Related papers: Principal component analysis for high-dimensional …
Principal Component Analysis (PCA) is a well known procedure to reduce intrinsic complexity of a dataset, essentially through simplifying the covariance structure or the correlation structure. We introduce a novel algebraic, model-based…
This article introduces a new signal analysis method, which can be interpreted as a principal component analysis in sparse decomposition of the signal. The method, called principal basis analysis, is based on a novel criterion:…
In this paper the exact linear relation between the leading eigenvectors of the modularity matrix and the singular vectors of an uncentered data matrix is developed. Based on this analysis the concept of a modularity component is defined,…
Having a large number of covariates can have a negative impact on the quality of causal effect estimation since confounding adjustment becomes unreliable when the number of covariates is large relative to the samples available. Propensity…
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 one of the most used tools for extracting low-dimensional representations of data, in particular for time series. Performances are known to strongly depend on the quality (amount of noise) and the…
The real-life data have a complex and non-linear structure due to their nature. These non-linearities and the large number of features can usually cause problems such as the empty-space phenomenon and the well-known curse of dimensionality.…
The statistical analysis of tree structured data is a new topic in statistics with wide application areas. Some Principal Component Analysis (PCA) ideas were previously developed for binary tree spaces. In this study, we extend these ideas…
In high-dimensional principal component analysis, important inferential targets include both leading spikes and the associated principal eigenspaces. Such problems arise naturally in high-dimensional factor models, where leading principal…
Principal Component Analysis (PCA) and its nonlinear extension Kernel PCA (KPCA) are widely used across science and industry for data analysis and dimensionality reduction. Modern deep learning tools have achieved great empirical success,…
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…
The literature provides strong evidence that stock prices can be predicted from past price data. Principal component analysis (PCA) is a widely used mathematical technique for dimensionality reduction and analysis of data by identifying a…
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…
Principal component analysis (PCA) is a key tool in the field of data dimensionality reduction. However, some applications involve heterogeneous data that vary in quality due to noise characteristics associated with each data sample.…
Principal component analysis (PCA) is by far the most widespread tool for unsupervised learning with high-dimensional data sets. Its application is popularly studied for the purpose of exploratory data analysis and online process…
A high-dimensional $r$-factor model for an $n$-dimensional vector time series is characterised by the presence of a large eigengap (increasing with $n$) between the $r$-th and the $(r+1)$-th largest eigenvalues of the covariance matrix.…
We propose a novel estimator for the principal component (PC) subspace tailored to the high-dimension, low-sample size (HDLSS) context. The method, termed Adaptive Reference-Guided (ARG) estimator, is designed for data exhibiting spiked…
The growing size of modern data sets brings many challenges to the existing statistical estimation approaches, which calls for new distributed methodologies. This paper studies distributed estimation for a fundamental statistical machine…
We propose a stable version of Principal Component Analysis (PCA) in the general framework of a separable Hilbert space. It consists in interpreting the projection on the first eigenvectors as a step function applied to the spectrum of the…
Scalability of statistical estimators is of increasing importance in modern applications and dimension reduction is often used to extract relevant information from data. A variety of popular dimension reduction approaches can be framed as…