Related papers: Consistent estimation of high-dimensional factor m…
This paper proposes a novel methodology for the online detection of changepoints in the factor structure of large matrix time series. Our approach is based on the well-known fact that, in the presence of a changepoint, a factor model can be…
Many high dimensional and high-throughput biological datasets have complex sample correlation structures, which include longitudinal and multiple tissue data, as well as data with multiple treatment conditions or related individuals. These…
The problem of principle component analysis (PCA) is traditionally solved by spectral or algebraic methods. We show how computing the leading principal component could be reduced to solving a \textit{small} number of well-conditioned {\it…
We consider the problem of decomposing a large covariance matrix into the sum of a low-rank matrix and a diagonally dominant matrix, and we call this problem the "Diagonally-Dominant Principal Component Analysis (DD-PCA)". DD-PCA is an…
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…
We study sparse principal components analysis in the high-dimensional setting, where $p$ (the number of variables) can be much larger than $n$ (the number of observations). We prove optimal, non-asymptotic lower and upper bounds on the…
We consider the estimation of a sparse factor model where the factor loading matrix is assumed sparse. The estimation problem is reformulated as a penalized M-estimation criterion, while the restrictions for identifying the factor loading…
We present a technique to perform dimensionality reduction on data that is subject to uncertainty. Our method is a generalization of traditional principal component analysis (PCA) to multivariate probability distributions. In comparison to…
Dimension reduction is crucial in functional data analysis (FDA). The key tool to reduce the dimension of the data is functional principal component analysis. Existing approaches for functional principal component analysis usually involve…
Financial time series are commonly decomposed into market factors, which capture shared price movements across assets, and residual factors, which reflect asset-specific deviations. To hedge the market-wide risks, such as the COVID-19…
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…
A prevalent feature of high-dimensional data is the dependence among covariates, and model selection is known to be challenging when covariates are highly correlated. To perform model selection for the high-dimensional Cox proportional…
We study the problem of factor modelling vector- and tensor-valued time series in the presence of heavy tails in the data, which produce extreme observations with non-negligible probability. We propose to combine a two-step procedure for…
In a very high-dimensional vector space, two randomly-chosen vectors are almost orthogonal with high probability. Starting from this observation, we develop a statistical factor model, the random factor model, in which factors are chosen at…
The case that the factor model does not account for all the covariances of the observed variables is considered. This is a quite realistic condition because some model error as well as some sampling error should usually occur with empirical…
High-dimensional statistical inference deals with models in which the the number of parameters p is comparable to or larger than the sample size n. Since it is usually impossible to obtain consistent procedures unless $p/n\rightarrow0$, a…
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…
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…
This paper studies the impact of bootstrap procedure on the eigenvalue distributions of the sample covariance matrix under a high-dimensional factor structure. We provide asymptotic distributions for the top eigenvalues of bootstrapped…
Latent factor models that integrate data from multiple sources/studies or modalities have garnered considerable attention across various disciplines. However, existing methods predominantly focus either on multi-study integration or…