# ePCA: High Dimensional Exponential Family PCA

arXiv: https://arxiv.org/abs/1611.05550 · HTML: https://mlsanity.com/paper/1611.05550/

## Key facts

- Cited by 4 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 17 Nov 2016.

## Built on by (most cited first, 4 of 4)

- [High-dimensional analysis of ridge regression for non-identically distributed data with a variance profile](https://mlsanity.com/paper/2403.20200/) (2024)
- [Multivariate Analysis for Multiple Network Data via Semi-Symmetric Tensor PCA](https://mlsanity.com/paper/2202.04719/) (2022)
- [eRPCA: Robust Principal Component Analysis for Exponential Family Distributions](https://mlsanity.com/paper/2310.19787/) (2023)
- [On Minimum Trace Factor Analysis -- An Old Song Sung to a New Tune](https://mlsanity.com/paper/2402.02459/) (2024)

## Abstract (arXiv)

Many applications, such as photon-limited imaging and genomics, involve large datasets with noisy entries from exponential family distributions. It is of interest to estimate the covariance structure and principal components of the noiseless distribution. Principal Component Analysis (PCA), the standard method for this setting, can be inefficient when the noise is non-Gaussian. We develop ePCA (exponential family PCA), a new methodology for PCA on exponential family distributions. ePCA can be used for dimensionality reduction and denoising of large data matrices. ePCA involves the eigendecomposition of a new covariance matrix estimator, constructed in a simple and deterministic way using moment calculations, shrinkage, and random matrix theory. We provide several theoretical justifications for our estimator, including the finite-sample convergence rate, and the Marchenko-Pastur law in high dimensions. ePCA compares favorably to PCA and various PCA alternatives for exponential families, in simulations as well as in XFEL and SNP data analysis. An open-source implementation is available.