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Principal component analysis (PCA) is a fundamental tool in multivariate statistics, yet its sensitivity to outliers and limitations in distributed environments restrict its effectiveness in modern large-scale applications. To address these…
This paper studies a regression model where both predictor and response variables are random functions. We consider a functional linear model where the conditional mean of the response variable at each time point is given by a linear…
Big data is transforming our world, revolutionizing operations and analytics everywhere, from financial engineering to biomedical sciences. The complexity of big data often makes dimension reduction techniques necessary before conducting…
The Principal Component Analysis (PCA) is a data dimensionality reduction technique well-suited for processing data from sensor networks. It can be applied to tasks like compression, event detection, and event recognition. This technique is…
Principal component analysis (PCA) is one of the most fundamental procedures in exploratory data analysis and is the basic step in applications ranging from quantitative finance and bioinformatics to image analysis and neuroscience.…
Incorporating covariates into functional principal component analysis (PCA) can substantially improve the representation efficiency of the principal components and predictive performance. However, many existing functional PCA methods do not…
Traditional principal component analysis (PCA) is well known in high-dimensional data analysis, but it requires to express data by a matrix with observations to be continuous. To overcome the limitations, a new method called flexible PCA…
Principal Component Analysis (PCA) and its exponential family extensions have three components: observations, latents and parameters of a linear transformation. We consider a generalised setting where the canonical parameters of the…
This paper re-examines the problem of estimating risk premia in linear factor pricing models. Typically, the data used in the empirical literature are characterized by weakness of some pricing factors, strong cross-sectional dependence in…
We consider estimation and inference for a regression coefficient in panels with interactive fixed effects (i.e., with a factor structure). We demonstrate that existing estimators and confidence intervals (CIs) can be heavily biased and…
Principal component regression (PCR) is a simple, but powerful and ubiquitously utilized method. Its effectiveness is well established when the covariates exhibit low-rank structure. However, its ability to handle settings with noisy,…
We propose a multiple imputation method based on principal component analysis (PCA) to deal with incomplete continuous data. To reflect the uncertainty of the parameters from one imputation to the next, we use a Bayesian treatment of the…
Multivariate binary data is becoming abundant in current biological research. Logistic principal component analysis (PCA) is one of the commonly used tools to explore the relationships inside a multivariate binary data set by exploiting the…
Principal Component Analysis (PCA) finds the best linear representation of data, and is an indispensable tool in many learning and inference tasks. Classically, principal components of a dataset are interpreted as the directions that…
In many applications, particularly in the natural sciences, the available high-dimensional set of features may contain variables that are not correlated with the response under consideration. Such irrelevant features can, in certain cases,…
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…
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…
We propose a "small-uniform" statistic for the inference of the functional PCA estimator in a functional linear regression model. The literature has shown two extreme behaviors: on the one hand, the FPCA estimator does not converge in…
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…
In this paper we develop a new approach to sparse principal component analysis (sparse PCA). We propose two single-unit and two block optimization formulations of the sparse PCA problem, aimed at extracting a single sparse dominant…