Related papers: Functional Horseshoe Priors for Subspace Shrinkage

We consider Gibbs samplers for a normal linear regression model with a global-local shrinkage prior and show that they produce geometrically ergodic Markov chains. First, under the horseshoe local prior and a three-parameter beta global…

Bayesian deep learning approaches assume model parameters to be latent random variables and infer posterior distributions to quantify uncertainty, increase safety and trust, and prevent overconfident and unpredictable behavior. However,…

High-dimensional vector autoregressive (VAR) models offer a versatile framework for multivariate time series analysis, yet face critical challenges from over-parameterization and uncertain lag order. In this paper, we systematically compare…

In many large-scale inverse problems, such as computed tomography and image deblurring, characterization of sharp edges in the solution is desired. Within the Bayesian approach to inverse problems, edge-preservation is often achieved using…

In Retrieval-Augmented Generation (RAG) and agent-based frameworks, the "Chain of Models" approach is widely used, where multiple specialized models work sequentially on distinct sub-tasks. This approach is effective but increases resource…

The explosion of data in recent years has generated an increasing need for new analysis techniques in order to extract knowledge from massive datasets. Machine learning has proved particularly useful to perform this task. Fully automatized…

The approximation of fixed-interval smoothing distributions is a key issue in inference for general state-space hidden Markov models (HMM). This contribution establishes non-asymptotic bounds for the Forward Filtering Backward Smoothing…

Bounded continuous responses -- such as proportions -- arise frequently in diverse scientific fields including climatology, biostatistics, and finance. Beta regression is a widely adopted framework for modeling such data, due to the…

A Bayesian pseudocoreset is a compact synthetic dataset summarizing essential information of a large-scale dataset and thus can be used as a proxy dataset for scalable Bayesian inference. Typically, a Bayesian pseudocoreset is constructed…

During the past decade, shrinkage priors have received much attention in Bayesian analysis of high-dimensional data. This paper establishes the posterior consistency for high-dimensional linear regression with a class of shrinkage priors,…

Isotonic regression or monotone function estimation is a problem of estimating function values under monotonicity constraints, which appears naturally in many scientific fields. This paper proposes a new Bayesian method with global-local…

We introduce functional adaptive shrinkage (FASH), an empirical Bayes method for joint analysis of observation units in which each unit estimates an effect function at several values of a continuous condition variable. The ideas in this…

Variable selection has received widespread attention over the last decade as we routinely encounter high-throughput datasets in complex biological and environment research. Most Bayesian variable selection methods are restricted to mixture…

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…

Macroeconomists using large datasets often face the choice of working with either a large Vector Autoregression (VAR) or a factor model. In this paper, we develop methods for combining the two using a subspace shrinkage prior. Subspace…

We investigate the frequentist properties of Bayesian procedures for estimation based on the horseshoe prior in the sparse multivariate normal means model. Previous theoretical results assumed that the sparsity level, that is, the number of…

We propose a flexible dual functional factor model for modelling high-dimensional functional time series. In this model, a high-dimensional fully functional factor parametrisation is imposed on the observed functional processes, whereas a…

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…

Precision matrix estimation in a multivariate Gaussian model is fundamental to network estimation. Although there exist both Bayesian and frequentist approaches to this, it is difficult to obtain good Bayesian and frequentist properties…

Multitask learning can be effective when features useful in one task are also useful for other tasks, and the group lasso is a standard method for selecting a common subset of features. In this paper, we are interested in a less restrictive…