Himel Mallick

Niccolo Anceschi, Federico Ferrari, David B. Dunson et al.

It is increasingly common to collect data of multiple different types on the same set of samples. Our focus is on studying relationships between such multiview features and responses. A motivating application arises in the context of precision medicine where multi-omics data are collected to correlate with clinical outcomes. It is of interest to infer dependence within and across views while combining multimodal information to improve the prediction of outcomes. The signal-to-noise ratio can vary substantially across views, motivating more nuanced statistical tools beyond standard late and early fusion. This challenge comes with the need to preserve interpretability, select features, and obtain accurate uncertainty quantification. To address these challenges, we introduce two complementary factor regression models. A baseline Joint Factor Regression (\textsc{jfr}) captures combined variation across views via a single factor set, and a more nuanced Joint Additive FActor Regression (\textsc{jafar}) that decomposes variation into shared and view-specific components. For \textsc{jfr}, we use independent cumulative shrinkage process (\textsc{i-cusp}) priors, while for \textsc{jafar} we develop a dependent version (\textsc{d-cusp}) designed to ensure identifiability of the components. We develop Gibbs samplers that exploit the model structure and accommodate flexible feature and outcome distributions. Prediction of time-to-labor onset from immunome, metabolome, and proteome data illustrates performance gains against state-of-the-art competitors. Our open-source software (\texttt{R} package) is available at https://github.com/niccoloanceschi/jafar.

Himel Mallick, Rahim Alhamzawi, Erina Paul et al.

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.