Review of priors in Bayesian deep learning models.
problem The importance of prior choices in Bayesian deep learning models.
method Overview of different priors and methods of learning priors from data.
result Motivate practitioners to think carefully about prior specification.
Researchers derive exact priors for finite Bayesian neural networks.
problem Understanding non-Gaussian priors in finite Bayesian neural networks.
method Analytical derivation of function space priors for finite fully-connected feedforward networks.
result Exact solutions for priors of finite networks, including Meijer G-function for linear networks and mixtures for ReLU networks.
Unified framework for Bayesian PDE-constrained inversion using physics-informed neural networks.
problem Incorporating prior distributions in function space into Bayesian PINN-based inversion.
method Functional-prior-based approaches (fpBPINN) to Bayesian PDE-constrained inversion using physics-informed neural networks (PINNs). Two complementary approaches: FPI-BPINN and fParVI-PINN.
result Accurate estimation of posterior distributions in seismic traveltime tomography and Darcy-flow permeability inversion.
BNNpriors library improves Bayesian neural network inference with various prior distributions.
problem Challenges in choosing good prior distributions for Bayesian neural networks.
method State-of-the-art Markov Chain Monte Carlo inference with a wide range of predefined priors.
result Facilitates foundational discoveries on the nature of the cold posterior effect.
Bayesian method corrects for model selection multiplicity in regression.
problem Model selection multiplicity in regression analysis.
method Developed a Bayesian prior distribution based on Holm procedure analogy.
result Adequate multiplicity correction requires sparsity not provided by recommended priors.
This work tackles the challenge of Bayesian deep learning by proposing a new framework for matching Gaussian process priors with neural network parameters.
problem The challenge of specifying priors over neural network parameters, which affects the induced functional prior and is uncontrolled.
method The approach involves defining functional priors using Gaussian processes and matching these priors with the functional prior of neural networks through the minimization of Wasserstein distance.
result The proposed framework offers systematic performance improvements over alternative priors and approximate Bayesian deep learning approaches.
Bayesian priors and penalties are equivalent in variational inference.
problem Understanding the relationship between Bayesian priors and penalties in variational inference.
method Characterizing the regularizers that can arise in variational inference and providing a systematic way to compute the prior corresponding to a given penalty.
result Equivalence between Bayesian priors and penalties in variational inference.
Bayesian priors offer a compact yet general means of incorporating domain knowledge into many learning tasks. The correctness of the Bayesian analysis and inference, however, largely depends on accuracy and correctness of these priors. PAC-Bayesian methods overcome this problem by providing bounds that hold regardless …
New method learns priors for Bayesian neural networks from datasets.
problem Lack of prior beliefs in Bayesian deep learning.
method Amortised variational inference to learn priors from datasets.
result Flexible Bayesian neural networks for meta-learning and within-task minibatching.
Paper introduces Bayesian EEF for model order selection using exponentially embedded family.
problem Model order selection in Bayesian statistics.
method Bayesian EEF method using exponentially embedded family.
result Bayesian EEF can use vague priors and reveals EEF mechanism for model selection.
New Bayesian method for sparse signal recovery using normal product priors.
problem Sparse signal recovery in compressive sensing.
method Developed a two-stage normal product-based hierarchical model using variational Bayesian inference.
result Demonstrated effectiveness through simulations compared to state-of-the-art algorithms.
Proposes MOPED method for choosing priors in Bayesian DNNs.
problem Challenges in specifying meaningful priors for deep neural networks.
method Two-stage hierarchical modeling with empirical Bayes.
result MOPED enables scalable variational inference and reliable uncertainty quantification.
Bayesian neural network achieves nearly optimal performance in Besov space.
problem Bayesian neural networks in Besov space.
method Spike-and-slab prior and shrinkage prior for posterior convergence rate.
result The posterior convergence rate is nearly minimax and adaptive to unknown smoothness.
Study proposes learning optimal priors from data for better Bayesian inference.
problem Challenges the use of noninformative uniform priors in Bayesian inference.
method Machine learning approach to learn optimal priors from data using a target function.
result Study models consistently outperformed baseline models in Wikipedia category classification.
A new Weyl prior is proposed for Bayesian statistics, offering a more canonical choice for parameter α.
problem Choosing a prior distribution for Bayesian inference.
method Proposed a new Weyl prior based on the Weyl structure on a statistical manifold.
result The Weyl prior is a special case of the α-parallel prior with α = -n, where n is the dimension of the statistical manifold.
Bayesian algorithms perform well even with misspecified priors, especially in meta-learning.
problem Performance degradation of Bayesian algorithms with misspecified priors.
method Thompson sampling and meta-learning analysis with misspecified priors.
result Thompson sampling's performance degrades gracefully with misspecification, with a bound of ildeO(H2ε). This work explores how overparametrization and priors affect Bayesian neural network posteriors.
problem Symmetries, non-identifiabilities, and weight-space priors fragment and inflate BNN posteriors.
method We study the interplay between overparametrization and priors in BNN posteriors, deriving key phenomena and validating through experiments.
result Overparametrization induces structured, prior-aligned weight posterior distributions.
Bayesian model learns bias for related tasks.
problem Learning appropriate bias for related machine learning tasks.
method Bayesian inference using objective prior distribution.
result Learning true prior distribution by sampling from objective prior.
The study examines how prior and likelihood choices affect Bayesian matrix factorisation on small datasets.
problem Improving predictive performance of Bayesian matrix factorisation on small datasets.
method Review and comparison of 16 Bayesian matrix factorisation models across four groups: Gaussian-likelihood with real-valued priors, nonnegative priors, semi-nonnegative models, and Poisson-likelihood approaches.
result Poisson models give poor predictions, and nonnegative models are more constrained than real-valued ones.
Bayesian neural networks use ridgelet prior for uncertainty quantification.
problem Combining strong predictive performance with uncertainty quantification in Bayesian neural networks.
method Proposes a ridgelet prior that approximates a Gaussian process covariance function in the output space of the network.
result Establishes universality property allowing Bayesian neural networks to approximate any Gaussian process.
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.
Bayesian priors for neural networks are improved by incorporating weight correlations and tail behavior.
problem Improving Bayesian priors for neural networks to better reflect true beliefs and performance.
method Analyzed summary statistics of neural network weights in different architectures and incorporated these observations into new priors.
result Improved performance on image classification datasets by using new priors that account for weight correlations and tail behavior.
The paper extends and applies a new shrinkage prior in Bayesian factor analysis.
problem Estimating the number of factors in sparse Bayesian factor analysis.
method Introduces and extends a generalized cumulative shrinkage process (CUSP) prior.
result Exchangeable spike-and-slab shrinkage priors imply increasing shrinkage as the column index increases.
Develops methods for constructing likelihoods and priors for Bayesian networks.
problem Learning parameters and structure of Bayesian networks from limited data.
method Introduces assumptions for constructing likelihoods and priors from small assessments.
result Allows construction of likelihoods and priors for a wide range of network structures.
We study deep Bayesian neural networks with Gaussian priors, revealing heavy-tailed unit activations.
problem Characterizing regularization effects in deep Bayesian neural networks.
method Investigation of deep Bayesian neural networks with Gaussian weight priors and ReLU-like nonlinearities.
result The prior distribution on units becomes increasingly heavy-tailed with depth, influencing activation patterns.
New method samples Jeffreys prior for objective Bayesian inference.
problem Sampling from Jeffreys prior is challenging.
method Metropolis-Adjusted Langevin Algorithm
result Samples can be directly used in Bayesian methods.
The paper improves Bayesian optimization by estimating unknown Gaussian process parameters.
problem The challenge of unknown parameters in Bayesian optimization.
method Adopting empirical Bayes to estimate Gaussian process prior and constructing unbiased estimators.
result Achieves near-zero regret bound, decreasing to a constant proportional to observational noise.
Study shows prior Lipschitz continuity can improve adversarial robustness of Bayesian Neural Networks.
problem Improving adversarial robustness of Bayesian Neural Networks.
method Analysis of i.i.d., zero-mean Gaussian priors and posteriors approximated via mean-field variational inference.
result Adversarial robustness is sensitive to the prior variance.
The study assesses sensitivity to prior choices in Bayesian nonparametric models.
problem Difficulty in specifying priors for Bayesian nonparametric models.
method Utilizes variational Bayesian methods to assess sensitivity to concentration parameter and stick-breaking distribution.
result Demonstrates how to evaluate sensitivity to prior choices in Dirichlet process mixtures and related models.
New method simplifies Bayesian inference for multi-Dirichlet priors.
problem Inference for models with hierarchical Multi-Dirichlet priors is tricky.
method Auxiliary variable scheme simplifies joint distribution of model parameters.
result Efficient inference schemes derived using the auxiliary variable scheme.
New method improves BLL models for complex datasets.
problem Limited expressive capacity of Gaussian priors in BLL models.
method Combines diffusion techniques and implicit priors for variational learning.
result Enhanced predictive accuracy and uncertainty quantification.
A new method learns priors for Bayesian optimisation to improve performance.
problem Bayesian optimisation tasks often assume strong similarity, which is violated in many cases.
method Replace strong similarity assumption with shape similarity, learn priors for hyperparameters.
result PLeBO and prior transfer find good inputs in fewer evaluations.
Unified approach to continual learning using Bayesian methods.
problem Challenges in evaluating posterior approximations for continual learning.
method Introduces a new approximate Bayesian derivation of the continual learning loss, adapting the model itself by changing the likelihood term.
result Combines prior- and likelihood-focused methods into one objective, achieving better performance.
Bayesian inverse problems solved with Gaussian models for PDEs.
problem Solving inverse problems with limited data for PDEs.
method Constructing PDE-informed Gaussian priors for Bayesian inversion.
result PDE-informed Gaussian priors outperform traditional priors.
Study compares priors for ABNs to improve model accuracy.
problem Inadequate priors lead to model selection issues in ABNs.
method Simulation study with three priors: Gaussian, Student's t, and strongly informative Gaussian.
result Informative Student's t-prior performs best, mitigating Lindley's paradox.
Bayesian framework inserts prior knowledge in RL for faster task solving.
problem Faster transfer learning across reinforcement learning tasks.
method Bayesian posterior distribution combining task-specific and prior knowledge.
result Significant speed ups achieved in maze solving.
Paper proposes MU+BDs score for Bayesian network structure learning.
problem Small sample sizes and sparse data cause issues with BDeu score.
method Proposes MU+BDs score with marginal uniform graph prior.
result MU+BDs score is more accurate and competitive than U+BDeu.
Bayesian method uses deep learning prior for CT reconstruction.
problem Imaging inverse problems in CT reconstruction.
method SA-Roundtrip prior with HMC-pCN sampler.
result Outperforms state-of-the-art methods in CT reconstruction.
New Gaussian priors for neural networks improve scalability and Bayesian inference stability.
problem Scalability and stability issues in Bayesian neural network inference.
method Introduces a new Gaussian neural network prior with decreasing variance in network width, enabling stable MCMC sampling.
result The new prior enables stable MCMC sampling for Bayesian neural network inference, improving scalability and stability.
The study analyzes when Bayesian averaging over decision trees is reliable.
problem When do Bayesian model averaging weights over decision trees provide reliable information?
method Closed-form solution for Bayesian decision trees with Catalan-exponential priors.
result Established a complete non-asymptotic theory of rational commitment thresholds.
Stabilizes deep Bayesian neural networks with self-stabilizing priors.
problem Brittleness and difficulty in training deep Bayesian neural networks.
method Signal propagation theory, reformulated ELBO, self-stabilizing priors.
result Improved convergence and robustness in training deeper networks and noisier settings.
Extends Gaussian Process regression for handling multiple prior distributions.
problem Handling multiple prior distributions in Bayesian Machine Learning models.
method Mixtures of Gaussian Processes with analytical and Sparse Variational approaches.
result Effective in accounting for prior misspecification in functional regression problems.
Bayesian methods for machine learning have been widely investigated, yielding principled methods for incorporating prior information into inference algorithms. In this survey, we provide an in-depth review of the role of Bayesian methods for the reinforcement learning (RL) paradigm. The major incentives for incorporati…
Bayesian method predicts labels on graph data.
problem Binary classification on graph data.
method Hierarchical Bayesian approach with graph Laplacian prior.
result The method improves prediction accuracy on graph data.
New method reduces over-pessimism in Bayesian control under parameter uncertainty.
problem Over-pessimism in Bayesian control due to misspecified priors.
method Distributionally robust Bayesian control (DRBC) with strong duality and optimization.
result Validated algorithm on synthetic and real data, reducing over-pessimism.
Optimizes Bayesian priors for matrix factorization without posterior inference.
problem Selecting optimal priors for Bayesian models in machine learning.
method Prior predictive distribution and virtual statistics matching user-provided or observed data statistics.
result Analytically determines hyperparameters for Poisson factorization models.
Thompson sampling used for linear bandits with normal-gamma priors.
problem Optimizing decisions in uncertain environments with linear dependencies and unknown parameters.
method Bayesian Thompson sampling with multivariate normal-gamma priors.
result Derivation of a Bayesian regret bound for the approach.
Framework incorporates prior knowledge into Bayesian models for data streams.
problem Effective use of prior knowledge in learning Bayesian models from streaming data.
method Proposes a novel framework that subsumes existing models for time-series data.
result Framework outperforms existing methods with a large margin.