Related papers: Selective inference after cross-validation

We introduce a novel procedure for obtaining cross-validated predictive estimates for Bayesian hierarchical regression models (BHRMs). Bayesian hierarchical models are popular for their ability to model complex dependence structures and…

This paper studies inference for quadratic forms of linear regression coefficients with clustered data and many covariates. Our framework covers three important special cases: instrumental variables regression with many instruments and…

We present large sample results for partitioning-based least squares nonparametric regression, a popular method for approximating conditional expectation functions in statistics, econometrics, and machine learning. First, we obtain a…

We study the problem of variable selection in convex nonparametric regression. Under the assumption that the true regression function is convex and sparse, we develop a screening procedure to select a subset of variables that contains the…

It is common to show the confidence intervals or $p$-values of selected features, or predictor variables in regression, but they often involve selection bias. The selective inference approach solves this bias by conditioning on the…

Many decisions in healthcare, business, and other policy domains are made without the support of rigorous evidence due to the cost and complexity of performing randomized experiments. Using observational data to answer causal questions is…

This paper introduces and analyzes a procedure called Testing-based forward model selection (TBFMS) in linear regression problems. This procedure inductively selects covariates that add predictive power into a working statistical model…

Cross-validation (CV) is one of the main tools for performance estimation and parameter tuning in machine learning. The general recipe for computing CV estimate is to run a learning algorithm separately for each CV fold, a computationally…

Cross-validation (CV) methods are popular for selecting the tuning parameter in the high-dimensional variable selection problem. We show the mis-alignment of the CV is one possible reason of its over-selection behavior. To fix this issue,…

Quantile regression has been successfully used to study heterogeneous and heavy-tailed data. Varying-coefficient models are frequently used to capture changes in the effect of input variables on the response as a function of an index or…

Although the leave-subject-out cross-validation (CV) has been widely used in practice for tuning parameter selection for various nonparametric and semiparametric models of longitudinal data, its theoretical property is unknown and solving…

When the model is not known and parameter testing or interval estimation is conducted after model selection, it is necessary to consider selective inference. This paper discusses this issue in the context of sparse estimation. Firstly, we…

In spite of the wealth of literature on the theoretical properties of the Lasso, there is very little known when the value of the tuning parameter is chosen using the data, even though this is what actually happens in practice. We give a…

This paper studies high-dimensional regression models with lasso when data is sampled under multi-way clustering. First, we establish convergence rates for the lasso and post-lasso estimators. Second, we propose a novel inference method…

In the network literature, a wide range of statistical models has been proposed to exploit structural patterns in the data. Therefore, model selection between different models is a fundamental problem. However, there remains a lack of…

We propose to address the common problem of linear estimation in linear statistical models by using a model selection approach via penalization. Depending then on the framework in which the linear statistical model is considered namely the…

Suppose that a data analyst wishes to report the results of a least squares linear regression only if the overall null hypothesis, $H_0^{1:p}: \beta_1= \beta_2 = \ldots = \beta_p=0$, is rejected. This practice, which we refer to as…

This paper presents the first general (supervised) statistical learning framework for point processes in general spaces. Our approach is based on the combination of two new concepts, which we define in the paper: i) bivariate innovations,…

The adaptive lasso refers to a class of methods that use weighted versions of the $L_1$-norm penalty, with weights derived from an initial estimate of the parameter vector to be estimated. Irrespective of the method chosen to compute this…

We investigate leave-one-out cross validation (CV) as a determinator of the weight of the penalty term in the least absolute shrinkage and selection operator (LASSO). First, on the basis of the message passing algorithm and a perturbative…