Efficient Bayesian variable selection for binomial and negative binomial data.
problem Computational challenges in Bayesian variable selection for complex models.
method Tempered Gibbs Sampling and MCMC scheme.
result Demonstrated effectiveness on cancer data with thousands of covariates.
Bayesian method tackles variable selection in high-dimensional data.
problem Challenges in Bayesian variable selection with large P.
method Efficient MCMC scheme with sublinear cost per iteration, extended to generalized linear models.
result Demonstrated effectiveness on cancer and maize genomic data.
Bayesian approach selects subsets of variables for interpretable prediction and identifies key factors in educational outcomes.
problem Challenges in subset selection for stability, regularization, and inference.
method Bayesian perspective on subset selection, deriving optimal subsets and variable importance metrics.
result Better prediction, interval estimation, and variable selection compared to competing methods.
A hybrid model for Bayesian optimization handles mixed variables using MCTS for categorical and GP for continuous.
problem Optimizing functions with mixed variable types (continuous, integer, categorical).
method Merges MCTS for categorical and GP for continuous variables, integrates UCTS search strategy, and dynamically selects kernels.
result Hybrid models outperform traditional methods in Bayesian optimization.
SVB method provides scalable Bayesian proportional hazards model for high-dimensional gene expression data.
problem Bayesian methods for high-dimensional sparse survival data often sacrifice uncertainty quantification or computational scalability.
method Mean-field variational approximation for scalable Bayesian proportional hazards model.
result SVB method offers posterior distribution for parameters and variable selection via posterior inclusion probabilities.
Bayesian framework selects features and lags for time series forecasting.
problem Variable selection and lagged error term identification in time series models.
method Hierarchical Bayesian models with spike-and-slab priors, two-stage MCMC algorithm.
result Posterior selection consistency under mild conditions, improved predictive performance.
Bayesian method selects important covariates in modal regression.
problem Bayesian modal regression with heavy-tailed responses.
method Expectation-maximization algorithm for parameter estimation; test statistic for variable selection.
result Efficacy of the proposed method in identifying important covariates.
We study the computational complexity of Markov chain Monte Carlo (MCMC) methods for high-dimensional Bayesian linear regression under sparsity constraints. We first show that a Bayesian approach can achieve variable-selection consistency under relatively mild conditions on the design matrix. We then demonstrate that t…
This work develops rigorous theoretical basis for the fact that deep Bayesian neural network (BNN) is an effective tool for high-dimensional variable selection with rigorous uncertainty quantification. We develop new Bayesian non-parametric theorems to show that a properly configured deep BNN (1) learns the variable im…
PliableBVS extends Bayesian lasso for modeling interactions with modifying variables.
problem Modeling interactions between large and small sets of variables, especially in omics studies.
method Bayesian variable selection with spike-and-slab priors and hierarchical structure.
result PliableBVS outperforms pliable lasso in identifying active main and interaction effects.
BayesBoost combines boosting and Bayesian methods for linear mixed models, improving uncertainty estimation and variable selection.
problem Lack of straightforward uncertainty estimation for parameters in high-dimensional linear mixed models.
method BayesBoost: Combines boosting and Bayesian inference for linear mixed models.
result Improves uncertainty estimation and variable selection in linear mixed models.
The paper decouples shrinkage and selection in Bayesian Quantile Regression.
problem Improving prediction accuracy in high-dimensional Bayesian Quantile Regression.
method Two-step procedure: shrinkage through continuous priors, sparsification through SAVS.
result The method reduces bias and provides interpretable variable selection.
New BO method efficiently optimizes high-dimensional functions by automatically selecting variables.
problem Efficiently optimizing functions with high-dimensional domains.
method Exploits variable selection to automatically learn sub-spaces without pre-specified dimensions.
result Empirically validated on synthetic and real problems, demonstrating efficiency.
Bayesian method selects subsets for LMMs with structured dependence.
problem Subset selection challenge in LMMs with structured dependence.
method Bayesian decision analysis with Mahalanobis loss function.
result Optimal linear coefficients for subsets and cardinality constraints.
We extend the Bayesian Information Criterion (BIC), an asymptotic approximation for the marginal likelihood, to Bayesian networks with hidden variables. This approximation can be used to select models given large samples of data. The standard BIC as well as our extension punishes the complexity of a model according to …
Unified framework for selecting variables with uncertainty quantification.
problem Uncertainty in nonlinear variable selection for various models.
method Develops a unified framework using integrated partial derivatives for quantifying variable importance and uncertainty.
result The approach provides a principled method for quantifying variable selection uncertainty and is generalizable to non-differentiable models.
Unified Bayesian Optimisation for mixed variables improves performance.
problem Efficient optimisation of problems with both categorical and continuous variables.
method Derive value proposals from the Expected Improvement criterion to optimise both categorical and continuous variables under a single acquisition metric.
result Unified approach significantly outperforms existing methods across mixed-variable tasks.
This paper addresses the issue of model selection for hidden Markov models (HMMs). We generalize factorized asymptotic Bayesian inference (FAB), which has been recently developed for model selection on independent hidden variables (i.e., mixture models), for time-dependent hidden variables. As with FAB in mixture model…
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.
Efficiently selects important variables in high-dimensional logistic regression.
problem Variable selection in high-dimensional logistic regression with binary responses.
method Developed a variational empirical Bayes approach for efficient model space marginal distribution.
result The variational approximation inherits strong selection consistency from the posterior distribution.
Bayesian non-parametric model selects latent dimensions automatically.
problem Non-linear, sparse latent variable selection.
method Indian buffet process prior, random Fourier approximation, MCMC sampling.
result Superior performance on synthetic, biological, and text datasets.
Bayesian method discovers PDEs with variable coefficients robustly.
problem Discovering PDEs from noisy data is challenging.
method Bayesian sparse learning with tBGL-SS and Gibbs sampler.
result Method enhances robustness and model selection criteria.
We present an Automatic Relevance Determination prior Bayesian Neural Network(BNN-ARD) weight l2-norm measure as a feature importance statistic for the model-x knockoff filter. We show on both simulated data and the Norwegian wind farm dataset that the proposed feature importance statistic yields statistically signific…
We propose a Monte Carlo algorithm to sample from high dimensional probability distributions that combines Markov chain Monte Carlo and importance sampling. We provide a careful theoretical analysis, including guarantees on robustness to high dimensionality, explicit comparison with standard Markov chain Monte Carlo me…
Bayesian approach controls FDR in high-dimensional models.
problem High-dimensional variable selection and inference.
method Adapted Mirror Statistic to Bayesian framework for FDR control.
result Effective FDR control without data splitting.
We develop the necessary theory in computational algebraic geometry to place Bayesian networks into the realm of algebraic statistics. We present an algebra{statistics dictionary focused on statistical modeling. In particular, we link the notion of effiective dimension of a Bayesian network with the notion of algebraic…
In the popular approach of "Bayesian variable selection" (BVS), one uses prior and posterior distributions to select a subset of candidate variables to enter the model. A completely new direction will be considered here to study BVS with a Gibbs posterior originating in statistical mechanics. The Gibbs posterior is con…
This paper is about variable selection, clustering and estimation in an unsupervised high-dimensional setting. Our approach is based on fitting constrained Gaussian mixture models, where we learn the number of clusters K and the set of relevant variables S using a generalized Bayesian posterior with a sparsity indu…
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 selection relative to traditional shrinkage methods. Here we consider a fully Bayesian f…
New algorithm tackles big data Bayesian problems with latent variables.
problem Bayesian computing for large-scale problems with missing data and dimension jumping.
method Extended stochastic gradient MCMC with latent variables.
result Highly scalable and more efficient than traditional MCMC algorithms.
New sampler reduces MCMC complexity for Bayesian variable selection.
problem High-dimensional Bayesian variable selection with high computation complexity.
method Variable-complexity subset weighted-Tempered Gibbs Sampler (wTGS) with Rao-Blackwellized estimator.
result Variances of Rao-Blackwellized estimator are smaller than those of subset wTGS.
Finite mixture model is an important branch of clustering methods and can be applied on data sets with mixed types of variables. However, challenges exist in its applications. First, it typically relies on the EM algorithm which could be sensitive to the choice of initial values. Second, biomarkers subject to limits of…
New method corrects selection bias in post-selective inference for Group LASSO.
problem Inference after Group LASSO selection is unreliable.
method Develops a consistent, post-selective Bayesian method to adjust for selection bias.
result Corrects bias in recovering effects of selected variables.
A fast and scalable method for variable selection in high-dimensional Gaussian processes.
problem Inefficient variable selection in high-dimensional Gaussian processes.
method Developed a fast and scalable variational inference algorithm for spike and slab Gaussian processes.
result Consistently outperforms vanilla and sparse variational GPs while retaining similar runtimes.
Efficiently identifies important variables in binary outcomes using variational Bayes.
problem Bayesian variable selection for binary outcomes with computational challenges.
method Mean-field variational Bayes approximation with closed-form updates and efficient inference algorithm.
result Successfully identifies important variables and is orders of magnitude faster than MCMC.
Sparse versions of principal component analysis (PCA) have imposed themselves as simple, yet powerful ways of selecting relevant features of high-dimensional data in an unsupervised manner. However, when several sparse principal components are computed, the interpretation of the selected variables is difficult since ea…
Proposes spBART for risk prediction using epigenetic signatures and covariates.
problem Complex high-dimensional epigenetic data and low-dimensional covariates for risk prediction.
method Semi-parametric Bayesian Additive Regression Trees (spBART) with cross-validation for variable selection.
result Achieves strong out-of-sample discrimination (AUC = 0.96) in held-out validation set.
Proposes a new method for feature selection using Bayesian ID with intervention.
problem Feature selection in data with varying importance.
method Probabilistic model for interpolative decomposition with Bayesian inference and Gibbs sampling.
result The proposed Bayesian ID algorithm with intervention selects features with higher priority and comparable reconstructive errors.
Nonlinear kernel regression models are often used in statistics and machine learning because they are more accurate than linear models. Variable selection for kernel regression models is a challenge partly because, unlike the linear regression setting, there is no clear concept of an effect size for regression coeffici…
A new method selects variables efficiently for fast and accurate dynamic system identification.
problem Efficiently selecting variables for scalable Gaussian processes.
method Forward variable selection using Karhunen-Loève decomposition and Gibbs sampling.
result Method yields competitive accuracies and inference times for dynamic systems.
Flexible model for complex relationships using Bayesian nonparametrics.
problem Complex relationships between variables not well captured by simple models.
method Hierarchical generation of nonlinear features, Bayesian inference, variable selection.
result Find interpretable models with a small set of important features.
Method selects the best deep learner for time-series prediction using Bayesian networks.
problem Selecting the most effective deep learning model for time-series prediction.
method Bayesian network selects deep learners based on input variables and cluster training data.
result Threshold value determines which deep learners predict time-series data robustly.
Bayesian Cox model identifies biomarkers from multi-omics data.
problem Produce interpretable survival prognosis from multi-omics data.
method Penalized semiparametric Bayesian Cox model with graph-structured selection priors.
result Model identifies new biomarkers and improves survival prediction.
Bayesian l0-regularized least squares is a variable selection technique for high dimensional predictors. The challenge is optimizing a non-convex objective function via search over model space consisting of all possible predictor combinations. Spike-and-slab (a.k.a. Bernoulli-Gaussian) priors are the gold standard f…
New algorithm learns Bayesian network structures with fewer samples.
problem Learning Bayesian network structures with limited observational data.
method Active sampling strategy to select variables for observation.
result Active algorithm finds structures close to optimal with fewer samples.
Proposes a method to learn sparse deep neural networks with theoretical guarantees.
problem Over-parameterized deep neural networks cause training, prediction, and interpretation difficulties.
method Frequentist-like method for sparse DNNs under Bayesian framework.
result Consistent sparse DNNs with at most O(n/log(n)) connections. Bayesian TNKMs automatically infer model complexity and feature relevance.
problem Manual tuning of TN rank and feature dimensions is error-prone and computationally expensive.
method Bayesian approach with hierarchical priors on TN factors for automatic rank and feature selection.
result Superior performance in prediction accuracy, uncertainty quantification, interpretability, and scalability.
fCBO optimizes interventions in causal graphs using Gaussian processes.
problem Optimizing interventions in known causal graphs.
method Functional causal Bayesian optimization (fCBO) using Gaussian processes and expected improvement acquisition.
result Functional interventions can lead to better target effects and optimal conditional effects.