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Principal component analysis (PCA) is a well-known linear dimension-reduction method that has been widely used in data analysis and modeling. It is an unsupervised learning technique that identifies a suitable linear subspace for the input…
Analyzing longitudinal data in health studies is challenging due to sparse and error-prone measurements, strong within-individual correlation, missing data and various trajectory shapes. While mixed-effect models (MM) effectively address…
In this work, we develop a novel principal component analysis (PCA) for semimartingales by introducing a suitable spectral analysis for the quadratic variation operator. Motivated by high-dimensional complex systems typically found in…
Hierarchical panel data models have recently garnered significant attention. This study contributes to the relevant literature by introducing a novel three-dimensional (3D) hierarchical panel data model, which integrates panel regression…
Modern empirical analysis often relies on high-dimensional panel datasets with non-negligible cross-sectional and time-series correlations. Factor models are natural for capturing such dependencies. A tensor factor model describes the…
In probabilistic principal component analysis (PPCA), an observed vector is modeled as a linear transformation of a low-dimensional Gaussian factor plus isotropic noise. We generalize PPCA to tensors by constraining the loading operator to…
We propose a new sparse principal component analysis (SPCA) method in which the solutions are obtained by projecting the full cardinality principal components onto subsets of variables. The resulting components are guaranteed to explain a…
Early work established convergence of the principal component estimators of the factors and loadings up to a rotation for large dimensional approximate factor models with weak factors in that the factor loading $\Lambda^{(0)}$ scales…
Ubiquitous linear Gaussian exploratory tools such as principle component analysis (PCA) and factor analysis (FA) remain widely used as tools for: exploratory analysis, pre-processing, data visualization and related tasks. However, due to…
Accurate predictions of pollutant concentrations at new locations are often of interest in air pollution studies on fine particulate matters (PM$_{2.5}$), in which data is usually not measured at all study locations. PM$_{2.5}$ is also a…
Model averaging has demonstrated superior performance for ensemble forecasting in high-dimensional framework, its extension to incomplete datasets remains a critical but underexplored challenge. Moreover, identifying the parsimonious model…
Principal Component Analysis (PCA) is a fundamental data preprocessing tool in the world of machine learning. While PCA is often thought of as a dimensionality reduction method, the purpose of PCA is actually two-fold: dimension reduction…
Functional Principal Component Analysis (FPCA) has become a widely-used dimension reduction tool for functional data analysis. When additional covariates are available, existing FPCA models integrate them either in the mean function or in…
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…
Confirmatory factor analysis (CFA) is a statistical method for identifying and confirming the presence of latent factors among observed variables through the analysis of their covariance structure. Compared to alternative factor models, CFA…
At the crossway of machine learning and data analysis, anomaly detection aims at identifying observations that exhibit abnormal behaviour. Be it measurement errors, disease development, severe weather, production quality default(s) (items)…
This work aims at performing Functional Principal Components Analysis (FPCA) with Horvitz-Thompson estimators when the observations are curves collected with survey sampling techniques. One important motivation for this study is that FPCA…
Principal component analysis (PCA) is a widely used technique for data analysis and dimension reduction with numerous applications in science and engineering. However, the standard PCA suffers from the fact that the principal components…
Functional principal component analysis (FPCA) is a widely used technique in functional data analysis for identifying the primary sources of variation in a sample of random curves. The eigenfunctions obtained from standard FPCA typically…
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…