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.
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
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.
Variational Prediction simplifies Bayesian inference without test time costs.
problem Bayesian inference's computational costs and posterior predictive distribution marginalization.
method Variational Prediction learns a variational approximation to the posterior predictive distribution using a variational bound.
result Directly learns a variational approximation to the posterior predictive distribution without test time marginalization costs.
VPR improves posterior uncertainty quantification by combining VI and predictive resampling.
problem Inaccurate posterior sampling with MCMC due to computational constraints.
method Variational predictive resampling (VPR) that uses VI's predictive strength and imputes future observations.
result VPR converges to the exact Bayesian posterior in a Gaussian location model and improves uncertainty quantification.
A new method learns posterior and predictive distributions together, reducing computational cost.
problem Sequential two-stage Bayesian inference is computationally expensive.
method Amortized variational inference targeting posterior-predictive distribution.
result Efficient online inference with more accurate predictive distributions.
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.
We quantify predictive uncertainty using the posterior predictive variance.
problem Quantifying uncertainty in predictive models.
method Using the law of total variance, we generate expansions for the posterior predictive variance.
result Identify the main contributors to prediction intervals and quantify term-wise uncertainty.
Recent decades have seen an interest in prediction problems for which Bayesian methodology has been used ubiquitously. Sampling from or approximating the posterior predictive distribution in a Bayesian model allows one to make inferential statements about potentially observable random quantities given observed data. Th…
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.
Paper uses averaging from many particle filters to approximate posterior predictive distributions.
problem Approximating posterior predictive distributions efficiently and accurately.
method Particle swarm filter algorithm that averages many particle filter approximations.
result Law of large numbers and central limit theorem support the method's effectiveness.
Bayesian neural networks reveal multimodal predictive distributions.
problem Uncertainty quantification and interpretability in neural networks.
method Discretized prior for inner layer weights, Gaussian mixture approximation of posterior predictive distribution.
result Distinct parameter realizations can produce the same training error but different posterior predictive distributions.
New criterion improves predictive evaluation in weighted inference scenarios.
problem Improving predictive evaluation in scenarios with different likelihoods for estimation and evaluation.
method Developed the posterior covariance information criterion (PCIC) to handle weighted likelihood inference.
result PCIC is asymptotically unbiased for quasi-Bayesian generalization error in weighted inference.
Bayesian Invariant Prediction models stable features from multi-environment data.
problem Analyzing stable features across multiple environments for better prediction and understanding.
method Developed Bayesian Invariant Prediction (BIP) model that encodes invariant feature indices as latent variables and infers them via posterior inference.
result BIP and its variational approximation (VI-BIP) outperform existing methods in accuracy and scalability for invariant prediction.
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.
Markov chain Monte Carlo (MCMC) methods have not been broadly adopted in Bayesian neural networks (BNNs). This paper initially reviews the main challenges in sampling from the parameter posterior of a neural network via MCMC. Such challenges culminate to lack of convergence to the parameter posterior. Nevertheless, thi…
Transformers can approximate posterior predictive distributions through in-context learning.
problem Bayesian prediction tasks, especially beyond point predictions.
method Gradient descent algorithm targeting posterior predictive mean and variance, followed by nonlinear mappings.
result Transformers can implement algorithms to approximate posterior predictive distributions.
One-round FL method improves robustness and reduces communication rounds.
problem Making predictions robust and reducing FL communication rounds in heterogeneous data.
method Bayesian predictive space aggregation of client posteriors in one round.
result One-round FL method outperforms other techniques on heterogeneous settings.
Bayesian models quantify uncertainty and facilitate optimal decision-making in downstream applications. For most models, however, practitioners are forced to use approximate inference techniques that lead to sub-optimal decisions due to incorrect posterior predictive distributions. We present a novel approach that corr…
Graph Posterior Network improves uncertainty estimation for node classification in interdependent graphs.
problem Uncertainty quantification for non-independent node-level predictions in graphs.
method Derives axioms for expected predictive uncertainty, proposes Graph Posterior Network (GPN) which performs Bayesian posterior updates.
result GPN outperforms existing approaches for uncertainty estimation in semi-supervised node classification.
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.
During the past five years the Bayesian deep learning community has developed increasingly accurate and efficient approximate inference procedures that allow for Bayesian inference in deep neural networks. However, despite this algorithmic progress and the promise of improved uncertainty quantification and sample effic…
Improved Bayesian FL method calibrates predictions for federated learning.
problem Overconfident predictions in Bayesian FL methods for federated learning.
method β-Predictive Bayes algorithm interpolates between mixture and product of local predictive posteriors, tuning parameter β for better calibration.
result Demonstrated superior calibration compared to other baselines, even with increased data heterogeneity.
Probabilistic modeling is cyclical: we specify a model, infer its posterior, and evaluate its performance. Evaluation drives the cycle, as we revise our model based on how it performs. This requires a metric. Traditionally, predictive accuracy prevails. Yet, predictive accuracy does not tell the whole story. We propose…
New method for density estimation without approximating posterior distributions.
problem Challenges in non-smooth data distributions for Bayesian density estimation.
method Autoregressive likelihood decomposition and Gaussian process prior in a quasi-Bayesian framework.
result Achieves state-of-the-art results in small-data regimes.
Improved predictive posterior density estimation through optimized importance sampling.
problem Low signal-to-noise ratio in posterior predictive densities.
method Optimized importance sampling using a test-time variational proxy.
result Significantly improved estimates of predictive posterior densities.
PosCal training improves classification models by calibrating posterior probabilities.
problem Poorly calibrated posterior probabilities in classification models.
method End-to-end training procedure that directly optimizes the objective while minimizing the difference between predicted and empirical posterior probabilities.
result PosCal training achieves about 2.5% task performance gain and 16.1% calibration error reduction.
Preconditioned neural posterior estimation improves reliability in misspecified models.
problem Reliability issues in neural posterior estimation for misspecified models.
method Preconditioning with data-dependent weights and forest-proximity scores to stabilize and improve accuracy.
result Preconditioned robust neural posterior estimation increases stability and accuracy over standard methods.
Bayesian neural networks use temperature adjustments to improve predictive performance.
problem Lack of theoretical generalization guarantees for Bayesian neural networks.
method Temperature adjustments to balance likelihood and prior regularization.
result Improved predictive performance through temperature adjustments.
Conformal Bayes under label shift: post-hoc calibration vs. in-training adaptation
problem Bayesian prediction sets under label shift
method Post-hoc calibration vs. In-training adaptation
result Both strategies achieve valid coverage equally in an unbiased training regime
This work introduces a method for visualizing high-dimensional posteriors using hierarchical tree-valued predictions.
problem Visualizing high-dimensional posterior distributions for complex problems like image restoration.
method A neural network predicts a tree-valued hierarchical summarization of the posterior distribution in a single forward pass.
result The method efficiently summarizes and visualizes posteriors, achieving comparable results to hierarchical clustering but at a much faster speed.
A new method selects optimal temperature for Bayesian Deep Learning.
problem Finding the optimal temperature for improving predictive performance in Bayesian Deep Learning.
method Data-driven approach to estimate temperature as a model parameter.
result Our method performs comparably to grid search but at a fraction of the cost.
MC Dropout is re-evaluated as not Bayesian, affecting predictive posterior and multimodality.
problem MC Dropout's Bayesian properties and predictive posterior are questioned.
method Re-evaluation of MC Dropout's properties, including a new VI engine in pytorch.
result MC Dropout does not produce a faithful Bayesian predictive posterior.
Bayesian inference improves neural network predictions by separating aleatoric and epistemic uncertainties.
problem Improving prediction accuracy of neural networks by quantifying and separating uncertainties.
method Approximated posterior distributions using deep ensembles for various neural network architectures.
result Prediction accuracy depends on both aleatoric and epistemic uncertainties, not just marginalized uncertainty.
Enhances predictive performance in Bayesian deep learning via generalized Laplace approximation.
problem Inconsistency in Bayesian deep learning.
method Interprets posterior tempering as a correction for model misspecification and recalibration of priors. Introduces generalized Laplace approximation.
result Generalized Laplace approximation enhances predictive performance.
Online distributional prediction with latent cluster geometry
problem Predicting the full data-generating distribution in non-stationary streams
method Representing candidate laws as latent cluster geometry and using Gibbs quasi-posterior
result Achieving sublinear cumulative Wasserstein regret under bounded support and stable latent geometry
FastMuyGPs speeds up GP predictions for large datasets.
problem High cost of Gaussian process predictions for large data.
method Combines cross-validation, batching, nearest neighbors sparsification, and precomputation.
result Superior accuracy and competitive runtime compared to other methods.
The paper solves the problem of optimal portfolio choice when the parameters of the asset returns distribution, like the mean vector and the covariance matrix are unknown and have to be estimated by using historical data of the asset returns. The new approach employs the Bayesian posterior predictive distribution which…
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.
Two approaches improve conformal Bayes for label shift, one post-hoc and one in-training.
problem Improving prediction sets for target domain under label shift.
method Two complementary approaches: post-hoc calibration and in-training adaptation.
result In-training adaptation achieves up to 43% width reduction at unchanged coverage.
Study improves posterior inference in neural processes with limited data.
problem Improving posterior predictive inference in probabilistic models with scarce conditioning data.
method Examined effects of pooling operators and variational families on posterior quality in neural processes.
result Novel neural process architectures lead to superior posterior predictive samples in image completion/in-painting tasks.
Proposes a new method to approximate Bayesian predictive uncertainty.
problem Bayesian uncertainty quantification in model predictions.
method Self-supervised learning approach to approximate posterior predictive distribution.
result SSLA and ASSLA outperform classical Laplace approximations in predictive calibration.
Bayesian Dark Knowledge is a method for compressing the posterior predictive distribution of a neural network model into a more compact form. Specifically, the method attempts to compress a Monte Carlo approximation to the parameter posterior into a single network representing the posterior predictive distribution. Fur…
CNR uses convex optimization to estimate conditional distributions.
problem Estimating uncertainty in predictions and posterior conditional distributions.
method Convex optimization of a posterior defined via non-linear transformations on Gaussians.
result CNR can fit arbitrary conditional distributions, including multimodal and non-symmetric ones.
PPT optimizes transformer behavior by steering its latent posterior using prior samples.
problem Eliciting desired behavior from transformers without backpropagation.
method Posterior Prefix Tuning (PPT) uses predictive Monte Carlo (PMC) samples and importance sampling to optimize the latent posterior.
result PPT optimizes transformer behavior without backpropagation, achieving high utility across different utility functions.
Proposes a new method for conformal prediction under covariate shift with posterior drift.
problem Improving classification performance in target domains with limited training data.
method Weighted conformal classifier that leverages source and target samples.
result Demonstrates favorable asymptotic properties and practical utility.
Bayesian deep ensembles improve prediction accuracy in various settings.
problem Improving prediction accuracy of deep ensembles in out-of-distribution settings.
method Introducing a randomised, untrainable function to each ensemble member, enabling a posterior predictive distribution interpretation.
result Bayesian deep ensembles make more conservative predictions and outperform standard ensembles in various tasks.
Brain uses synaptic failure to sample from posterior distributions.
problem Bayesian inference in the brain's probabilistic computations.
method Adapting synaptic failure to sample posterior predictive distributions.
result Synaptic failure enables sampling of complete posterior predictive distributions.