Related papers: Parameter expansion in local-shrinkage models
This paper explores the versatility and depth of Bayesian modeling by presenting a comprehensive range of applications and methods, combining Markov chain Monte Carlo (MCMC) techniques and variational approximations. Covering topics such as…
We consider Bayesian model selection in generalized linear models that are high-dimensional, with the number of covariates p being large relative to the sample size n, but sparse in that the number of active covariates is small compared to…
Expanding a lower-dimensional problem to a higher-dimensional space and then projecting back is often beneficial. This article rigorously investigates this perspective in the context of finite mixture models, namely how to improve inference…
Sampling orthogonal polynomial bases via Monte Carlo is of interest for uncertainty quantification of models with high-dimensional random inputs, using Polynomial Chaos (PC) expansions. It is known that bounding a probabilistic parameter,…
We consider a Bayesian framework for estimating a high-dimensional sparse precision matrix, in which adaptive shrinkage and sparsity are induced by a mixture of Laplace priors. Besides discussing our formulation from the Bayesian…
Bayesian optimization is normally performed within fixed variable bounds. In cases like hyperparameter tuning for machine learning algorithms, setting the variable bounds is not trivial. It is hard to guarantee that any fixed bounds will…
Sparse models are desirable for many applications across diverse domains as they can perform automatic variable selection, aid interpretability, and provide regularization. When fitting sparse models in a Bayesian framework, however,…
Cox proportional hazards model is one of the most popular models in biomedical data analysis. There have been continuing efforts to improve the flexibility of such models for complex signal detection, for example, via additive functions.…
Pseudo-marginal Metropolis-Hastings (pmMH) is a powerful method for Bayesian inference in models where the posterior distribution is analytical intractable or computationally costly to evaluate directly. It operates by introducing…
We study full Bayesian procedures for high-dimensional linear regression under sparsity constraints. The prior is a mixture of point masses at zero and continuous distributions. Under compatibility conditions on the design matrix, the…
Bayesian factor models are widely used for dimensionality reduction and pattern discovery in high-dimensional datasets across diverse fields. These models typically focus on imposing priors on factor loading to induce sparsity and improve…
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…
Higher-order Markov chains are frequently used to model categorical time series. However, a major problem with fitting such models is the exponentially growing number of parameters in the model order. A popular approach to parsimonious…
In this paper we propose an algorithm for recovering sparse orthogonal polynomials using stochastic collocation. Our approach is motivated by the desire to use generalized polynomial chaos expansions (PCE) to quantify uncertainty in models…
Particle Markov Chain Monte Carlo methods are used to carry out inference in non-linear and non-Gaussian state space models, where the posterior density of the states is approximated using particles. Current approaches usually perform…
Sparsity has become a key concept for solving of high-dimensional inverse problems using variational regularization techniques. Recently, using similar sparsity-constraints in the Bayesian framework for inverse problems by encoding them in…
In this work, we study the problem of finding approximate, with minimum support set, solutions to matrix max-plus equations, which we call sparse approximate solutions. We show how one can obtain such solutions efficiently and in polynomial…
This paper presents a new Bayesian collaborative sparse regression method for linear unmixing of hyperspectral images. Our contribution is twofold; first, we propose a new Bayesian model for structured sparse regression in which the…
There is a wide variety of models in which the dimension of the parameter space is unknown. For example, in factor analysis the number of latent factors is typically not known and has to be inferred from the observed data. Although…
Matrix factorization (MF) has become a common approach to collaborative filtering, due to ease of implementation and scalability to large data sets. Two existing drawbacks of the basic model is that it does not incorporate side information…