Related papers: Sparse Principal Components Analysis
A system with many degrees of freedom can be characterized by a covariance matrix; principal components analysis (PCA) focuses on the eigenvalues of this matrix, hoping to find a lower dimensional description. But when the spectrum is…
This article establishes a new and comprehensive estimation and inference theory for principal component analysis (PCA) under the weak factor model that allow for cross-sectional dependent idiosyncratic components under the nearly minimal…
Principal component analysis (PCA) is a key tool in the field of data dimensionality reduction that is useful for various data science problems. However, many applications involve heterogeneous data that varies in quality due to noise…
Principal component analysis (PCA) is one of the most widely used dimension reduction and multivariate statistical techniques. From a probabilistic perspective, PCA seeks a low-dimensional representation of data in the presence of…
Principal component analysis (PCA) is an important tool in exploring data. The conventional approach to PCA leads to a solution which favours the structures with large variances. This is sensitive to outliers and could obfuscate interesting…
We extend the principal component analysis (PCA) to second-order stationary vector time series in the sense that we seek for a contemporaneous linear transformation for a $p$-variate time series such that the transformed series is segmented…
Principal component analysis (PCA) is a most frequently used statistical tool in almost all branches of data science. However, like many other statistical tools, there is sometimes the risk of misuse or even abuse. In this paper, we…
Principal component analysis (PCA), the most popular dimension-reduction technique, has been used to analyze high-dimensional data in many areas. It discovers the homogeneity within the data and creates a reduced feature space to capture as…
Principal component analysis is an important pattern recognition and dimensionality reduction tool in many applications. Principal components are computed as eigenvectors of a maximum likelihood covariance $\widehat{\Sigma}$ that…
Recently popularized randomized methods for principal component analysis (PCA) efficiently and reliably produce nearly optimal accuracy --- even on parallel processors --- unlike the classical (deterministic) alternatives. We adapt one of…
We consider estimation of large approximate factor models in high-dimensional panels of stationary time series using Principal Component Analysis (PCA). We review the key results establishing the necessary and sufficient conditions for…
Principal component analysis (PCA) is traditionally implemented through a covariance or kernel matrix, leading-eigenvector extraction, and hard rank-$k$ projection. These steps can be computationally costly in high-dimensional and…
We propose a new high dimensional semiparametric principal component analysis (PCA) method, named Copula Component Analysis (COCA). The semiparametric model assumes that, after unspecified marginally monotone transformations, the…
Causal mediation analysis aims to quantify the intermediate effect of a mediator on the causal pathway from treatment to outcome. With multiple mediators, which are potentially causally dependent, the possible decomposition of pathway…
We study semiparametric factor models in high-dimensional panels where the factor loadings consist of a nonparametric component explained by observed covariates and an idiosyncratic component capturing unobserved heterogeneity. A key…
In the past decade, sparse principal component analysis has emerged as an archetypal problem for illustrating statistical-computational tradeoffs. This trend has largely been driven by a line of research aiming to characterize the…
In this paper, a new method is proposed for sparse PCA based on the recursive divide-and-conquer methodology. The main idea is to separate the original sparse PCA problem into a series of much simpler sub-problems, each having a closed-form…
Principal component analysis (PCA) is a tool to capture factors that explain variation in data. Across domains, data are now collected across multiple contexts (for example, individuals with different diseases, cells of different types, or…
The research detailed in this paper scrutinizes Principal Component Analysis (PCA), a seminal method employed in statistics and machine learning for the purpose of reducing data dimensionality. Singular Value Decomposition (SVD) is often…
Principal component analysis (PCA) is a classical and ubiquitous method for reducing data dimensionality, but it is suboptimal for heterogeneous data that are increasingly common in modern applications. PCA treats all samples uniformly so…