of large data sets. Many important results have been obtained for the Lasso in linear regression which have led to a deeper understanding of…
Feature selection is a critical component in predictive analytics that significantly affects the prediction accuracy and interpretability of models. Intrinsic methods for feature selection are built directly into model learning, providing a…
High-dimensional time series datasets are becoming increasingly common in many areas of biological and social sciences. Some important applications include gene regulatory network reconstruction using time course gene expression data, brain…
It is common practice in statistical data analysis to perform data-driven variable selection and derive statistical inference from the resulting model. Such inference enjoys none of the guarantees that classical statistical theory provides…
This paper proposes a sparse regression method that continuously interpolates between Forward Stepwise selection (FS) and the LASSO. When tuned appropriately, our solutions are much sparser than typical LASSO fits but, unlike FS fits,…
To perform inference after model selection, we propose controlling the selective type I error; i.e., the error rate of a test given that it was performed. By doing so, we recover long-run frequency properties among selected hypotheses…
This paper considers generalized linear models in the presence of many controls. We lay out a general methodology to estimate an effect of interest based on the construction of an instrument that immunize against model selection mistakes…
Reward models (RMs) are a core component in the post-training of large language models (LLMs), serving as proxies for human preference evaluation and guiding model alignment. However, training reliable RMs under limited resources remains…
Two-step estimators often called upon to fit censored regression models in many areas of science and engineering. Since censoring incurs a bias in the naive least-squares fit, a two-step estimator first estimates the bias and then fits a…
This paper describes a method for performing inference on models chosen by cross-validation. When the test error being minimized in cross-validation is a residual sum of squares it can be written as a quadratic form. This allows us to apply…
Sparse Bayesian learning models are typically used for prediction in datasets with significantly greater number of covariates than observations. Such models often take a reproducing kernel Hilbert space (RKHS) approach to carry out the task…
Sequential recommender systems have become increasingly important in real-world applications that model user behavior sequences to predict their preferences. However, existing sequential recommendation methods predominantly rely on…
Covariance regression offers an effective way to model the large covariance matrix with the auxiliary similarity matrices. In this work, we propose a sparse covariance regression (SCR) approach to handle the potentially high-dimensional…
Applied statisticians use sequential regression procedures to produce a ranking of explanatory variables and, in settings of low correlations between variables and strong true effect sizes, expect that variables at the very top of this…