Related papers: R2 priors for Grouped Variance Decomposition in Hi…
Shrinkage priors are a popular Bayesian paradigm to handle sparsity in high-dimensional regression. Still limited, however, is a flexible class of shrinkage priors to handle grouped sparsity, where covariates exhibit some natural grouping…
The adoption of continuous shrinkage priors in high-dimensional linear models has gained widespread attention due to their practical and theoretical advantages. Among them, the R2D2 prior has gained popularity for its intuitive…
The training of high-dimensional regression models on comparably sparse data is an important yet complicated topic, especially when there are many more model parameters than observations in the data. From a Bayesian perspective, inference…
Prior distributions for high-dimensional linear regression require specifying a joint distribution for the unobserved regression coefficients, which is inherently difficult. We instead propose a new class of shrinkage priors for linear…
We present the ARR2 prior, a joint prior over the auto-regressive components in Bayesian time-series models and their induced $R^2$. Compared to other priors designed for times-series models, the ARR2 prior allows for flexible and intuitive…
Multi-group covariance estimation for matrix-variate data with small within group sample sizes is a key part of many data analysis tasks in modern applications. To obtain accurate group-specific covariance estimates, shrinkage estimation…
In high dimensional regression, global local shrinkage priors have gained significant traction for their ability to yield sparse estimates, improve parameter recovery, and support accurate predictive modeling. While recent work has explored…
In this paper we study grouped variable selection problems by proposing a specified prior, called the nested spike and slab prior, to model collective behavior of regression coefficients. At the group level, the nested spike and slab prior…
In many regression settings the unknown coefficients may have some known structure, for instance they may be ordered in space or correspond to a vectorized matrix or tensor. At the same time, the unknown coefficients may be sparse, with…
We consider the problem of model selection when grouping structure is inherent within the regressors. Using a Bayesian approach, we model the mean vector by a one-group global-local shrinkage prior belonging to a broad class of such priors…
Most estimates for penalised linear regression can be viewed as posterior modes for an appropriate choice of prior distribution. Bayesian shrinkage methods, particularly the horseshoe estimator, have recently attracted a great deal of…
Lack of independence in the residuals from linear regression motivates the use of random effect models in many applied fields. We start from the one-way anova model and extend it to a general class of one-factor Bayesian mixed models,…
Projected priors were originally introduced to accommodate parameter constraints, but have recently regained popularity due to their ability to assign probability mass to low-dimensional parameter sets, such as the spaces of sparse vectors,…
In Bayesian analysis, the selection of a prior distribution is typically done by considering each parameter in the model. While this can be convenient, in many scenarios it may be desirable to place a prior on a summary measure of the model…
In recent years, shrinkage priors have received much attention in high-dimensional data analysis from a Bayesian perspective. Compared with widely used spike-and-slab priors, shrinkage priors have better computational efficiency. But the…
We propose a flexible class of models based on scale mixture of uniform distributions to construct shrinkage priors for covariance matrix estimation. This new class of priors enjoys a number of advantages over the traditional scale mixture…
Machine learning models often perform poorly under subpopulation shifts in the data distribution. Developing methods that allow machine learning models to better generalize to such shifts is crucial for safe deployment in real-world…
Ordinal regression with a high-dimensional covariate space has many important application areas including gene expression studies. The lack of an intrinsic numeric value associated with ordinal responses, however, makes methods based on…
Heavy-tailed continuous shrinkage priors, such as the horseshoe prior, are widely used for sparse estimation problems. However, there is limited work extending these priors to predictors with grouping structures. Of particular interest in…
Spatially dependent data arises in many applications, and Gaussian processes are a popular modelling choice for these scenarios. While Bayesian analyses of these problems have proven to be successful, selecting prior distributions for these…