Related papers: Confidence Areas for Fixed-Effects PCA
This is a tutorial and survey paper on factor analysis, probabilistic Principal Component Analysis (PCA), variational inference, and Variational Autoencoder (VAE). These methods, which are tightly related, are dimensionality reduction and…
Intermittency analysis of factorial moments is a promising method used for the detection of power-law scaling in high-energy collision data. In particular, it has been employed in the search of fluctuations characteristic of the critical…
Principal component analysis (PCA) is a widely used method for data processing, such as for dimension reduction and visualization. Standard PCA is known to be sensitive to outliers, and thus, various robust PCA methods have been proposed.…
We present a novel class of projected methods, to perform statistical analysis on a data set of probability distributions on the real line, with the 2-Wasserstein metric. We focus in particular on Principal Component Analysis (PCA) and…
Classical Principal Component Analysis (PCA) approximates data in terms of projections on a small number of orthogonal vectors. There are simple procedures to efficiently compute various functions of the data from the PCA approximation. The…
Estimating intrinsic dimensionality of data is a classic problem in pattern recognition and statistics. Principal Component Analysis (PCA) is a powerful tool in discovering dimensionality of data sets with a linear structure; it, however,…
Independent component analysis (ICA) is a powerful computational tool for separating independent source signals from their linear mixtures. ICA has been widely applied in neuroimaging studies to identify and characterize underlying brain…
We study the estimation of a high dimensional approximate factor model in the presence of both cross sectional dependence and heteroskedasticity. The classical method of principal components analysis (PCA) does not efficiently estimate the…
Dimension reduction is useful for exploratory data analysis. In many applications, it is of interest to discover variation that is enriched in a "foreground" dataset relative to a "background" dataset. Recently, contrastive principal…
Linear mixed-effects models are widely used in analyzing clustered or repeated measures data. We propose a quasi-likelihood approach for estimation and inference of the unknown parameters in linear mixed-effects models with high-dimensional…
In this paper we offer a unified approach to the problem of nonparametric regression on the unit interval. It is based on a universal, honest and non-asymptotic confidence region which is defined by a set of linear inequalities involving…
We study the accuracy of forecasts in the diffusion index forecast model with possibly weak loadings. The default option to construct forecasts is to estimate the factors through principal component analysis (PCA) on the available predictor…
Artificial neural networks that learn to perform Principal Component Analysis (PCA) and related tasks using strictly local learning rules have been previously derived based on the principle of similarity matching: similar pairs of inputs…
Betas from spot regressions are central to asset pricing and risk management, as measures of systematic risk. This paper develops a new estimation and inference framework for spot regressions by leveraging high-frequency candlesticks,…
Functional data analysis is concerned with the analysis of infinite-dimensional data functions. Functional principal component analysis (FPCA) is a key method to obtain finite-dimensional summaries. Consistency of FPCA has been…
We consider a sparse high-dimensional varying coefficients model with random effects, a flexible linear model allowing covariates and coefficients to have a functional dependence with time. For each individual, we observe discretely sampled…
Principal component analysis (PCA) is a classical method for dimensionality reduction based on extracting the dominant eigenvectors of the sample covariance matrix. However, PCA is well known to behave poorly in the ``large $p$, small $n$''…
Principal Component Analysis (PCA) has wide applications in machine learning, text mining and computer vision. Classical PCA based on a Gaussian noise model is fragile to noise of large magnitude. Laplace noise assumption based PCA methods…
This chapter covers different approaches to policy evaluation for assessing the causal effect of a treatment or intervention on an outcome of interest. As an introduction to causal inference, the discussion starts with the experimental…
Sparse principal component analysis (sparse PCA) is a widely used technique for dimensionality reduction in multivariate analysis, addressing two key limitations of standard PCA. First, sparse PCA can be implemented in high-dimensional low…