Related papers: Classification of high-dimensional data with spike…
We consider the Sparse Principal Component Analysis (SPCA) problem under the well-known spiked covariance model. Recent work has shown that the SPCA problem can be reformulated as a Mixed Integer Program (MIP) and can be solved to global…
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…
Linear discriminant analysis (LDA) is a typical method for classification problems with large dimensions and small samples. There are various types of LDA methods that are based on the different types of estimators for the covariance…
In this study, we introduce an innovative methodology aimed at enhancing Fisher's Linear Discriminant Analysis (LDA) in the context of high-dimensional data classification scenarios, specifically addressing situations where each feature…
Motivated by dimension reduction in regression analysis and signal detection, we investigate the order determination for large dimension matrices including spiked models of which the numbers of covariates are proportional to the sample…
Covariance and Hessian matrices have been analyzed separately in the literature for classification problems. However, integrating these matrices has the potential to enhance their combined power in improving classification performance. We…
We study the problem of estimating the leading eigenvectors of a high-dimensional population covariance matrix based on independent Gaussian observations. We establish lower bounds on the rates of convergence of the estimators of the…
We study the estimation of the covariance matrix $\Sigma$ of a $p$-dimensional normal random vector based on $n$ independent observations corrupted by additive noise. Only a general nonparametric assumption is imposed on the distribution of…
This paper considers sparse spiked covariance matrix models in the high-dimensional setting and studies the minimax estimation of the covariance matrix and the principal subspace as well as the minimax rank detection. The optimal rate of…
In this paper, we consider the problem of determining the presence of a given signal in a high-dimensional observation with unknown covariance matrix by using an adaptive matched filter. Traditionally such filters are formed from the sample…
Applications of high-dimensional regression often involve multiple sources or types of covariates. We propose methodology for this setting, emphasizing the "wide data" regime with large total dimensionality p and sample size n<<p. We focus…
We study estimation of the covariance matrix under relative condition number loss $\kappa(\Sigma^{-1/2} \hat{\Sigma} \Sigma^{-1/2})$, where $\kappa(\Delta)$ is the condition number of matrix $\Delta$, and $\hat{\Sigma}$ and $\Sigma$ are the…
The problem of estimating the covariance matrix $\Sigma$ of a $p$-variate distribution based on its $n$ observations arises in many data analysis contexts. While for $n>p$, the classical sample covariance matrix $\hat{\Sigma}_n$ is a good…
This paper investigates the high-dimensional linear regression with highly correlated covariates. In this setup, the traditional sparsity assumption on the regression coefficients often fails to hold, and consequently many model selection…
Matrix valued data has become increasingly prevalent in many applications. Most of the existing clustering methods for this type of data are tailored to the mean model and do not account for the dependence structure of the features, which…
Sparse principal component analysis (sPCA) has become one of the most widely used techniques for dimensionality reduction in high-dimensional datasets. The main challenge underlying sPCA is to estimate the first vector of loadings of the…
We formulate the sparse classification problem of $n$ samples with $p$ features as a binary convex optimization problem and propose a cutting-plane algorithm to solve it exactly. For sparse logistic regression and sparse SVM, our algorithm…
In this paper, we propose a new Bayesian inference method for a high-dimensional sparse factor model that allows both the factor dimensionality and the sparse structure of the loading matrix to be inferred. The novelty is to introduce a…
This paper considers the estimation and inference of the low-rank components in high-dimensional matrix-variate factor models, where each dimension of the matrix-variates ($p \times q$) is comparable to or greater than the number of…
We study distributed principal component analysis (PCA) in high-dimensional settings under the spiked model. In such regimes, sample eigenvectors can deviate significantly from population ones, introducing a persistent bias. Existing…