Empirical Bayes Covariance Decomposition, and a solution to the Multiple Tuning Problem in Sparse PCA

no code implementations • 6 Dec 2023 • Joonsuk Kang, Matthew Stephens

We show that this formulation also leads to a penalized decomposition of the covariance (or Gram) matrix, $\mathbf{X}^T\mathbf{X}$.

A flexible empirical Bayes approach to multiple linear regression and connections with penalized regression

1 code implementation • 23 Aug 2022 • Youngseok Kim, Wei Wang, Peter Carbonetto, Matthew Stephens

We introduce a new empirical Bayes approach for large-scale multiple linear regression.

regression

Non-negative matrix factorization algorithms greatly improve topic model fits

1 code implementation • 27 May 2021 • Peter Carbonetto, Abhishek Sarkar, ZiHao Wang, Matthew Stephens

We report on the potential for using algorithms for non-negative matrix factorization (NMF) to improve parameter estimation in topic models.

Topic Models Variational Inference

Solving the Empirical Bayes Normal Means Problem with Correlated Noise

1 code implementation • 18 Dec 2018 • Lei Sun, Matthew Stephens

The Normal Means problem plays a fundamental role in many areas of modern high-dimensional statistics, both in theory and practice.

A fast algorithm for maximum likelihood estimation of mixture proportions using sequential quadratic programming

3 code implementations • 4 Jun 2018 • Youngseok Kim, Peter Carbonetto, Matthew Stephens, Mihai Anitescu

It is substantially faster than the interior point method, and just as accurate.

Computation Methodology

Empirical Bayes Matrix Factorization

1 code implementation • 20 Feb 2018 • Wei Wang, Matthew Stephens

This yields a sparse EBMF approach - essentially a version of sparse FA/PCA - that automatically adapts the amount of sparsity to the data.

Methodology

Empirical Bayes Shrinkage and False Discovery Rate Estimation, Allowing For Unwanted Variation

1 code implementation • 28 Sep 2017 • David Gerard, Matthew Stephens

This yields new, powerful EB methods for analyzing genomics experiments that account for both sparse effects and unwanted variation.

Methodology

Unifying and Generalizing Methods for Removing Unwanted Variation Based on Negative Controls

2 code implementations • 23 May 2017 • David Gerard, Matthew Stephens

In realistic simulations based on real data we found that RUVB is competitive with existing methods in terms of both power and calibration, although we also highlight the challenges of providing consistently reliable calibration among data sets.

Methodology Statistics Theory Statistics Theory 62J15 (Primary) 62F15, 62H25, 62P10 (Secondary)

Smoothing via Adaptive Shrinkage (smash): denoising Poisson and heteroskedastic Gaussian signals

1 code implementation • 25 May 2016 • Zhengrong Xing, Matthew Stephens

We describe the idea of "Adaptive Shrinkage" (ASH), a general purpose Empirical Bayes (EB) method for shrinkage estimation, and demonstrate its application to several signal denoising problems.

Methodology