Related papers: A Model-free Variable Screening Method Based on Le…

Leverage score sampling is a powerful technique that originates from theoretical computer science, which can be used to speed up a large number of fundamental questions, e.g. linear regression, linear programming, semi-definite programming,…

Feature selection can be a crucial factor in obtaining robust and accurate predictions. Online feature selection models, however, operate under considerable restrictions; they need to efficiently extract salient input features based on a…

Variable screening methods have been shown to be effective in dimension reduction under the ultra-high dimensional setting. Most existing screening methods are designed to rank the predictors according to their individual contributions to…

For a robust leverage diagnostic in linear regression, Rousseeuw and van Zomeren [1990] proposed using robust distance (Mahalanobis distance computed using robust estimates of location and covariance). However, a design matrix X that…

We propose an iterative variable selection scheme for high-dimensional data with binary outcomes. The scheme adopts a structured screen-and-select framework and uses non-local prior-based Bayesian model selection within the same. The…

Originally introduced in game theory, Shapley values have emerged as a central tool in explainable machine learning, where they are used to attribute model predictions to specific input features. However, computing Shapley values exactly is…

We apply methods from randomized numerical linear algebra (RandNLA) to develop improved algorithms for the analysis of large-scale time series data. We first develop a new fast algorithm to estimate the leverage scores of an autoregressive…

The development of molecular diagnostic tools to achieve individualized medicine requires identifying predictive biomarkers associated with subgroups of individuals who might receive beneficial or harmful effects from different available…

Identifying important biomarkers that are predictive for cancer patients' prognosis is key in gaining better insights into the biological influences on the disease and has become a critical component of precision medicine. The emergence of…

Commonly, machine learning models minimize an empirical expectation. As a result, the trained models typically perform well for the majority of the data but the performance may deteriorate in less dense regions of the dataset. This issue…

Sure Independence Screening is a fast procedure for variable selection in ultra-high dimensional regression analysis. Unfortunately, its performance greatly deteriorates with increasing dependence among the predictors. To solve this issue,…

Shapley data valuation provides a principled, axiomatic framework for assigning importance to individual datapoints, and has gained traction in dataset curation, pruning, and pricing. However, it is a combinatorial measure that requires…

Low-rank matrix completion is an important problem with extensive real-world applications. When observations are uniformly sampled from the underlying matrix entries, existing methods all require the matrix to be incoherent. This paper…

In large-scale biomedical research, it's common to gather ultra-high dimensional data that includes right-censored survival times. Feature screening has emerged as a crucial statistical technique for handling such data. In this paper, we…

The selection of essential variables in logistic regression is vital because of its extensive use in medical studies, finance, economics and related fields. In this paper, we explore four main typologies (test-based, penalty-based,…

In big data analysis, a simple task such as linear regression can become very challenging as the variable dimension $p$ grows. As a result, variable screening is inevitable in many scientific studies. In recent years, randomized algorithms…

In problems involving matrix computations, the concept of leverage has found a large number of applications. In particular, leverage scores, which relate the columns of a matrix to the subspaces spanned by its leading singular vectors, are…

Many computer vision and medical imaging problems are faced with learning from large-scale datasets, with millions of observations and features. In this paper we propose a novel efficient learning scheme that tightens a sparsity constraint…

The low-rank canonical polyadic tensor decomposition is useful in data analysis and can be computed by solving a sequence of overdetermined least squares subproblems. Motivated by consideration of sparse tensors, we propose sketching each…

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…