Empirical Bayes rates via variational approximations and prior decomposition.
problem Nonparametric and high-dimensional inference convergence rates.
method Variational perspective and prior decomposition.
result Empirical Bayes posterior rates derived from variational Bayes.
Unified empirical and variational Bayes for unnormalized densities.
problem Approximating unnormalized densities using latent variable models.
method Formulate a latent variable model for Y=X+N(0,σ2Id), use ELBO as parametrization of Y's energy function, and estimate X with empirical Bayes least-squares. result UVB has higher capacity to approximate energy functions than MLPs in DEEN.
Develops a fast variational approximation for high-dimensional empirical Bayes posteriors.
problem Optimal posterior computation in high-dimensional settings with prior tails effect.
method Variational approximation of empirical Bayes posterior with data-driven centers and thin-tailed conjugate priors.
result Retains optimal concentration rate properties and superior performance compared to existing methods.
New method for high-dimensional linear regression using empirical Bayes.
problem Estimating prior in high-dimensional linear regression.
method Variational empirical Bayes approach with NPMLE and mean field approximation.
result Established asymptotic consistency and computational efficiency of the method.
The paper analyzes high-dimensional linear regression using parametric empirical Bayes methods.
problem Estimation of i.i.d. priors in high-dimensional Bayesian linear regression with random design.
method Parametric empirical Bayes estimation, variational lower bound maximization, phase transition analysis.
result The vEB estimator is information theoretically optimal up to p=o(n2/3) but sub-optimal in higher dimensions. Bayesian Empirical Bayes extends EB to complex structures using probabilistic symmetry.
problem Improving simultaneous inference in complex settings like arrays and graphs.
method Generalized empirical Bayes approach based on probabilistic symmetry.
result BEB outperforms existing methods in denoising arrays and spatial data.
Meta-learning framework improves model performance on few-shot classification tasks.
problem Improving model performance on few-shot classification tasks.
method Empirical Bayes formulation with synthetic gradients for transductive meta-learning.
result Meta-learning framework outperforms previous state-of-the-art methods on benchmarks.
Stochastic variational inference for Bayesian deep neural network (DNN) requires specifying priors and approximate posterior distributions over neural network weights. Specifying meaningful weight priors is a challenging problem, particularly for scaling variational inference to deeper architectures involving high dime…
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.
Gradient-based optimization improves variational empirical Bayes regression.
problem Sparse, large-scale multiple regression models.
method Gradient-based optimization (GradVI) for variational empirical Bayes (VEB) regression.
result GradVI produces similar predictive performance to CAVI but converges faster and is faster in certain settings.
Neural Empirical Bayes estimates source distributions from noisy simulations.
problem Estimating source distributions from noisy, simulated data.
method Uses neural density estimators to estimate a prior or source distribution over uncorrupted samples, then performs posterior inference.
result Recovering ground truth source distributions up to symmetries.
VIB balances empirical and Bayesian approaches in predictive models.
problem Balancing empirical and Bayesian methods in predictive models.
method VIB as a compromise between empirical and Bayesian objectives.
result VIB minimizes risks due to finite sampling of targets.
Flexible empirical Bayes for large-scale multiple linear regression.
problem Large-scale multiple linear regression with flexible priors and efficient computation.
method Adaptive shrinkage priors combined with variational approximations for hyperparameter estimation.
result The posterior mean from the empirical Bayes method solves a penalized regression problem.
A new optimization algorithm for Gaussian Variational Inference on precision matrices.
problem Complex models with positive definite constraints on covariance matrices.
method Manifold Gaussian Variational Bayes (MGVBP) with natural gradient updates.
result Empirically validated as a feasible and efficient solution for VI in complex models.
We propose an empirical Bayes estimator based on Dirichlet process mixture model for estimating the sparse normalized mean difference, which could be directly applied to the high dimensional linear classification. In theory, we build a bridge to connect the estimation error of the mean difference and the misclassificat…
RQMC improves optimization in variational Bayes problems.
problem Optimizing variational Bayes problems with noisy objective functions.
method Use of randomized quasi-Monte Carlo (RQMC) sampling with stochastic L-BFGS.
result RQMC can significantly speed up optimization and find better parameter values.
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…
A new meta-learning method using shared variational inference.
problem Meta-learning with uncertainty over model parameters.
method Shared amortized variational inference network for conditional prior and posterior.
result Prevents collapse of conditional prior to Dirac delta function.
Bayesian model for multi-environment prediction with latent variable changes.
problem Prediction in environments with changing latent variable distributions.
method Bayesian model with empirical Bayes prior and amortized variational algorithm.
result Method outperforms previous approaches in new environments.
Flexible Bayesian approach for generalized linear models, especially for sparse logistic regression.
problem Sparse logistic regression challenges in machine learning.
method Empirical Bayes approach with mean-field variational inference, tuning-free and scalable.
result Superior predictive performance in sparse logistic regression compared to existing methods.
Adaptive variational Bayes framework improves inference adaptively.
problem Lack of general and computationally tractable variational Bayes method for adaptive inference.
method Proposes a novel adaptive variational Bayes framework combining variational posteriors over individual models.
result Adaptive variational Bayes achieves optimal contraction rates adaptively under general conditions.
Variational Gaussian Processes solve linear inverse problems efficiently.
problem Solving inverse problems where indirect observations are corrupted by noise.
method Variational Bayesian methods with Gaussian process priors and inducing variables.
result Posterior contraction rates can be attained by correctly tuned variational procedures.
New approach to meta-learning with variational Bayes for unlabeled data.
problem Improving machine learning systems' adaptability to small data.
method Generative meta-learning using AEVB and mean-field variational Bayes.
result Relevant VB updates do not depend on generative neural networks for certain models.
New method selects FMM components via variational Bayes.
problem Selecting the correct number of components in finite mixture models.
method Variational Bayes with mean-field approximation.
result Consistency of model selection based on ELBO maximization.
VBphenoR uses variational Bayes for EHR-based patient phenotyping.
problem Phenotyping patients from EHR data for targeted treatments.
method Variational Bayes Gaussian Mixture Model (GMM) and logistic regression.
result Closed-form inference for efficient patient phenotype determination.
Bayesian neural networks (BNNs) hold great promise as a flexible and principled solution to deal with uncertainty when learning from finite data. Among approaches to realize probabilistic inference in deep neural networks, variational Bayes (VB) is theoretically grounded, generally applicable, and computationally effic…
HEBAE improves VAEs by adaptively balancing reconstruction and regularization.
problem Posterior collapse in VAEs leading to over-regularization and poor latent encoding.
method Hierarchical Empirical Bayes approach to probabilistic generative models.
result HEBAE generates higher quality samples with better FID scores.
Simplified Variational Bayes for easier inference.
problem Complex derivation of Variational Bayes.
method 3-step recipe to identify posterior form and directly write updates.
result Easier, faster, shorter derivation of Variational Bayes.
The VAE's reconstruction ability is studied using PAC-Bayes theory.
problem Understanding the performance of VAEs for unseen data.
method PAC-Bayes theory is applied to analyze VAE's reconstruction error.
result Generalization bounds on VAE's reconstruction error are provided.
A new method combines Laplace and Variational Bayes for scalable inference.
problem Complex models and large datasets make exact inference infeasible.
method Low-Rank Variational Bayes Correction (VBC) using Laplace method and Variational Bayes correction in a lower dimension.
result The method ensures scalability in both model complexity and data size.
A practical guide to Variational Bayes methods.
problem Bayesian inference for data analysis practitioners.
method Explains and demonstrates commonly used Variational Bayes methods.
result Quick derivation and implementation of VB algorithms.
This paper presents studies on a deterministic annealing algorithm based on quantum annealing for variational Bayes (QAVB) inference, which can be seen as an extension of the simulated annealing for variational Bayes (SAVB) inference. QAVB is as easy as SAVB to implement. Experiments revealed QAVB finds a better local …
We study a mean-field spike and slab variational Bayes (VB) approximation to Bayesian model selection priors in sparse high-dimensional linear regression. Under compatibility conditions on the design matrix, oracle inequalities are derived for the mean-field VB approximation, implying that it converges to the sparse tr…
VL finds flatter solutions at edge of stability, matching theory with practice.
problem Understanding implicit regularization in deep learning.
method Edge of Stability framework, controlling variational posterior shape and sample number.
result VL finds even flatter solutions than gradient descent.
New clustering algorithm for time series data using RNN and variational Bayes.
problem Lack of generative model-based clustering methods for time series data.
method Recurrent Neural Network (RNN) with variational Bayes method.
result Robustness against phase shift, amplitude, and signal length variations.
Many applications of Bayesian data analysis involve sensitive information, motivating methods which ensure that privacy is protected. We introduce a general privacy-preserving framework for Variational Bayes (VB), a widely used optimization-based Bayesian inference method. Our framework respects differential privacy, t…
A framework uses variational Bayes for solving inverse problems efficiently.
problem Solving inverse problems in various dimensions with flexibility and accuracy.
method Variational Bayes approximations with message passing and factor graph approach.
result Efficient algorithm updates for higher dimensions and computational advantage over MCMC.
Early-stopped aggregation improves computational efficiency in adaptive statistical inference.
problem Computational inefficiency in model selection and aggregation for adaptive inference.
method Early-stopped aggregation (ESA) framework: compute only a few simpler models using early-stopping criteria.
result ESA achieves optimal adaptive contraction rates in variational Bayes and frequentist settings.
Paper proposes a method to estimate total variation distance for synthetic data fidelity.
problem Assessing the fidelity of synthetic data generated by AI.
method Discriminative approach to estimate total variation distance between two distributions.
result Estimation of total variation distance reduces to quantifying Bayes risk in classification.
Parameter estimation for model-based clustering using a finite mixture of normal inverse Gaussian (NIG) distributions is achieved through variational Bayes approximations. Univariate NIG mixtures and multivariate NIG mixtures are considered. The use of variational Bayes approximations here is a substantial departure fr…
Bayesian method learns PDEs from noisy data.
problem Discovering PDEs from noisy data.
method Combining variational Bayes and sparse linear regression.
result Proposes a new method to discover PDEs accurately.
Bayes-CATSI uses variational Bayesian deep learning for medical time series data imputation.
problem Missing values in medical time series data.
method Bayes-CATSI integrates variational inference for uncertainty quantification and context-aware imputation.
result Bayes-CATSI outperforms CATSI by 9.57% in imputation performance.
LTMs use latent vectors for efficient autoregressive generation.
problem Efficient autoregressive generation in language models.
method Dual-rate optimization in variational Bayes framework.
result LTMs achieve superior sample and parameter efficiency.
We introduce Deep Variational Bayes Filters (DVBF), a new method for unsupervised learning and identification of latent Markovian state space models. Leveraging recent advances in Stochastic Gradient Variational Bayes, DVBF can overcome intractable inference distributions via variational inference. Thus, it can handle …
The paper improves Gaussian process regression by optimizing hyperparameters.
problem Hyperparameter tuning for Gaussian process regression models.
method Adaptive sparse variational approximations using variational Bayes.
result Minimax optimal rates of convergence for variational posterior.
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.
Bayesian supertrees method uses variational Bayes for overlapping taxon subsets.
problem Inference of phylogenetic tree topologies for overlapping taxon sets.
method Variational Bayesian approach.
result Demonstrates effectiveness of variational Bayes for Bayesian supertrees.
New estimators outperform maximum likelihood without hyper-parameter estimation.
problem Improving system identification performance without hyper-parameter estimation.
method Developed generalized Bayes and closed-form biased estimators using excess MSE.
result New estimators have comparable performance to empirical-Bayes-based regularized estimator.