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.
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.
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.
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.
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. Enhanced Gaussian process models accelerate optimization and posterior approximation.
problem Improving the accuracy and speed of Gaussian process models for optimization and inference.
method Introduces a random exploration step to classical GP-UCB algorithms, facilitating faster convergence.
result New algorithms achieve nearly optimal convergence rates and provide bounds for Hellinger distance.
Posterior sampling-based EI achieves sublinear regret bounds for expensive function optimization.
problem Theoretical analysis of expected improvement (EI) in Bayesian optimization.
method Randomized posterior sampling of EI.
result Achieves sublinear Bayesian cumulative regret bounds.
Optimal posterior distributions improve SVM classifiers and parameter selection.
problem Improving SVM classifiers and selecting optimal regularization parameters.
method PAC-Bayesian approach with optimal posterior identification for stochastic classifiers.
result Optimal posteriors yield tight risk bounds and improved SVM performance.
Thompson sampling (TS) is a class of algorithms for sequential decision-making, which requires maintaining a posterior distribution over a model. However, calculating exact posterior distributions is intractable for all but the simplest models. Consequently, efficient computation of an approximate posterior distributio…
Accelerates pulsar light curve inference with learned representations and optimization.
problem Computational expense of Markov chain Monte Carlo methods for posterior inference.
method Combining U-Net latent representations with local simulator-guided optimization.
result 120x reduction in inference time (24 hours to 12 minutes) with accuracy preserved.
Proposes MIVI for efficient posterior estimation and design of MCMC transitions.
problem Efficiently estimating posterior distributions in constrained time.
method Combines variational inference and MCMC with a variational distribution and optimized Markov chain.
result Optimized Markov chain improves variational distribution and vice versa, leading to more accurate posteriors.
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…
SPOT improves differentiable causal discovery by estimating skeleton posterior for latent confounders.
problem Scalable and accurate estimation of causal skeletons in the presence of latent confounders.
method SPOT (Skeleton Posterior-guided OpTimization) framework that estimates skeleton posterior and integrates it with differentiable causal discovery.
result SPOT enhances differentiable causal discovery by reducing the search space and improving accuracy.
Improves Bayesian optimization using Gaussian process Thompson sampling.
problem Global optimization of Gaussian process posterior samples.
method Carefully selects starting points for gradient-based multi-start optimizers, identifies all local optima via univariate global rootfinding, and optimizes the posterior sample.
result Dramatic improvements in overall performance of Bayesian optimization.
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.
Researchers estimate optimal PAC-Bayes bounds using Hamiltonian Monte Carlo.
problem Estimating tight PAC-Bayes bounds with restricted posterior families.
method Sampling from optimal Gibbs posterior using Hamiltonian Monte Carlo, estimating KL divergence, and proposing high-probability bounds.
result Significant tightness gaps in PAC-Bayes bounds, up to 5-6% in some cases.
A new ensemble filter uses transport maps and MMD optimization for high-dimensional data assimilation.
problem High-dimensional data assimilation challenges in ensemble filtering.
method Optimized Maximum Mean Discrepancy (MMD) for transport map construction.
result Significant improvement in robustness and posterior approximation.
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.
Posterior sampling estimator achieves near-optimal recovery guarantees for signals from any prior distribution.
problem Characterizing measurement complexity for signals from any prior distribution, including the entire space.
method Characterization of measurement complexity using posterior sampling estimator for Gaussian measurements and any prior distribution.
result Posterior sampling estimator achieves near-optimal recovery guarantees for signals from any prior distribution, robust to model mismatch.
A new algorithm optimizes Gaussian process posterior mean functions efficiently.
problem Optimizing Gaussian process posterior mean functions over hyperrectangles is challenging due to nonlinearity and nonconvexity.
method PALM-Mean, a piecewise-analytic lower-bounding framework embedded in reduced-space spatial branch-and-bound.
result PALM-Mean improves scalability for large datasets compared to general-purpose solvers.
Combines MALA and Adam for efficient uncertainty quantification in deep learning.
problem Uncertainty estimation in deep neural networks.
method Integrates Metropolis Adjusted Langevin Algorithm (MALA) with momentum-based optimization (Adam) for efficient sampling from posterior distributions.
result The algorithm approximates the Gibbs posterior in total variation distance and efficiently quantifies epistemic uncertainty.
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.
Bayesian neural networks achieve optimal posterior contraction rates in Besov spaces with intrinsic dimensionality.
problem High-dimensional structured estimation problems with unknown smoothness levels.
method Sparse Bayesian neural networks with either sparse or continuous shrinkage priors.
result Optimal posterior contraction rates are achieved, adapting to the unknown smoothness level of the true function.
Sparse matrices simplify computation of GP variances and likelihoods.
problem Efficient computation of posterior variance and log-likelihood for additive Matérn GPs.
method Represented posterior mean, variance, log-likelihood, and gradient using sparse matrices.
result Efficient computation of posterior mean, variance, log-likelihood, and gradient in O(nlogn) time. 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…
New framework tackles DG under posterior drift, where optimal classifier varies by domain.
problem Generalizing from multiple domains with varying optimal classifiers.
method Decision-theoretic framework for DG under posterior drift.
result Optimal classifier can vary significantly across domains, challenging existing DG approaches.
Label switching is a phenomenon arising in mixture model posterior inference that prevents one from meaningfully assessing posterior statistics using standard Monte Carlo procedures. This issue arises due to invariance of the posterior under actions of a group; for example, permuting the ordering of mixture components …
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.
Optimizes expensive experiments by incorporating expert knowledge.
problem Expensive experiments require minimizing the number of trials.
method Bayesian optimization with posterior sampling of expert knowledge.
result Demonstrates significant efficiency gains in experiments and hyperparameter tuning.
BNRE improves simulation-based inference by producing more conservative posteriors.
problem Overconfident posteriors from current simulation-based inference algorithms risk false inferences.
method Balanced Neural Ratio Estimation (BNRE) that produces more conservative posterior approximations.
result BNRE produces more conservative posterior surrogates on all tested benchmarks and simulation budgets.
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.
A Bayesian approach termed BAyesian Least Squares Optimization with Nonnegative L1-norm constraint (BALSON) is proposed. The error distribution of data fitting is described by Gaussian likelihood. The parameter distribution is assumed to be a Dirichlet distribution. With the Bayes rule, searching for the optimal parame…
Method reformulates constrained optimization as latent space inference.
problem Optimizing black-box functions with hard constraints.
method Posterior inference in latent space using flow-based models and diffusion models.
result Method achieves superior performance across various tasks.
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 quantifies uncertainty for near-optimal ML algorithms.
problem Uncertainty quantification for near-Bayes optimal ML algorithms.
method Developed a martingale posterior to recover Bayesian posterior from ML algorithms.
result Proved practical uncertainty quantification method applicable to general ML algorithms.
Bayesian model infers factor dimensionality and sparse loading matrix adaptively.
problem Inference of high-dimensional sparse factor model with varying sparsity and factor dimensions.
method Adaptive Bayesian sparse factor model with posterior concentration.
result Posterior distribution asymptotically concentrates on true factor dimensionality and sparsity.
SDG uses optimal control to improve classifier guidance in low-density regions.
problem Inefficient guidance in low-density regions of posterior distributions.
method Integrates stochastic optimal control with Stein variational inference to compute the steepest descent direction.
result SDG improves guidance in low-density regions, outperforming standard methods.
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.
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.
New theory for BNNs with Gaussian priors achieves optimal posterior concentration rates.
problem Lack of theoretical results for BNNs with Gaussian priors.
method New approximation theory for non-sparse DNNs with bounded parameters.
result BNNs with non-sparse general priors can achieve near-minimax optimal posterior concentration rates.
Focal loss improves classification but not class-posterior probability estimation.
problem Improving class-posterior probability estimation from focal loss.
method Proved classification-calibration and derived a transformation to recover true class-posterior probabilities.
result A transformation of the confidence score from focal loss minimization allows recovery of true class-posterior probabilities.
Study on optimal information acquisition in Kyle model with entropy cost.
problem Optimal information acquisition in Kyle model with entropy cost.
method Continuous signals are optimal, and any signal with a logit posterior distribution yields the same ex-ante value.
result Posterior expected payoff becomes normally distributed as information acquisition cost increases.
Levenshtein VAE prevents posterior collapse in text generation models.
problem Posterior collapse in VAEs where generators ignore latent variables.
method Replaces ELBO with a Levenshtein distance-based objective to prevent collapse.
result Levenshtein VAE produces more informative latent representations.
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 framework improves variational inference for high-dimensional posteriors.
problem Challenges in choosing variational objectives and approximating families for high-dimensional posteriors.
method Conceptual framework and experimental tools to understand and optimize variational objectives and families.
result For moderate-to-high-dimensional posteriors, exclusive KL divergence is recommended due to optimization ease; for low-dimensional, heavy-tailed variational families are effective.
JADAI optimizes design and inference for parameter estimation.
problem Parameter estimation with active optimization of design variables.
method Jointly trains a policy, history network, and inference network to minimize posterior error.
result Achieves superior or competitive performance across benchmarks.
Improved VAE models avoid posterior collapse in text modeling.
problem Posterior collapse in VAEs leads to poor data manifold parameterization.
method Coupled-VAE couples a VAE with a deterministic autoencoder to improve encoder and decoder parameterizations.
result Coupled-VAE consistently improves results in probability estimation and latent space richness.
In many domains, scientists build complex simulators of natural phenomena that encode their hypotheses about the underlying processes. These simulators can be deterministic or stochastic, fast or slow, constrained or unconstrained, and so on. Optimizing the simulators with respect to a set of parameter values is common…