Related papers: Variable Selection in High Dimensional Linear Regr…

We consider the problem of simultaneous variable selection and estimation in partially linear models with a divergent number of covariates in the linear part, under the assumption that the vector of regression coefficients is sparse. We…

The problem of model selection arises in a number of contexts, such as compressed sensing, subset selection in linear regression, estimation of structures in graphical models, and signal denoising. This paper generalizes the notion of…

Applying standard statistical methods after model selection may yield inefficient estimators and hypothesis tests that fail to achieve nominal type-I error rates. The main issue is the fact that the post-selection distribution of the data…

The paper considers variable selection in linear regression models where the number of covariates is possibly much larger than the number of observations. High dimensionality of the data brings in many complications, such as (possibly…

Suppose one has a collection of parameters indexed by a (possibly infinite dimensional) set. Given data generated from some distribution, the objective is to estimate the maximal parameter in this collection evaluated at this distribution.…

Orthogonal statistical learning and double machine learning have emerged as general frameworks for two-stage statistical prediction in the presence of a nuisance component. We establish non-asymptotic bounds on the excess risk of orthogonal…

We address the issue of variable selection in the regression model with very high ambient dimension, that is, when the number of variables is very large. The main focus is on the situation where the number of relevant variables, called…

With nonignorable nonresponse, an effective method to construct valid estimators of population parameters is to use a covariate vector called instrument that can be excluded from the nonresponse propensity but are still useful covariate…

Model selection criteria are one of the most important tools in statistics. Proofs showing a model selection criterion is asymptotically optimal are tailored to the type of model (linear regression, quantile regression, penalized…

We study the parameter estimation method for linear regression models with possibly skewed stable distributed errors. Our estimation procedure consists of two stages: first, for the regression coefficients, the Cauchy quasi-maximum…

This paper addresses the problem of learning linear dynamical systems from noisy observations. In this setting, existing algorithms either yield biased parameter estimates or have large sample complexities. We resolve these issues by…

In pool-based active learning, the learner is given an unlabeled data set and aims to efficiently learn the unknown hypothesis by querying the labels of the data points. This can be formulated as the classical Optimal Decision Tree (ODT)…

In this paper, we review state-of-the-art methods for feature selection in statistics with an application-oriented eye. Indeed, sparsity is a valuable property and the profusion of research on the topic might have provided little guidance…

Variable selection in linear regression settings is a much discussed problem. Best subset selection (BSS) is often considered the intuitive 'gold standard', with its use being restricted only by its NP-hard nature. Alternatives such as the…

Estimation of signal-to-noise ratios and residual variances in high-dimensional linear models has various important applications including, e.g. heritability estimation in bioinformatics. One commonly used estimator, usually referred to as…

As technology advanced, collecting data via automatic collection devices become popular, thus we commonly face data sets with lengthy variables, especially when these data sets are collected without specific research goals beforehand. It…

This article investigates unsupervised classification techniques for categorical multivariate data. The study employs multivariate multinomial mixture modeling, which is a type of model particularly applicable to multilocus genotypic data.…

Stability selection (Meinshausen and Buhlmann, 2010) makes any feature selection method more stable by returning only those features that are consistently selected across many subsamples. We prove (in what is, to our knowledge, the first…

We study the asymptotic properties of Lasso+mLS and Lasso+Ridge under the sparse high-dimensional linear regression model: Lasso selecting predictors and then modified Least Squares (mLS) or Ridge estimating their coefficients. First, we…

Machine learning (ML) systems are increasingly deployed in high-stakes domains where reliability is paramount. This thesis investigates how uncertainty estimation can enhance the safety and trustworthiness of ML, focusing on selective…