相关论文: Penalized Orthogonal-Components Regression for Lar…

Principal Component Analysis (PCA) is a popular tool for dimensionality reduction and feature extraction in data analysis. There is a probabilistic version of PCA, known as Probabilistic PCA (PPCA). However, standard PCA and PPCA are not…

We study high-dimensional regression in principal components space when the predictors are observed with additive measurement error and the response errors may be heavy-tailed. The starting point is the $\ell_1$-penalized…

Principal component analysis (PCA) has been widely applied to dimensionality reduction and data pre-processing for different applications in engineering, biology and social science. Classical PCA and its variants seek for linear projections…

In our previous work, a reduced order model (ROM) for a stochastic system was made, where noisy data was projected onto principal component analysis (PCA)-derived basis vectors to obtain an accurate reconstruction of the noise-free data.…

In genetic studies, not only can the number of predictors obtained from microarray measurements be extremely large, there can also be multiple response variables. Motivated by such a situation, we consider semiparametric dimension reduction…

Probabilistic principal component analysis (PPCA) seeks a low dimensional representation of a data set in the presence of independent spherical Gaussian noise. The maximum likelihood solution for the model is an eigenvalue problem on the…

We propose a new method based on sparse optimal discriminant clustering (SODC), incorporating a penalty term into the scoring matrix based on convex clustering. With the addition of this penalty term, it is expected to improve the accuracy…

In this paper we consider the trace regression model. Assume that we observe a small set of entries or linear combinations of entries of an unknown matrix $A_0$ corrupted by noise. We propose a new rank penalized estimator of $A_0$. For…

Sparse principal component analysis (SPCA) addresses the poor interpretability and variable redundancy often encountered by principal component analysis (PCA) in high-dimensional data. However, SPCA typically imposes uniform penalties on…

Quantile regression is studied in combination with a penalty which promotes structured (or group) sparsity. A mixed $\ell_{1,\infty}$-norm on the parameter vector is used to impose structured sparsity on the traditional quantile regression…

High dimensional data has introduced challenges that are difficult to address when attempting to implement classical approaches of statistical process control. This has made it a topic of interest for research due in recent years. However,…

A wide range of problems in computational science and engineering require estimation of sparse eigenvectors for high dimensional systems. Here, we propose two variants of the Truncated Orthogonal Iteration to compute multiple leading…

High throughput genetic sequencing arrays with thousands of measurements per sample and a great amount of related censored clinical data have increased demanding need for better measurement specific model selection. In this paper we…

We study the problem of multivariate regression where the data are naturally grouped, and a regression matrix is to be estimated for each group. We propose an approach in which a dictionary of low rank parameter matrices is estimated across…

Principal component analysis (PCA) is a classical dimension reduction method which projects data onto the principal subspace spanned by the leading eigenvectors of the covariance matrix. However, it behaves poorly when the number of…

Principal component analysis (PCA) is an exploratory tool widely used in data analysis to uncover dominant patterns of variability within a population. Despite its ability to represent a data set in a low-dimensional space, the…

Principal Component Analysis (PCA) is a dimension reduction technique. It produces inconsistent estimators when the dimensionality is moderate to high, which is often the problem in modern large-scale applications where algorithm…

We consider the nonparametric regression and the classification problems for $\psi$-weakly dependent processes. This weak dependence structure is more general than conditions such as, mixing, association, $\ldots$. A penalized estimation…

In this paper, we develop a parameterized proximal point algorithm (P-PPA) for solving a class of separable convex programming problems subject to linear and convex constraints. The proposed algorithm is provable to be globally convergent…

We propose a novel sparse sliced inverse regression method based on random projections in a large $p$ small $n$ setting. Embedded in a generalized eigenvalue framework, the proposed approach finally reduces to parallel execution of…