FP-BMA improves generalization by encouraging flat posteriors in Bayesian Model Averaging.
problem Lack of flat posterior in approximate Bayesian inference methods hinders effective Bayesian Model Averaging.
method Proposes Flat Posterior-aware Bayesian Model Averaging (FP-BMA) and Flat Posterior-aware Bayesian Transfer Learning schemes.
result FP-BMA successfully captures flat posteriors, improving generalization performance.
New research shows CPE only occurs when Bayesian posterior underfits.
problem Model misspecification leading to CPE under perfect model specification.
method Theoretical analysis of Bayesian posterior and underfitting.
result No CPE if there is no underfitting of the Bayesian posterior.
Differential privacy of Gaussian process posterior sampling
problem Privacy of posterior sample paths from Gaussian process
method Intrinsic randomness yields DP guarantees
result Intrinsic randomness yields DP guarantees
Theoretical framework for M-posteriors connects Bayesian and frequentist statistics.
problem Connecting Bayesian and frequentist approaches in statistical inference.
method Developed a theoretical framework for M-posteriors, showing asymptotic normality and frequentist consistency.
result M-posteriors are robust and contract around M-estimators under mild conditions.
New method improves generative model performance by fully conditioning variational posteriors.
problem Inaccurate inference due to partial conditioning of variational posteriors in sequential LVMs.
method Introduces fully-conditioned approximate posteriors to improve generative model performance.
result Improves generative modelling and multi-step prediction performance.
PVI seeks a posterior that makes predictions closer to true data, not approximating the Bayesian posterior.
problem Finding meaningful posterior distributions under model misspecification.
method Predictive variational inference (PVI) seeks an optimal posterior density for close predictive matching to true data.
result PVI learns a posterior that is not the same as the Bayesian posterior, but is closer to the true data generating process.
Optimized α-posteriors reduce KL divergence from true posterior in parametric misspecification.
problem Reduction of KL divergence from true posterior in parametric model misspecification.
method Derivation of Bernstein-von Mises theorem and optimization of α-posteriors. result Optimized α-posteriors minimize KL divergence from true posterior, especially in severe misspecification. 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.
New priors can update posteriors without re-estimating likelihoods.
problem Degradation of classification approaches when class priors change.
method Recompute posteriors using recovered likelihoods from original posteriors and new priors.
result Dynamic update of original posteriors is possible without re-estimating likelihoods.
Bayesian learning made scalable with posteriors library.
problem Computational challenges in Bayesian learning with modern models.
method Introducing posteriors library and tempered MCMC.
result Bayesian approximations are useful and scalable.
The representation of the approximate posterior is a critical aspect of effective variational autoencoders (VAEs). Poor choices for the approximate posterior have a detrimental impact on the generative performance of VAEs due to the mismatch with the true posterior. We extend the class of posterior models that may be l…
New decision-theoretic characterization separates belief and decision posteriors.
problem Understanding the conditions under which loss-based updating coincides with Bayesian updating.
method Decision-theoretic approach to distinguish belief and decision posteriors.
result Generalized Bayes coincides with ordinary Bayesian updating only if the loss is proportional to negative log-likelihood.
Improved MALA method for neural networks uncertainty quantification.
problem Uncertainty quantification in Bayesian neural networks.
method Corrected Stochastic MALA (csMALA) with a simplified correction term.
result Improved surrogate posterior for quantifying uncertainties in neural networks.
Increasingly complex datasets pose a number of challenges for Bayesian inference. Conventional posterior sampling based on Markov chain Monte Carlo can be too computationally intensive, is serial in nature and mixes poorly between posterior modes. Further, all models are misspecified, which brings into question the val…
New methods for scalable inference in modular models with misspecified sub-models.
problem Model misspecification in multi-modular models complicates evidence combination.
method Variational methods for approximating Cut and SMI posteriors, and Variational Meta-Posterior.
result Feasibility of analysis with multiple cuts using a single set of variational parameters.
New method controls posterior collapse in VAEs without network architecture constraints.
problem Posterior collapse in VAEs reduces diversity of generated samples.
method Introduces Latent Reconstruction (LR) loss to control posterior collapse.
result Controls posterior collapse on various datasets without architectural constraints.
This paper explores Bayesian Neural Network posteriors, uncovering symmetries and their impact.
problem Understanding the complex posterior distribution of deep Bayesian Neural Networks.
method Investigates optimal approaches for approximating posteriors, analyzes modes, and explores visualizations.
result Uncovered weight-space symmetries and their impact on the posterior, particularly scaling symmetries.
TARP tests accuracy of generative posterior estimators.
problem Assessing the accuracy of posterior estimators from generative models.
method TARP coverage testing method.
result TARP can detect inaccurate inferences in high-dimensional spaces.
Bayes posterior yields worse predictions than simpler methods in deep neural networks.
problem Understanding and improving predictive performance in Bayesian deep learning.
method Careful MCMC sampling and evaluation of cold posteriors.
result Cold posteriors yield significantly better predictive performance than the true Bayes posterior.
BF-VI improves posterior approximation in complex models.
problem Inefficient posterior approximations in complex models.
method Combines normalizing flows and Bernstein polynomial transformations.
result BF-VI outperforms other VI methods in approximating complex multivariate posteriors.
We use neural networks to estimate complex model posteriors efficiently.
problem Intractable likelihood functions in complex models.
method Train a neural network to map data to posterior distributions of model parameters.
result Our method converges to true posteriors in Kullback-Leibler divergence.
Bayesian nonparametric models get better posterior estimates via SPDE methods.
problem Estimating posterior distributions in nonparametric Bayesian models.
method Extending diffusion methods to SPDEs on Hilbert spaces for posterior contraction and Laplace approximation.
result Derivation of posterior contraction rates and finite-sample Bernstein von Mises results.
Proposes sampling from reverse diffusion posteriors for contextual bandits.
problem Complex distributions in contextual bandits.
method Approximate posterior sampling with a diffusion model prior using Laplace approximation.
result Empirically consistent and efficient approximations for contextual bandits.
New algorithms for fast online decision making using neural networks and martingale posteriors.
problem Online sequential decision making under uncertainty.
method Martingale posterior neural networks for fast online learning and decision making.
result Achieves competitive performance-speed trade-offs in non-stationary contextual bandits and Bayesian optimization.
New perspective on federated learning as posterior inference, improving optimization.
problem Optimizing global models in distributed learning settings.
method Formulated as posterior inference problem, using MCMC for approximate inference and federated averaging for refinement.
result Federated posterior averaging (FedPA) outperforms existing methods on benchmarks.
Estimates high-dimensional posterior densities by marginal distributions and neural networks.
problem High-dimensional probability density estimation for inference is difficult.
method Direct estimation of lower-dimensional marginal distributions, using Moment Networks for fast computation of moments.
result Demonstrates estimation of gravitational wave time series and applications in cosmology.
MFVI can overestimate predictive variance compared to the exact posterior
problem MFVI underestimates posterior variance
method Analyzing conjugate Bayesian Linear Regression
result MFVI can overestimate predictive variance compared to the exact posterior
Meta-learning improves Bayesian causal discovery by sampling from the posterior.
problem Difficulty in estimating the full posterior over causal structures due to large number of possible graphs and functional relationships.
method Proposes a Bayesian meta-learning model that encodes key properties of the posterior and allows for sampling causal structures.
result Meta-Bayesian causal discovery allows for reliable sampling from the posterior over causal structures.
New method uses fractional posteriors for semiparametric inference with improved uncertainty quantification.
problem Semiparametric inference with nonparametric priors and fractional posteriors.
method Established a general Bernstein--von Mises theorem for fractional posterior distributions, proposed shifted-and-rescaled credible sets.
result Fractional posterior credible sets provide reliable uncertainty quantification but have inflated size; shifted-and-rescaled set is an efficient confidence set.
Study compares chi-squared divergence and KL-divergence posteriors for PAC-Bayesian bounds.
problem Investigates optimal posteriors for PAC-Bayesian bounds using chi-squared divergence.
method Analyzes bounds for three distance functions, derives FP equations for computation.
result Chi-squared divergence based posteriors have weaker bounds and worse test errors.
Variational inference struggles with weight symmetries in neural networks, leading to biased posteriors.
problem Weight space symmetries in neural networks cause multimodal posteriors, challenging variational inference.
method Developed a symmetrization mechanism to create permutation invariant variational posteriors.
result Symmetrized variational posteriors have a better fit to the true posterior and improved predictive performance.
Flow Annealing Posterior Sampling unifies stochastic-process regression and PDE inverse problems.
problem Function-space posterior sampling for stochastic processes and inverse problems.
method Flow Annealing Posterior Sampling (FAPS) using pretrained function-space flow-matching priors.
result Coherent posterior samples with accurate uncertainty quantification.
New method improves sample-efficiency in neural posterior estimation using simulator gradients.
problem High-fidelity posterior estimation with complex physical simulations is time-consuming.
method Neural Posterior Estimation (NPE) with differentiable simulators and gradient information.
result Improves sample-efficiency in posterior density estimation.
Posterior refinement improves sample efficiency in Bayesian neural networks.
problem Bayesian neural networks suffer from poor predictive performance due to inaccurate posterior approximations.
method Propose refining Gaussian approximate posteriors with normalizing flows to improve predictive distributions.
result Posterior refinement yields competitive predictive performance with minimal computational overhead.
Advocates for a new posterior that predicts better than classical and generalised Bayes.
problem Combining parameter inference and density estimation for better predictive models.
method Predictively Oriented (PrO) posterior using mean field Langevin dynamics.
result PrO posteriors converge to the predictively optimal model average, adapting to model misspecification.
Implied posterior probability of a given model (say, Support Vector Machines (SVM)) at a point x is an estimate of the class posterior probability pertaining to the class of functions of the model applied to a given dataset. It can be regarded as a score (or estimate) for the true posterior probability, which ca…
New methods for tuning alpha in Gibbs posteriors improve speed and accuracy.
problem Inconsistency in Bayesian inference and lack of fast tuning methods for alpha.
method Proposed two data-driven methods: sample-splitting and bootstrapping. Formulated alpha-posteriors for three models.
result Sample-splitting outperforms SafeBayes in speed and accuracy, especially in complex models.
Bayesian inference for Levy density with Gibbs posterior in discrete sampling.
problem Inference on Levy density for financial models with jumps.
method Gibbs posterior framework using a loss function for intractable likelihood.
result Gibbs posterior achieves nearly optimal rate of convergence under certain conditions.
Sampling from posterior distributions using Markov chain Monte Carlo (MCMC) methods can require an exhaustive number of iterations, particularly when the posterior is multi-modal as the MCMC sampler can become trapped in a local mode for a large number of iterations. In this paper, we introduce the pseudo-extended MCMC…
We consider the problem of sequential learning from categorical observations bounded in [0,1]. We establish an ordering between the Dirichlet posterior over categorical outcomes and a Gaussian posterior under observations with N(0,1) noise. We establish that, conditioned upon identical data with at least two observatio…
This work extends balancing to various simulation-based inference algorithms for more conservative posterior approximations.
problem Overconfident posterior approximations in simulation-based inference.
method Introduces a balanced version of neural posterior estimation and contrastive neural ratio estimation.
result Balanced versions tend to produce conservative posterior approximations on various benchmarks.
A common problem in disciplines of applied Statistics research such as Astrostatistics is of estimating the posterior distribution of relevant parameters. Typically, the likelihoods for such models are computed via expensive experiments such as cosmological simulations of the universe. An urgent challenge in these rese…
A novel diffusion method for Bayesian posterior sampling with theoretical guarantees.
problem Efficiently sampling from complex posterior distributions in Bayesian inversion.
method Diffusion-based posterior sampling using Langevin dynamics and PnP framework.
result The method converges even for multi-modal posterior distributions with theoretical error bounds.
The paper simplifies Bayesian posterior using clustering to make inference more manageable.
problem Handling large-scale, redundant datasets in Bayesian learning.
method Construct an approximate posterior by replacing data points in the same cluster with the centroid.
result The approximate posterior is close to the exact posterior and easier to sample from.
A new method for sampling complex posterior distributions in DDMs.
problem Challenging posterior distributions in DDMs.
method Divide-and-Conquer Posterior Sampling (DCPS)
result Significantly reduces approximation error without retraining.
Bayesian neural networks approximate Gaussian, this method adapts to non-Gaussian posteriors.
problem Bayesian neural networks struggle with non-Gaussian posteriors, leading to poor performance.
method Proposes a Riemannian Laplace approximation to adapt to the shape of the true posterior.
result Consistently improves over conventional Laplace approximation across tasks.
New method samples from posterior distributions efficiently.
problem Posterior sampling in score-based models is intractable.
method Annealed Langevin Monte Carlo with KL and Fisher divergence.
result Tractable sampling from distributions close to posterior and prior.
SwISS improves scalability of Bayesian inference for large datasets.
problem Scalability issues in Bayesian inference for large datasets.
method Divide-and-conquer approach with SwISS for recombining sub-posterior samples.
result SwISS accurately approximates the original posterior distribution.