The paper corrects Bayesian neural network approximations to improve decision quality.
problem Inaccurate posterior approximations in Bayesian neural networks lead to suboptimal decisions.
method Develops methods to calibrate approximate posterior predictive distributions for better decision making.
result Empirically produces higher quality decisions compared to previous methods.
Bayesian Neural Networks (BNNs) place priors over the parameters in a neural network. Inference in BNNs, however, is difficult; all inference methods for BNNs are approximate. In this work, we empirically compare the quality of predictive uncertainty estimates for 10 common inference methods on both regression and clas…
This paper argues against using calibration metrics for assessing posterior probabilities and proposes expected proper scoring rules instead.
problem The assessment of posterior probabilities generated by machine learning classifiers using calibration metrics is flawed and should be replaced with expected proper scoring rules.
method The paper reviews proper scoring rules from a practical perspective, explains why expected PSRs are a principled measure of posterior quality, and introduces a new calibration metric called calibration loss.
result Calibration loss is superior to expected calibration error and expected score divergence calibration metrics for assessing posterior probabilities.
RePS improves diffusion models for solving inverse problems efficiently.
problem Solving inverse problems with incomplete or noisy measurements.
method Restart for Posterior Sampling (RePS) using pre-trained diffusion models.
result RePS achieves faster convergence and superior reconstruction quality.
One of the core problems in statistical models is the estimation of a posterior distribution. For topic models, the problem of posterior inference for individual texts is particularly important, especially when dealing with data streams, but is often intractable in the worst case. As a consequence, existing methods for…
This work improves bounds on Bayesian coreset quality.
problem Limitations of existing theoretical analysis of Bayesian coresets.
method Develops general upper and lower bounds on KL divergence.
result Demonstrates flexibility of new theoretical bounds in various models.
Generative model improves sample quality on ImageNet32.
problem Improving sample quality in generative models.
method Iterative Gaussian posterior inference, treating generated sample as unknown variable.
result Improves sample quality on ImageNet32 over BFNs and VDMs.
A new method for generating synthetic data using posterior distribution learning accelerates inference.
problem Generating high-quality synthetic data requires many discretization steps, which is computationally expensive.
method Learning the posterior distribution of clean data samples given noisy versions, using a scoring rule instead of regression loss.
result Consistently outperforms standard diffusion models at few discretization steps.
This work explores function-space inference using KL divergence and proposes Bayesian linear regression as a benchmark.
problem Approximating the predictive posterior distribution of Bayesian models without parameter posterior approximation.
method Employing Kullback-Leibler divergence and proposing featurized Bayesian linear regression as a benchmark.
result Minimizing KL divergence leads to an ill-defined objective function, highlighting limitations of this approach.
Bayesian inference using stochastic neural networks ensembles.
problem Approximating Bayesian posterior distributions.
method Formulate stochastic ensembles of neural networks, train with variational inference, and evaluate using Monte Carlo dropout.
result Stochastic ensembles provide more accurate posterior estimates than other methods.
Variational Auto-encoders (VAEs) have been very successful as methods for forming compressed latent representations of complex, often high-dimensional, data. In this paper, we derive an alternative variational lower bound from the one common in VAEs, which aims to minimize aggregate information loss. Using our lower bo…
TM-VI uses flexible transformation models to approximate complex posteriors in Bayesian models.
problem Approximating complex posteriors in Bayesian models with limited flexibility.
method Transformation models for variational inference (TM-VI).
result TM-VI allows accurate approximation of complex posteriors in models with one parameter and works in a mean-field fashion for multi-parameter models.
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.
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.
TGD improves conditional sampling by concentrating computation on promising trajectories.
problem Efficiently training-free conditional sampling with diffusion priors.
method Tempered Guided Diffusion (TGD) using annealed sequential Monte Carlo.
result TGD yields a consistent particle approximation to the posterior as the number of particles grows.
Statistical inference of analytically non-tractable posteriors is a difficult problem because of marginalization of correlated variables and stochastic methods such as MCMC and VI are commonly used. We argue that stochastic KL divergence minimization used by MCMC and VI is noisy, and we propose instead EL_2O, expectati…
Efficiently estimates marginal posteriors for complex simulations.
problem Bayesian inference in high-dimensional, intractable likelihood scenarios.
method Simulates and estimates low-dimensional marginal posteriors, using truncated indicators.
result Simulator efficiency and robustness testing of inference results.
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.
The paper studies conditions for exact posterior modeling in Bayesian networks.
problem Exact modeling of posterior distributions in Bayesian networks.
method Derives conditions for a recognition network to model the true posterior distribution exactly.
result Perfectness of the recognition network is crucial for local conditions to hold.
The choice of approximate posterior distribution is one of the core problems in variational inference. Most applications of variational inference employ simple families of posterior approximations in order to allow for efficient inference, focusing on mean-field or other simple structured approximations. This restricti…
Adaptive workflow combines fast amortized inference with MCMC for many datasets.
problem Trade-off between computational speed and sampling accuracy in Bayesian inference.
method Adaptive workflow integrating amortized inference and MCMC with principled diagnostics.
result Efficiency gains with high posterior quality on tens of thousands of datasets.
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.
A new Fusion method combines multiple distributions efficiently.
problem Combining multiple distributions for big data or privacy.
method Recursive divide-and-conquer Monte Carlo approach.
result A robust Fusion method for many sub-posteriors.
Diffusion models tackle noisy inverse problems with posterior sampling.
problem Efficiently solving general noisy inverse problems.
method Approximation of posterior sampling for diffusion models.
result Diffusion models can handle various noise statistics and nonlinear problems.
High-dimensional VAEs inevitably collapse to prior, requiring large datasets for good performance.
problem Posterior collapse in VAEs leads to poor representation learning quality.
method Analyzed a minimal VAE in a high-dimensional limit, evaluating conditions for posterior collapse with respect to beta and dataset size.
result VAEs face 'inevitable posterior collapse' beyond a certain beta threshold, regardless of dataset size.
Improved VAEs learn consistent posterior distributions from missing data.
problem Learning VAEs from data with missing values, especially in the encoder.
method Formal definition of posterior consistency and regularization approach.
result Regularization leads to improved performance in reconstruction and downstream tasks.
Cold posteriors improve Bayesian neural networks by reducing overestimation of aleatoric uncertainty.
problem Overestimation of aleatoric uncertainty in Bayesian neural networks.
method Tuning the temperature of the posterior on a validation set.
result Reducing temperature leads to better reflection of true prior beliefs.
QEM uses parallel importance weighting for fast approximate Bayesian inference.
problem Bayesian inference challenges in large models with many observations and latent variables.
method Expectation Maximization (EM) with massively parallel importance weighting.
result QEM is faster and more scalable than RWS and VI.
TRUST improves structure learning with tractable uncertainty.
problem Capturing uncertainty in structure learning for causal DAGs.
method Probabilistic circuits for posterior inference.
result Probabilistic circuits enhance structure learning quality and uncertainty.
Gradient-guided nested sampling improves posterior inference efficiency.
problem Efficiently sampling from complex posterior distributions.
method Gradient-guided nested sampling combining differentiable programming, Hamiltonian slice sampling, clustering, mode separation, dynamic nested sampling, and parallelization.
result Significantly faster mode discovery and more accurate partition function estimates.
The automation of posterior inference in Bayesian data analysis has enabled experts and nonexperts alike to use more sophisticated models, engage in faster exploratory modeling and analysis, and ensure experimental reproducibility. However, standard automated posterior inference algorithms are not tractable at the scal…
This work tackles posterior collapse in conditional and hierarchical VAEs.
problem Posterior collapse in VAEs leads to poor latent variable representations.
method Theoretical analysis of linear conditional and hierarchical VAEs, empirical validation.
result Theoretical and empirical evidence of posterior collapse causes in conditional and hierarchical VAEs.
New method simplifies Bayesian analysis for categorical data.
problem Difficulties in scaling GLMs for categorical data due to non-conjugacy or posterior dependencies.
method Defining CB models with binary approximations for tractable inference.
result Fast and scalable inference for thousands of categories, outperforming competitors.
Gaussian processes (GPs) offer a flexible class of priors for nonparametric Bayesian regression, but popular GP posterior inference methods are typically prohibitively slow or lack desirable finite-data guarantees on quality. We develop an approach to scalable approximate GP regression with finite-data guarantees on th…
Paper introduces STSL, a second-order Tweedie sampler for efficient posterior sampling in inverse problems.
problem Computational challenges in sampling from posterior distributions using latent diffusion models.
method Introduces STSL, a novel second-order Tweedie sampler with tractable reverse process.
result STSL achieves 4X and 8X reduction in neural function evaluations compared to state-of-the-art solvers.
Proposes a method to sample from flat basins of posterior distributions in Bayesian deep learning.
problem Sampling from multi-modal posterior distributions leads to overfitting due to trapping in bad modes.
method Introduces an auxiliary guiding variable to bias MCMC sampling towards flat basins of the energy landscape.
result The method converges faster and outperforms existing methods in sampling from flat basins of the posterior.
Geometric framework analyzes bias in variational inference for posterior functionals.
problem Analyzing the bias of posterior functionals under variational approximations.
method Developed a geometric framework to evaluate the bias of posterior functionals using the variational tangent space.
result The leading-order bias of a posterior functional is determined by its component orthogonal to the variational tangent space.
A scalable method for efficient inference in Gaussian process regression networks.
problem Intractable inference in Gaussian process regression networks (GPRN).
method Tensorization of output space, tensor/matrix-normal variational posteriors, joint optimization, and exploiting Kronecker product structure.
result Captures posterior dependencies and improves inference quality for large number of outputs.
The paper presents a method for generating well-calibrated prediction intervals using quality-driven deep ensembles.
problem Generating reliable prediction intervals for regression analysis.
method A multi-objective loss function combining quality measures for prediction intervals and point estimates, with a penalty function to ensure semantic integrity and stability.
result The method produces well-calibrated prediction intervals and point estimates, capturing both aleatoric and epistemic uncertainty.
S-VBMC improves VBMC's exploration of complex posterior distributions.
problem Efficient inference for computationally expensive models with complex posterior distributions.
method Stacking multiple independent VBMC runs to create a robust global posterior approximation.
result Significant improvements in posterior approximation quality across various applications.
Post-process Bayesian inference speeds up posterior approximation.
problem Leveraging pre-existing model evaluations for quick posterior approximation.
method Variational Sparse Bayesian Quadrature (VSBQ) using sparse Gaussian process (GP) surrogate model.
result VSBQ builds high-quality posterior approximations from existing optimization traces.
We propose a novel approach to approximate complex high-dimensional posteriors using neural samplers.
problem Accurately capturing complex, multimodal, and correlated posteriors in high-dimensional spaces.
method Implicit variational inference with neural samplers and local linearisation bounds.
result Our method enables implicit distributions over tens of millions of latent variables, recovering correlations across layers in large Bayesian neural networks.
KL annealing helps VAEs avoid posterior collapse and overfitting.
problem Posterior collapse and overfitting in VAEs.
method Theoretical analysis of learning dynamics with KL annealing.
result Posterior collapse is inevitable when β exceeds a threshold. Stochastic variational inference allows for fast posterior inference in complex Bayesian models. However, the algorithm is prone to local optima which can make the quality of the posterior approximation sensitive to the choice of hyperparameters and initialization. We address this problem by replacing the natural gradi…
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.
New method optimizes Bayesian optimization for high-dimensional posterior samples.
problem Difficult inner-loop optimization of posterior sample paths in Bayesian optimization.
method Global rootfinding approach with carefully selected starting points.
result The method discovers the global optimum most of the time with just one starting point per set.
Nonparametric mixture models based on the Dirichlet process are an elegant alternative to finite models when the number of underlying components is unknown, but inference in such models can be slow. Existing attempts to parallelize inference in such models have relied on introducing approximations, which can lead to in…
Improved VAEs by training a contrastive prior to match posterior.
problem Prior hole problem in VAEs, leading to poor image generation.
method Introduced a contrastive energy-based prior and trained it using noise contrastive estimation.
result Significant improvement in VAE generative performance on various datasets.