A method for efficient CV estimates in Bayesian hierarchical models.
problem Computational infeasibility of cross-validation in Bayesian hierarchical regression models.
method Conditioning on variance-covariance parameters to transform CV into an optimization problem.
result Equivalent or improved predictive estimates compared to full cross-validation.
Bayesian estimators for causal inference using hierarchical Gaussian Processes.
problem Estimating causal effects in sharp and fuzzy RD/RK designs.
method Hierarchical Gaussian Process models for regression and classification.
result Hierarchical GP models improve precision and coverage of RD/RK estimations.
A new method for Bayesian neural networks using probabilistic backpropagation.
problem Approximating posterior distributions in Bayesian neural networks.
method Variational Expectation Propagation (VEP) with probabilistic backpropagation.
result Efficient algorithm for approximate integration over posterior distributions.
Develops a Bayesian framework for symbolic regression of scientific expressions.
problem Lack of principled uncertainty quantification and interpretability in existing symbolic regression methods.
method Hierarchical Bayesian framework with tree-structured symbolic expressions and Markov chain Monte Carlo inference.
result Robust performance on various datasets, including single-atom catalysis.
We propose a nonparametric Bayesian factor regression model that accounts for uncertainty in the number of factors, and the relationship between factors. To accomplish this, we propose a sparse variant of the Indian Buffet Process and couple this with a hierarchical model over factors, based on Kingman's coalescent. We…
A scalable Bayesian linear regression framework for spatial data.
problem Scalable methodologies for analyzing large spatial datasets.
method Conjugate Bayesian linear regression framework.
result Exact sampling from joint posterior distribution without iterative algorithms.
HBR improves normative modeling of neuroimaging data across multiple sites.
problem Dealing with nuisance variation in neuroimaging data across different sites.
method Hierarchical Bayesian regression (HBR) for multi-site normative modeling.
result HBR provides more accurate normative ranges compared to existing methods.
Paper proposes a new method for Bayesian linear regression using spike-and-slab priors.
problem Identifying predictors with similar relationships in linear regression models.
method Hierarchical Bayesian models with spike-and-slab priors and a Gibbs sampler.
result The proposed method outperforms previous methods in simulations and real data analysis.
In this paper a new Bayesian model for sparse linear regression with a spatio-temporal structure is proposed. It incorporates the structural assumptions based on a hierarchical Gaussian process prior for spike and slab coefficients. We design an inference algorithm based on Expectation Propagation and evaluate the mode…
metabeta uses neural networks to speed up Bayesian mixed-effects regression.
problem Bayesian mixed-effects regression is computationally expensive.
method metabeta is a neural network model that pre-trains to estimate posterior distributions.
result metabeta achieves comparable performance to MCMC at a fraction of the time.
Novel Bayesian framework for spatio-temporal neuroimaging data.
problem Inference on multi-task sparse hierarchical regression models with complex spatio-temporal dynamics.
method Flexible hierarchical Bayesian framework with Kronecker product covariance structure, majorization-minimization optimization, and Riemannian geometry.
result Improved performance on synthetic and real M/EEG data.
A new method for efficient BNC parameter estimation outperforms HDP smoothing.
problem Efficiently estimating parameters for Bayesian network classifiers to match or exceed random forest performance.
method Uses log-linear regression to approximate hierarchical Dirichlet process (HDP) smoothing, making the approach simpler and faster.
result Our method outperforms HDP smoothing while being orders of magnitude faster and competitive with random forests.
SmallML predicts customer churn for SMEs with small data, improving accuracy by 24.2 points.
problem AI exclusion of SMEs due to data scale mismatch.
method Bayesian transfer learning with hierarchical pooling and conformal prediction.
result 96.7% AUC on 100 obs SMEs, 24.2 point improvement over logistic regression.
Bayesian approach for learning spatiotemporal systems from noisy data.
problem Efficiently modeling and learning from spatiotemporal dynamical systems with noisy data.
method Hierarchical state-space models with Gaussian process regression for efficient interpolation and training.
result Efficient modeling and learning of spatiotemporal dynamics using Bayesian methods.
New hierarchical model improves on standard practice for high-dimensional data.
problem Poor statistical performance in high-dimensional hierarchical models.
method Model effects as exchangeable across covariates and correlated across datasets.
result Empirical Bayes estimator outperforms classic approach in high-dimensional settings.
The Bayesian Lasso is constructed in the linear regression framework and applies the Gibbs sampling to estimate the regression parameters. This paper develops a new sparse learning model, named the Bayesian Lasso Sparse (BLS) model, that takes the hierarchical model formulation of the Bayesian Lasso. The main differenc…
Bayesian predictive inference analyzes a dataset to make predictions about new observations. When a model does not match the data, predictive accuracy suffers. We develop population empirical Bayes (POP-EB), a hierarchical framework that explicitly models the empirical population distribution as part of Bayesian analys…
The SLOPE estimates regression coefficients by minimizing a regularized residual sum of squares using a sorted-ℓ1-norm penalty. The SLOPE combines testing and estimation in regression problems. It exhibits suitable variable selection and prediction properties, as well as minimax optimality. This paper introduces …
Paper analyzes consistency of Bayesian and machine learning methods for hierarchical parameter estimation.
problem Learning hierarchical parameters in complex and real-world problems.
method Empirical Bayes and Kernel Flow approaches.
result Consistency results for Matérn-like model on the torus, and comparison of algorithms.
This paper explores approximations for fully Bayesian Gaussian Process Regression.
problem Learning in Gaussian Process models through hyperparameter adaptation.
method Two approximation schemes: Hamiltonian Monte Carlo and Variational Inference.
result Predictive performance analysis on various benchmark datasets.
In this paper we introduce ZhuSuan, a python probabilistic programming library for Bayesian deep learning, which conjoins the complimentary advantages of Bayesian methods and deep learning. ZhuSuan is built upon Tensorflow. Unlike existing deep learning libraries, which are mainly designed for deterministic neural netw…
We investigate the choice of tuning parameters for a Bayesian multi-level group lasso model developed for the joint analysis of neuroimaging and genetic data. The regression model we consider relates multivariate phenotypes consisting of brain summary measures (volumetric and cortical thickness values) to single nucleo…
Study on Metropolis-within-Gibbs schemes for high-dimensional Bayesian models.
problem Improving the scalability of MCMC methods for complex Bayesian models.
method Relating convergence properties to conditional conductance for non-conjugate hierarchical models.
result Established dimension-free convergence results for Metropolis-within-Gibbs schemes.
Paper develops a dynamic Bayesian approach for active learning that optimizes exploration-exploitation balance.
problem Balancing exploration and exploitation in active learning for unknown functions.
method Develops BHEEM, a Bayesian hierarchical approach with approximate Bayesian computation for sampling trade-off parameters.
result BHEEM achieves at least 21% and 11% improvement over pure exploration and exploitation strategies respectively.
We propose the supervised hierarchical Dirichlet process (sHDP), a nonparametric generative model for the joint distribution of a group of observations and a response variable directly associated with that whole group. We compare the sHDP with another leading method for regression on grouped data, the supervised latent…
Bayesian Hierarchical Invariant Prediction refines ICP for better scalability and prior integration.
problem Improving computational scalability and invariance testing for causal inference.
method Bayesian Hierarchical structure to test invariance under heterogeneous data.
result Demonstrated improved scalability and potential as an alternative to ICP.
This paper introduces a new sparse spatio-temporal structured Gaussian process regression framework for online and offline Bayesian inference. This is the first framework that gives a time-evolving representation of the interdependencies between the components of the sparse signal of interest. A hierarchical Gaussian p…
Bayesian pliable lasso with horseshoe prior models interactions in GLMs with missing data.
problem Modeling interactions in sparse regression problems with missing responses.
method Bayesian pliable lasso with hierarchical horseshoe prior for sparsity and uncertainty quantification.
result Advantages over existing methods in recovering complex interaction patterns under incomplete data.
One of the challenges in model-based control of stochastic dynamical systems is that the state transition dynamics are involved, and it is not easy or efficient to make good-quality predictions of the states. Moreover, there are not many representational models for the majority of autonomous systems, as it is not easy …
Improves sampling efficiency for complex Bayesian models.
problem Inference challenges in hierarchical Gaussian-process models.
method Optimised Riemannian-manifold Hamiltonian Monte Carlo (RMHMC) with dynamic programming.
result Significant improvement in sampling efficiency and model evidence calculation.
Paper proposes fully Bayesian approach for RVM classification, improving accuracy especially in imbalanced data.
problem Difficulty in conducting RVM classification due to lack of closed-form solution for weight parameter posterior.
method Proposes Generic Bayesian and Fully Bayesian approaches with hierarchical hyperprior structure.
result Improves classification performance, especially in imbalanced data.
Posterior regularization enhances Bayesian hierarchical mixture clustering by improving node separation.
problem High nodal variance in BHMC trees, leading to weak separation between nodes at higher levels.
method Employing Posterior Regularization to impose max-margin constraints on nodes at every level.
result Improves cluster separation in BHMC models, enhancing overall model performance.
Deep Gaussian processes (DGPs) are multi-layer hierarchical generalisations of Gaussian processes (GPs) and are formally equivalent to neural networks with multiple, infinitely wide hidden layers. DGPs are nonparametric probabilistic models and as such are arguably more flexible, have a greater capacity to generalise, …
Proposes HDBEN for heteroscedastic regression with improved sparsity and variance modeling.
problem Violation of constant error variance in high-dimensional regression.
method HDBEN framework using hierarchical Bayesian priors with ℓ1 and ℓ2 penalties. result Achieves posterior concentration, variable selection consistency, and asymptotic normality.
Motivation: Recent advances in technology for brain imaging and high-throughput genotyping have motivated studies examining the influence of genetic variation on brain structure. Wang et al. (Bioinformatics, 2012) have developed an approach for the analysis of imaging genomic studies using penalized multi-task regressi…
New Bayesian method for joint sparse parameter inference.
problem Inference of jointly sparse parameter vectors from multiple measurements.
method Hierarchical Bayesian learning with joint sparsity-promoting priors.
result New algorithms consistently outperform existing methods in numerical experiments.
This work analyzes Gibbs samplers for Bayesian hierarchical models without dimensionality constraints.
problem Analyzing convergence properties of Gibbs samplers for Bayesian hierarchical models.
method Using Bayesian asymptotics and total variation mixing times, the study provides dimension-free convergence results.
result Dimension-free convergence results for Gibbs samplers targeting hierarchical models under random data-generating assumptions.
Mean-field variational methods are widely used for approximate posterior inference in many probabilistic models. In a typical application, mean-field methods approximately compute the posterior with a coordinate-ascent optimization algorithm. When the model is conditionally conjugate, the coordinate updates are easily …
Paper proposes efficient methods for forecasting with large datasets.
problem Forecasting with large, high-dimensional economic data sets.
method Bayesian hierarchical priors, factor graphs, message passing algorithms, Generalized Approximate Message Passing (GAMP).
result The proposed methods outperform traditional approaches in forecasting U.S. price inflation.
The Hierarchical Mixture of Experts (HME) is a well-known tree-based model for regression and classification, based on soft probabilistic splits. In its original formulation it was trained by maximum likelihood, and is therefore prone to over-fitting. Furthermore the maximum likelihood framework offers no natural metri…
The paper revisits and improves on a Bayesian relevance vector machine method for small sample sizes.
problem Statistical modeling with small sample sizes relative to the number of covariates.
method Introduces a new class of global-local priors and provides theoretical properties.
result Results on posterior consistency and contraction rates are provided.
Generalized linear models (GLMs) -- such as logistic regression, Poisson regression, and robust regression -- provide interpretable models for diverse data types. Probabilistic approaches, particularly Bayesian ones, allow coherent estimates of uncertainty, incorporation of prior information, and sharing of power acros…
GRASP simplifies Bayesian regression with grouped predictors using an adaptive NBP prior.
problem Regression with grouped predictors and adaptive shrinkage.
method Normal Beta Prime (NBP) prior with tunable hyperparameters for flexible sparsity control.
result Empirical validation of robust and versatile GRASP across various sparsity and signal-to-noise ratios.
Develops Bayesian inference methods for gamma models.
problem Challenges in inference for models with gamma functions.
method Data augmentation scheme using Exponential Reciprocal Gamma distributions.
result Scalable EM and MCMC algorithms developed.
Bayesian algorithm improves word representations using semantic taxonomy.
problem Improving word representations in semantic taxonomy.
method Bayesian Hierarchical Words Representation (BHWR) learning algorithm combining Variational Bayes and semantic taxonomy modeling.
result BHWR produces better representations for rare words.
Bayesian stacking improves model performance with varying model weights.
problem Improving model predictions with heterogeneous input performance.
method Bayesian hierarchical stacking with varying model weights inferred via Bayesian inference.
result Hierarchical stacking yields better predictions than linear averaging.
Unified Bayesian framework for PTA data analysis tackles hierarchical model issues.
problem Hierarchical Bayesian modeling challenges in PTA data analysis.
method Reparameterization strategy using Normalizing Flows (NFs) and i-nessai nested sampler.
result Improved statistical robustness and computational efficiency in PTA analysis.
In this paper we discuss Bayesian nonconvex penalization for sparse learning problems. We explore a nonparametric formulation for latent shrinkage parameters using subordinators which are one-dimensional Lévy processes. We particularly study a family of continuous compound Poisson subordinators and a family of discrete…