Related papers: Optimality and computational barriers in variable …
Best subset selection in linear regression is well known to be nonconvex and computationally challenging to solve, as the number of possible subsets grows rapidly with increasing dimensionality of the problem. As a result, finding the…
In recent years, sparse principal component analysis has emerged as an extremely popular dimension reduction technique for high-dimensional data. The theoretical challenge, in the simplest case, is to estimate the leading eigenvector of a…
We consider the high-dimensional discriminant analysis problem. For this problem, different methods have been proposed and justified by establishing exact convergence rates for the classification risk, as well as the l2 convergence results…
Subset selection in multiple linear regression aims to choose a subset of candidate explanatory variables that tradeoff fitting error (explanatory power) and model complexity (number of variables selected). We build mathematical programming…
The best subset selection (or "best subsets") estimator is a classic tool for sparse regression, and developments in mathematical optimization over the past decade have made it more computationally tractable than ever. Notwithstanding its…
Variable selection is central to high-dimensional data analysis, and various algorithms have been developed. Ideally, a variable selection algorithm shall be flexible, scalable, and with theoretical guarantee, yet most existing algorithms…
Sparse linear regression is a central problem in high-dimensional statistics. We study the correlated random design setting, where the covariates are drawn from a multivariate Gaussian $N(0,\Sigma)$, and we seek an estimator with small…
We study the problem of optimal subset selection from a set of correlated random variables. In particular, we consider the associated combinatorial optimization problem of maximizing the determinant of a symmetric positive definite matrix…
We consider the problem of hypothesis testing for discrete distributions. In the standard model, where we have sample access to an underlying distribution $p$, extensive research has established optimal bounds for uniformity testing,…
In this paper, we consider the problem of column subset selection. We present a novel analysis of the spectral norm reconstruction for a simple randomized algorithm and establish a new bound that depends explicitly on the sampling…
Machine learning algorithms in high-dimensional settings are highly susceptible to the influence of even a small fraction of structured outliers, making robust optimization techniques essential. In particular, within the…
Survey sampling is concerned with the estimation of finite population parameters. In practice, survey data suffer from item nonresponse, which is commonly handled through imputation, i.e., replacing missing values with predicted values. As…
The problem of best subset selection in linear regression is considered with the aim to find a fixed size subset of features that best fits the response. This is particularly challenging when the total available number of features is very…
Given a sample covariance matrix, we solve a maximum likelihood problem penalized by the number of nonzero coefficients in the inverse covariance matrix. Our objective is to find a sparse representation of the sample data and to highlight…
We consider in this paper the problem of optimal experiment design where a decision maker can choose which points to sample to obtain an estimate $\hat{\beta}$ of the hidden parameter $\beta^{\star}$ of an underlying linear model. The key…
For many tasks of data analysis, we may only have the information of the explanatory variable and the evaluation of the response values are quite expensive. While it is impractical or too costly to obtain the responses of all units, a…
In subset selection we search for the best linear predictor that involves a small subset of variables. From a computational complexity viewpoint, subset selection is NP-hard and few classes are known to be solvable in polynomial time. Using…
Sparse principal component analysis addresses the problem of finding a linear combination of the variables in a given data set with a sparse coefficients vector that maximizes the variability of the data. This model enhances the ability to…
Many conventional statistical procedures are extremely sensitive to seemingly minor deviations from modeling assumptions. This problem is exacerbated in modern high-dimensional settings, where the problem dimension can grow with and…
Although a majority of the theoretical literature in high-dimensional statistics has focused on settings which involve fully-observed data, settings with missing values and corruptions are common in practice. We consider the problems of…