相关论文: Covariate Assisted Variable Ranking

Optimization problems with rank constraints arise in many applications, including matrix regression, structured PCA, matrix completion and matrix decomposition problems. An attractive heuristic for solving such problems is to factorize the…

We propose new methods for multivariate linear regression when the regression coefficient matrix is sparse and the error covariance matrix is dense. We assume that the error covariance matrix has equicorrelation across the response…

This paper presents new algorithms to solve the feature-sparsity constrained PCA problem (FSPCA), which performs feature selection and PCA simultaneously. Existing optimization methods for FSPCA require data distribution assumptions and are…

Sparse principal component analysis (PCA) is a popular dimensionality reduction technique for obtaining principal components which are linear combinations of a small subset of the original features. Existing approaches cannot supply…

Sparse PCA is a widely used technique for high-dimensional data analysis. In this paper, we propose a new method called low-rank principal eigenmatrix analysis. Different from sparse PCA, the dominant eigenvectors are allowed to be dense…

Principal component analysis (PCA) requires the computation of a low-rank approximation to a matrix containing the data being analyzed. In many applications of PCA, the best possible accuracy of any rank-deficient approximation is at most a…

Factor analysis aims to describe high dimensional random vectors by means of a small number of unknown common factors. In mathematical terms, it is required to decompose the covariance matrix $\Sigma$ of the random vector as the sum of a…

How can we discern whether the covariance operator of a stochastic process is of reduced rank, and if so, what its precise rank is? And how can we do so at a given level of confidence? This question is central to a great deal of methods for…

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…

Machine learning models used in medical applications often face challenges due to the covariate shift, which occurs when there are discrepancies between the distributions of training and target data. This can lead to decreased predictive…

It is known that the common factors in a large panel of data can be consistently estimated by the method of principal components, and principal components can be constructed by iterative least squares regressions. Replacing least squares…

Principal component analysis (PCA) is arguably the most widely used approach for large-dimensional factor analysis. While it is effective when the factors are sufficiently strong, it can be inconsistent when the factors are weak and/or the…

Bayes additive regression trees(BART) is a nonparametric regression model which has gained wide -spread popularity in recent years due to its flexibility and high accuracy of estimation .In spatio-temporal related model,the spatio or…

Emerging applications increasingly demand flexible covariate adaptive randomization (CAR) methods that support unequal targeted allocation ratios. While existing procedures can achieve covariate balance, they often suffer from the shift…

Sparse covariance matrices play crucial roles by encoding the interdependencies between variables in numerous fields such as genetics and neuroscience. Despite substantial studies on sparse covariance matrices, existing methods face several…

Sparse Principal Component Analysis (PCA) is a dimensionality reduction technique wherein one seeks a low-rank representation of a data matrix with additional sparsity constraints on the obtained representation. We consider two…

Functional principal component analysis (FPCA) is a key tool in the study of functional data, driving both exploratory analyses and feature construction for use in formal modeling and testing procedures. However, existing methods for FPCA…

We present a novel Bayesian nonparametric regression model for covariates X and continuous, real response variable Y. The model is parametrized in terms of marginal distributions for Y and X and a regression function which tunes the…

A new sparse semiparametric model is proposed, which incorporates the influence of two functional random variables in a scalar response in a flexible and interpretable manner. One of the functional covariates is included through a…

We introduce \underline{F}actor-\underline{A}ugmented \underline{Ma}trix \underline{R}egression (FAMAR) to address the growing applications of matrix-variate data and their associated challenges, particularly with high-dimensionality and…