Biwhitening Reveals the Rank of a Count Matrix

Boris Landa, Yuval Kluger, Unnamed Author

Publication date: 30 March 2023

Published in: SIAM Journal on Mathematics of Data Science (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/2103.13840

zbMATH Keywords

count data PCA Poisson noise rank estimation Marchenko-Pastur law heteroskedastic noise

Mathematics Subject Classification ID

Factor analysis and principal components; correspondence analysis (62H25) Estimation in multivariate analysis (62H12)

Uses Software

ePCA
ScreeNOT

Cites Work

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Bi-cross-validation of the SVD and the nonnegative matrix factorization
The singular values and vectors of low rank perturbations of large rectangular random matrices
Local law for random Gram matrices
The eigenvalues and eigenvectors of finite, low rank perturbations of large random matrices
Selecting the number of principal components: estimation of the true rank of a noisy matrix
Biproportional scaling of matrices and the iterative proportional fitting procedure
Finite sample approximation results for principal component analysis: A matrix perturbation approach
Spectral analysis of large dimensional random matrices
Natural exponential families with quadratic variance functions: Statistical theory
On the limit of the largest eigenvalue of the large dimensional sample covariance matrix
A limit theorem for the norm of random matrices
Natural exponential families with quadratic variance functions
A note on universality of the distribution of the largest eigenvalues in certain sample covariance matrices
Asymptotic performance of PCA for high-dimensional heteroscedastic data
\(e\)PCA: high dimensional exponential family PCA
On the distribution of the largest eigenvalue in principal components analysis
Rate of convergence in probability to the Marchenko-Pastur law
On orthogonal and symplectic matrix ensembles
Subspace estimation from unbalanced and incomplete data matrices: \({\ell_{2,\infty}}\) statistical guarantees
Low-rank matrix denoising for count data using unbiased Kullback-Leibler risk estimation
Heteroskedastic PCA: algorithm, optimality, and applications
Permutation methods for factor analysis and PCA
Rapid evaluation of the spectral signal detection threshold and Stieltjes transform
Poisson noise reduction with non-local PCA
Low-rank model with covariates for count data with missing values
Local law and Tracy-Widom limit for sparse sample covariance matrices
Matrix estimation by universal singular value thresholding
Eigenvalues of large sample covariance matrices of spiked population models
Concerning nonnegative matrices and doubly stochastic matrices
The diagonal equivalence of a nonnegative matrix to a stochastic matrix
The DAD theorem for symmetric non-negative matrices
Phase transition of the largest eigenvalue for nonnull complex sample covariance matrices
The Optimal Hard Threshold for Singular Values is <inline-formula> <tex-math notation="TeX">\(4/\sqrt {3}\) </tex-math></inline-formula>
Deterministic Parallel Analysis: An Improved Method for Selecting Factors and Principal Components
A Generalization of the Poisson Distribution
The Sinkhorn–Knopp Algorithm: Convergence and Applications
Diagonal Equivalence to Matrices with Prescribed Row and Column Sums. II
The DAD Theorem for Arbitrary Row Sums
Cross-Validatory Estimation of the Number of Components in Factor and Principal Components Models
Poisson Matrix Recovery and Completion
Generalized SURE for optimal shrinkage of singular values in low-rank matrix denoising
Optimal Spectral Shrinkage and PCA With Heteroscedastic Noise
Low-rank matrix completion and denoising under Poisson noise
Matrix Denoising for Weighted Loss Functions and Heterogeneous Signals
Large Sample Covariance Matrices and High-Dimensional Data Analysis
Model Averaging and Dimension Selection for the Singular Value Decomposition
Roy’s largest root test under rank-one alternatives
Analysis of call centre arrival data using singular value decomposition
DISTRIBUTION OF EIGENVALUES FOR SOME SETS OF RANDOM MATRICES
Diagonal Equivalence to Matrices with Prescribed Row and Column Sums
HePPCAT: Probabilistic PCA for Data With Heteroscedastic Noise
Estimating Number of Factors by Adjusted Eigenvalues Thresholding
Estimation of the Number of Spiked Eigenvalues in a Covariance Matrix by Bulk Eigenvalue Matching Analysis

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