arXiv subjects

Erina Paul

Publications and source records attributed to Erina Paul.

2 recordsLinked to original sources

arXiv2025

High-dimensional Array Bayesian Screening Based on Distributions with Structural Zeroes

In many biomedical applications with high-dimensional features, such as single-cell RNA-sequencing, it is not uncommon to observe numerous structural zeros. Identifying important features from a pool of high-dimensional data for subsequent detailed analysis is often of interest. Here, we describe an exact, rapid Bayesian screening approach with attractive diagnostic properties, utilizing a Tweedie model. The method provides the likelihood that a feature with structural zeros merits further investigation, as well as distributions of the effect magnitudes and the proportion of features with the same expected responses under alternative conditions. The method is agnostic to assay, data type, and application. Through numerical studies, we demonstrate that the proposed methodology is effective in identifying important features for follow-up experimentation across a range of applications, including single-cell differential expression analysis of embryonic stem cells and embryonic fibroblasts in mice and differential analysis of CD4 and CD8 Peripheral Blood Mononuclear Cells (PBMCs) in humans.

stat.AP↗

arXiv2021

The Reciprocal Bayesian LASSO

A reciprocal LASSO (rLASSO) regularization employs a decreasing penalty function as opposed to conventional penalization approaches that use increasing penalties on the coefficients, leading to stronger parsimony and superior model selection relative to traditional shrinkage methods. Here we consider a fully Bayesian formulation of the rLASSO problem, which is based on the observation that the rLASSO estimate for linear regression parameters can be interpreted as a Bayesian posterior mode estimate when the regression parameters are assigned independent inverse Laplace priors. Bayesian inference from this posterior is possible using an expanded hierarchy motivated by a scale mixture of double Pareto or truncated normal distributions. On simulated and real datasets, we show that the Bayesian formulation outperforms its classical cousin in estimation, prediction, and variable selection across a wide range of scenarios while offering the advantage of posterior inference. Finally, we discuss other variants of this new approach and provide a unified framework for variable selection using flexible reciprocal penalties. All methods described in this paper are publicly available as an R package at: https://github.com/himelmallick/BayesRecipe.

stat.ME↗