Related papers: Robust high dimensional factor models with applica…
High-Dimensional Dynamic Factor Models are presented in detail: The main assumptions and their motivation, main results, illustrations by means of elementary examples. In particular, the role of singular ARMA models in the theory and…
The paper considers linear regression problems where the number of predictor variables is possibly larger than the sample size. The basic motivation of the study is to combine the points of view of model selection and functional regression…
Principal Component Analysis (PCA) finds a linear mapping and maximizes the variance of the data which makes PCA sensitive to outliers and may cause wrong eigendirection. In this paper, we propose techniques to solve this problem; we use…
Principal component analysis (PCA) is widely used for dimensionality reduction, with well-documented merits in various applications involving high-dimensional data, including computer vision, preference measurement, and bioinformatics. In…
We study principal components regression (PCR) in an asymptotic high-dimensional regression setting, where the number of data points is proportional to the dimension. We derive exact limiting formulas for the estimation and prediction…
This article considers a novel and widely applicable approach to modeling high-dimensional dependent data when a large number of explanatory variables are available and the signal-to-noise ratio is low. We postulate that a $p$-dimensional…
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…
Principal component analysis (PCA) is often used for analyzing data in the most diverse areas. In this work, we report an integrated approach to several theoretical and practical aspects of PCA. We start by providing, in an intuitive and…
The article discusses selected problems related to both principal component analysis (PCA) and factor analysis (FA). In particular, both types of analysis were compared. A vector interpretation for both PCA and FA has also been proposed.…
Principal component analysis (PCA) is a classical feature extraction method, but it may be adversely affected by outliers, resulting in inaccurate learning of the projection matrix. This paper proposes a robust method to estimate both the…
The use of machine learning for statistical modeling (and thus, generative modeling) has grown in popularity with the proliferation of time series models, text-to-image models, and especially large language models. Fundamentally, the goal…
Researchers often have datasets measuring features $x_{ij}$ of samples, such as test scores of students. In factor analysis and PCA, these features are thought to be influenced by unobserved factors, such as skills. Can we determine how…
Factor analysis is a critical component of high dimensional biological data analysis. However, modern biological data contain two key features that irrevocably corrupt existing methods. First, these data, which include longitudinal,…
Principal component analysis (PCA) is a popular dimension reduction technique often used to visualize high-dimensional data structures. In genomics, this can involve millions of variables, but only tens to hundreds of observations.…
We propose a dynamic multiplicative factor model for process data, which arise from complex problem-solving items, an emerging testing mode in large-scale educational assessment. The proposed model can be viewed as an extension of the…
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…
Principal Component Analysis (PCA) is a ubiquitous tool with many applications in machine learning including feature construction, subspace embedding, and outlier detection. In this paper, we present an algorithm for computing the top…
We introduce a HD DCC-HEAVY class of hierarchical-type factor models for high-dimensional covariance matrices, employing the realized measures built from higher-frequency data. The modelling approach features straightforward estimation and…
In many longitudinal studies, a large number of variables are measured repeatedly over time, with substantial missing data. Existing methods, such as probabilistic principal component analysis (PPCA), are ill-equipped to handle such…
Over the past decades, statisticians and machine-learning researchers have developed literally thousands of new tools for the reduction of high-dimensional data in order to identify the variables most responsible for a particular trait.…