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.
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…
R package for Bayesian empirical likelihood sampling using HMC.
problem Sampling from non-convex Bayesian empirical likelihood posteriors.
method Hamiltonian Monte Carlo (HMC) algorithm for numerical integration.
result Efficient HMC sampling from BayesEL posteriors.
Bayesian neural networks with data augmentation show a persistent cold posterior effect.
problem Understanding the cold posterior effect in Bayesian neural networks with data augmentation.
method Developed principled Bayesian neural networks using data augmentation, providing exact likelihoods and tight bounds.
result The cold posterior effect persists even in models incorporating data augmentation, suggesting it's not an artifact.
Cold posteriors in BNNs harm performance, likely due to incorrect likelihood.
problem Cold posteriors in Bayesian neural networks degrade performance.
method Developed a generative model explaining cold posteriors and matched it to the tempered likelihoods.
result Cold posteriors are a result of using the wrong likelihood for image classification datasets.
SNPLA uses normalizing flows for efficient inference in implicit models.
problem Efficient inference in implicit models with complex likelihood and posterior learning.
method Sequential Neural Posterior and Likelihood Approximation (SNPLA) algorithm using normalizing flows.
result SNPLA achieves competitive performance with faster posterior draws compared to MCMC methods.
Bayesian deep learning faces posterior collapse due to likelihood vs. prior competition.
problem Posterior collapse in Bayesian deep learning models.
method Identified competition between likelihood and prior regularization in a linear latent variable model.
result Posterior collapse is related to neural and dimensional collapse, suggesting a broader learning issue.
Improved diffusion sampling for inverse problems with faster and more robust inference.
problem High computational cost and lack of robustness in diffusion posterior sampling.
method Amortized variational inference with explicit likelihood guidance.
result Improved trade-off between inference speed and robustness to unseen degradations.
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. 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.
How can one perform Bayesian inference on stochastic simulators with intractable likelihoods? A recent approach is to learn the posterior from adaptively proposed simulations using neural network-based conditional density estimators. However, existing methods are limited to a narrow range of proposal distributions or r…
Generative Bayesian Inference uses GANs for approximate posterior sampling.
problem Bayesian inference without explicit likelihoods.
method Develops Bayesian GAN (B-GAN) for posterior simulation.
result B-GAN achieves highly competitive performance in posterior sampling.
Recent work in variational inference (VI) uses ideas from Monte Carlo estimation to tighten the lower bounds on the log-likelihood that are used as objectives. However, there is no systematic understanding of how optimizing different objectives relates to approximating the posterior distribution. Developing such a conn…
Linear VAEs explain posterior collapse in VAEs via local maxima in log marginal likelihood.
problem Posterior collapse in VAEs where variational posterior matches prior for some latent variables.
method Analysis of linear VAEs and their relation to pPCA, proving ELBO does not introduce spurious local maxima.
result Linear VAEs have identifiable global maxima corresponding to principal component directions, explaining posterior collapse.
New methods improve statistical accuracy of complex models without high computational cost.
problem Improving statistical accuracy of complex models without high computational cost.
method Neural posterior and likelihood estimation (NPE and NLE) methods.
result NPE and NLE methods have similar theoretical guarantees to ABC and BSL, but achieve accuracy at a reduced computational cost.
Pseudo-Likelihood Inference improves ABC for high-dimensional Bayesian inference.
problem Intractable likelihood in Bayesian system identification.
method PLI combines neural approximation with integral probability metrics and adaptive bandwidth.
result PLI outperforms SNPE on challenging tasks, especially with more data.
In this paper we revisit the weighted likelihood bootstrap, a method that generates samples from an approximate Bayesian posterior of a parametric model. We show that the same method can be derived, without approximation, under a Bayesian nonparametric model with the parameter of interest defined as minimising an expec…
Improved likelihood-free inference using preconditioned neural posterior estimation.
problem Inaccurate posterior estimation in likelihood-free inference methods.
method Preconditioned Neural Posterior Estimation (PNPE) and Sequential PNPE (PSNPE) methods.
result PNPE and PSNPE improve posterior estimation accuracy over NPE and SNPE.
Improved SBI with neural networks for complex models.
problem Accurate inference for complex models with intractable likelihood.
method Structured mixtures of probability distributions for likelihood and posterior approximation.
result Accurate posterior inference with smaller computational footprint.
ABI bypasses likelihood intractability with nonparametric distribution matching.
problem Approximate Bayesian computation's inefficiency in high-dimensional settings and under diffuse priors.
method Adaptive Bayesian Inference (ABI) compares posterior distributions directly using nonparametric distribution matching and MSW distance.
result ABI significantly outperforms other methods in high-dimensional or dependent observation regimes.
JANA trains networks to approximate Bayesian models efficiently.
problem Intractable likelihood functions and posterior densities in Bayesian models.
method End-to-end training of three networks: summary, posterior, and likelihood networks.
result JANA provides accurate amortized marginal likelihood and posterior predictive estimation.
A new method improves Bayesian inference for multimodal posteriors.
problem Insensitivity to well-separated modes in multimodal posteriors.
method Weighted Kernel Stein Discrepancy method.
result Significantly improved mode sensitivity compared to standard KSD-Bayes.
Normalizing flow regression approximates posterior distributions without additional sampling.
problem Bayesian inference with computationally expensive likelihood evaluations.
method Normalizing flow regression (NFR) for offline inference.
result NFR yields a tractable posterior approximation through regression on existing log-density evaluations.
EG-LF-MCMC infers posterior densities without likelihoods.
problem Posterior inference for models with intractable likelihoods.
method Two-phase approach: error recording and classification for MCMC.
result EG-LF-MCMC provides approximate posterior densities efficiently.
Improves likelihood-free inference by using a new sampling approach to avoid biased data collection.
problem Efficient Bayesian inference without likelihood evaluation for real-world datasets.
method Introduces Neural Proposal (NP) to sample simulation inputs i.i.d. for unbiased posterior inference.
result Demonstrates improved performance, especially for multi-modal posteriors, through experiments.
Paper proposes nested MLMC for SNPE with intractable likelihoods.
problem Estimating posterior distributions from intractable likelihoods.
method Nested MLMC for loss function and gradients, with convergence results.
result Effective methods for approximating complex multimodal posteriors.
In this paper we study the probabilistic properties of the posteriors in a speech recognition system that uses a deep neural network (DNN) for acoustic modeling. We do this by reducing Kaldi's DNN shared pdf-id posteriors to phone likelihoods, and using test set forced alignments to evaluate these using a calibration s…
Paper proposes MMD-Bayes for robust Bayesian estimation in misspecified models.
problem Inconsistent estimates in Bayesian statistics due to model misspecification.
method Uses Maximum Mean Discrepancy (MMD) to create a robust pseudo-likelihood.
result MMD-Bayes posterior is consistent and robust to model misspecification.
We improve likelihood-free inference using distillation of importance sampling.
problem Challenging likelihood-free inference with high-dimensional, dependent posterior.
method Approximate posterior with normalizing flows trained on likelihood-free importance sampling.
result Improved accuracy in inference without needing summary statistics.
SNVI combines likelihood estimation with variational inference for efficient Bayesian inference.
problem Bayesian inference in models with intractable likelihoods.
method Sequential Neural Variational Inference (SNVI) that combines likelihood-estimation with variational inference.
result SNVI is more computationally efficient than previous algorithms without sacrificing accuracy.
Develops a new Bayesian inference method for discrete data.
problem Computational challenges in discrete state spaces, especially intractable likelihoods.
method Uses a discrete Fisher divergence to update beliefs about model parameters, circumventing the intractable normalising constant.
result Establishes statistical properties of the generalised posterior and proposes a calibration approach.
Markov Chain Monte Carlo (MCMC) sampling from a posterior distribution corresponding to a massive data set can be computationally prohibitive since producing one sample requires a number of operations that is linear in the data size. In this paper, we introduce a new communication-free parallel method, the Likelihood I…
Improved likelihood-free inference by localizing and refining low-dimensional approximations.
problem Poor performance of common likelihood-free methods in high-dimensional models.
method Localisation followed by refinement of low-dimensional summaries.
result Improved accuracy in marginal posteriors through localized and refined approximations.
Gaussian process regression helps approximate Bayesian inverse problems efficiently.
problem Computational intractability of Bayesian posterior distributions in inverse problems.
method Gaussian process regression to build a surrogate model for the likelihood.
result Error between true and approximate posterior can be bounded by weighted L2-norm error between true and approximate likelihood. This paper proposes a new method to approximate posterior distributions using generative neural networks trained via scoring rule minimization.
problem Bayesian Likelihood-Free Inference for models with intractable likelihood.
method Approximate posterior with generative neural networks trained via scoring rule minimization, avoiding the instability of adversarial training.
result Scoring Rule minimization leads to better performance and uncertainty quantification compared to adversarial training.
A new two-step MH method for Bayesian EL computation.
problem Complex likelihood support in Bayesian EL.
method Hierarchical Metropolis Hastings with reversible jump MCMC.
result Improved sampling from BayesEL posteriors.
New method uses neural exponential families for likelihood-free inference.
problem Bayesian Likelihood-Free Inference with intractable likelihood.
method Score Matching neural conditional exponential families for approximate likelihood.
result State-of-the-art performance in posterior sampling for intractable likelihood models.
Study of maximum likelihood under biased constraints reveals novel degeneracies and anomalous statistical behavior.
problem Investigating maximum likelihood under biased estimating equations.
method Analyzing the behavior of optimal distributions and log-likelihood statistics under mis-specification.
result Degeneracies in optimal distributions and anomalous behavior of log-likelihood statistics under mis-specification.
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.
Some machine learning applications require continual learning - where data comes in a sequence of datasets, each is used for training and then permanently discarded. From a Bayesian perspective, continual learning seems straightforward: Given the model posterior one would simply use this as the prior for the next task.…
In likelihood-free settings where likelihood evaluations are intractable, approximate Bayesian computation (ABC) addresses the formidable inference task to discover plausible parameters of simulation programs that explain the observations. However, they demand large quantities of simulation calls. Critically, hyperpara…
Unified framework for model-based RL with sample complexity guarantees.
problem Designing efficient posterior sampling methods for model-based RL.
method Optimistic posterior sampling, Hellinger distance reduction, data likelihood measurement.
result Unified algorithms with state-of-the-art sample complexity guarantees.
MINIMALIST maximizes mutual information for likelihood estimation from simulated data.
problem Learning model parameters from likelihood functions that cannot be computed.
method Maximizes mutual information between simulated data and model parameters using neural networks.
result Different methods aiming at the same optimal energy form can be directly benchmarked.
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.
Privacy preserving mechanisms such as differential privacy inject additional randomness in the form of noise in the data, beyond the sampling mechanism. Ignoring this additional noise can lead to inaccurate and invalid inferences. In this paper, we incorporate the privacy mechanism explicitly into the likelihood functi…
New SMC sampler improves diffusion model sampling efficiency.
problem Sampling generative diffusion models efficiently.
method Constructs correlated observation paths and designs a sampler.
result Improved statistical efficiency, especially under outlier conditions.
Learning latent variable models with stochastic variational inference is challenging when the approximate posterior is far from the true posterior, due to high variance in the gradient estimates. We propose a novel rejection sampling step that discards samples from the variational posterior which are assigned low likel…
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.