Related papers: Bayesian Bootstrap Spike-and-Slab LASSO
We investigate the problem of deriving adaptive posterior rates of contraction on $\mathbb{L}^{\infty}$ balls in density estimation. Although it is known that log-density priors can achieve optimal rates when the true density is…
Identifying variables associated with clinical endpoints is of much interest in clinical trials. With the rapid growth of cell and gene therapy (CGT) and therapeutics for ultra-rare diseases, there is an urgent need for statistical methods…
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…
In exciting new work, Bertsimas et al. (2016) showed that the classical best subset selection problem in regression modeling can be formulated as a mixed integer optimization (MIO) problem. Using recent advances in MIO algorithms, they…
Over the past decade and a half, adoption of Bayesian inference in pulsar timing analysis has led to increasingly sophisticated models. The recent announcement of evidence for a stochastic background of gravitational waves by various pulsar…
In this work, we developed a new Bayesian method for variable selection in function-on-scalar regression (FOSR). Our method uses a hierarchical Bayesian structure and latent variables to enable an adaptive covariate selection process for…
Residual bootstrap is a classical method for statistical inference in regression settings. With massive data sets becoming increasingly common, there is a demand for computationally efficient alternatives to residual bootstrap. We propose a…
The high cost and data scarcity in scientific exploration have motivated the use of large language models (LLMs) as knowledge-driven components in Bayesian optimization (BO). However, existing approaches typically embed LLMs directly into…
Bayesian hierarchical models have been demonstrated to provide efficient algorithms for finding sparse solutions to ill-posed inverse problems. The models comprise typically a conditionally Gaussian prior model for the unknown, augmented by…
Semi-supervised learning by self-training heavily relies on pseudo-label selection (PLS). The selection often depends on the initial model fit on labeled data. Early overfitting might thus be propagated to the final model by selecting…
Bayesian methods for learning Gaussian graphical models offer a principled framework for quantifying model uncertainty and incorporating prior knowledge. However, their scalability is constrained by the computational cost of jointly…
Due to its self-regularizing nature and its ability to quantify uncertainty, the Bayesian approach has achieved excellent recovery performance across a wide range of sparse signal recovery applications. However, most existing methods are…
Many statistical models can be simulated forwards but have intractable likelihoods. Approximate Bayesian Computation (ABC) methods are used to infer properties of these models from data. Traditionally these methods approximate the posterior…
Stochastic gradients have been widely integrated into Langevin-based methods to improve their scalability and efficiency in solving large-scale sampling problems. However, the proximal sampler, which exhibits much faster convergence than…
The bootstrap provides a simple and powerful means of assessing the quality of estimators. However, in settings involving large datasets---which are increasingly prevalent---the computation of bootstrap-based quantities can be prohibitively…
High-dimensional data are routinely collected in many areas. We are particularly interested in Bayesian classification models in which one or more variables are imbalanced. Current Markov chain Monte Carlo algorithms for posterior…
Likelihood-free methods, such as approximate Bayesian computation, are powerful tools for practical inference problems with intractable likelihood functions. Markov chain Monte Carlo and sequential Monte Carlo variants of approximate…
The paper presents a novel approach for unsupervised techniques in the field of clustering. A new method is proposed to enhance existing literature models using the proper Bayesian bootstrap to improve results in terms of robustness and…
Two major bottlenecks to the solution of large-scale Bayesian inverse problems are the scaling of posterior sampling algorithms to high-dimensional parameter spaces and the computational cost of forward model evaluations. Yet incomplete or…
Spike-and-slab and horseshoe regression are arguably the most popular Bayesian variable selection approaches for linear regression models. However, their performance can deteriorate if outliers and heteroskedasticity are present in the…