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.
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.
DDVI uses diffusion models for variational inference, improving latent variable model performance.
problem Improving variational inference in latent variable models.
method Introduces diffusion-based variational posteriors trained with a regularized ELBO.
result Outperforms alternative variational posteriors on various benchmarks and a biology task.
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.
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.
SoftCVI uses contrastive estimation to infer complex posteriors.
problem Estimating complex posteriors in Bayesian inference.
method Contrastive variational inference with self-generated soft labels.
result SoftCVI outperforms other variational approaches in stability and coverage.
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.
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.
Improved Bayesian inference via variational approximations of generalized rho-posteriors.
problem Robust Bayesian inference under model misspecification and data contamination.
method Introducing a modified ρ-posterior and using PAC-Bayesian analysis with variational approximations. result Theoretical guarantees for tractable inference with competitive robustness and computational efficiency.
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 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.
Sparse variational approximations allow for principled and scalable inference in Gaussian Process (GP) models. In settings where several GPs are part of the generative model, theses GPs are a posteriori coupled. For many applications such as regression where predictive accuracy is the quantity of interest, this couplin…
Study trade-offs between statistical and computational efficiency in variational inference.
problem Optimizing statistical accuracy vs. computational efficiency in Bayesian inference.
method Case study on Gaussian inferential models with diagonal plus low-rank precision matrices, analyzing Bayesian posterior inference and frequentist uncertainty quantification errors.
result Lower-rank models reduce variance and accelerate convergence but increase posterior inference error.
The Laplace approximation has been one of the workhorses of Bayesian inference. It often delivers good approximations in practice despite the fact that it does not strictly take into account where the volume of posterior density lies. Variational approaches avoid this issue by explicitly minimising the Kullback-Leibler…
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.
Bayesian neural networks ignore data in infinite units limit.
problem Pathological behavior of posterior in over-parameterized networks.
method Mean-field variational inference in infinite hidden units limit.
result Posterior mean converges to zero, ignoring data.
Recent progress in variational inference has paid much attention to the flexibility of variational posteriors. One promising direction is to use implicit distributions, i.e., distributions without tractable densities as the variational posterior. However, existing methods on implicit posteriors still face challenges of…
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.
Boosting Variational Inference improves posterior approximations with adaptive step-sizes.
problem Limited resources hinder the widespread adoption of Boosting Variational Inference.
method Characterized global curvature impact, introduced local curvature, and developed an approximate backtracking algorithm.
result New theoretical convergence rates and experimental validation demonstrate improved performance.
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.
Stacking improves inference for multimodal Bayesian posterior distributions.
problem Difficulty of MCMC in moving between modes and underestimation of posterior uncertainty.
method Parallel runs of MCMC, variational, or mode-based inference, combined using Bayesian stacking.
result Stacking efficiently samples from multimodal posterior distributions and represents uncertainty better than variational inference.
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.
FTIP uses normalizing flows to improve posterior inference in function space.
problem Challenges in posterior inference with implicit-process priors.
method FTIP uses normalizing flows to define a richer variational distribution over combination weights.
result FTIP captures asymmetric and multimodal posterior structure better than Gaussian coefficient approximations.
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.
New method DDVI improves posterior inference for deep Gaussian processes.
problem Inference of inducing points in DGPs is challenging and biased.
method DDVI uses denoising diffusion SDE and score matching for posterior approximation.
result Empirically shows DDVI outperforms baseline methods in inducing point inference.
FlowVAT improves variational inference for multi-modal distributions.
problem Mode-seeking behavior and collapse in variational inference for complex posteriors.
method Conditional tempering approach for normalizing flow variational inference.
result FlowVAT outperforms traditional and adaptive annealing methods in multi-modal distributions, finding more modes and achieving better ELBO values.
This paper introduces a spline-based method for nonparametric ADVI that handles complex posterior distributions.
problem Learning complex posterior distributions with skewness, multimodality, and bounded support.
method Develops a spline-based nonparametric approximation approach for ADVI.
result Establishes the asymptotic consistency of the derived lower bound for importance weighted autoencoder.
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. A new particle algorithm improves mean-field variational inference.
problem Efficiently approximating nonparametric posterior distributions in machine learning.
method Introduces PArticle VI (PAVI), a novel particle-based algorithm for nonparametric mean-field approximation.
result Obtains non-asymptotic error bounds for PArticle VI, providing the first end-to-end guarantee for particle-based MFVI.
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.
Paper presents IPVI for unbiased DGP inference with efficiency.
problem Intractable exact inference in deep Gaussian processes.
method Implicit posterior variational inference framework.
result IPVI achieves unbiased posterior belief with efficiency.
Deep Bayesian neural nets can use simpler weight approximations without sacrificing performance.
problem The need for complex weight posterior approximations in deep Bayesian neural networks.
method Theoretical and empirical analysis of mean-field variational inference in deep networks.
result Mean-field variational weight posteriors in deep networks can induce similar function-space distributions as complex approximations in shallower networks.
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 variational inference for Neyman-Scott processes for faster sampling.
problem Slow mixing time in MCMC for posterior sampling in Neyman-Scott processes.
method Variational inference algorithm for Neyman-Scott processes, minimizing KL divergence.
result Achieves better prediction performance than MCMC with limited computational time.
The paper proves consistency of GVI posteriors under minimal conditions.
problem Consistency of generalized variational inference posteriors.
method Proves consistency using Γ-convergence theory. result GVI posteriors are consistent and collapse to the population-optimal parameter value.
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.
Particle-based variational inference offers a flexible way of approximating complex posterior distributions with a set of particles. In this paper we introduce a new particle-based variational inference method based on the theory of semi-discrete optimal transport. Instead of minimizing the KL divergence between the po…
Variational inference methods often focus on the problem of efficient model optimization, with little emphasis on the choice of the approximating posterior. In this paper, we review and implement the various methods that enable us to develop a rich family of approximating posteriors. We show that one particular method …
Classical approaches for approximate inference depend on cleverly designed variational distributions and bounds. Modern approaches employ amortized variational inference, which uses a neural network to approximate any posterior without leveraging the structures of the generative models. In this paper, we propose Amorti…
One of the core problems in variational inference is a choice of approximate posterior distribution. It is crucial to trade-off between efficient inference with simple families as mean-field models and accuracy of inference. We propose a variant of a greedy approximation of the posterior distribution with tractable bas…
We propose a black-box variational inference method to approximate intractable distributions with an increasingly rich approximating class. Our method, termed variational boosting, iteratively refines an existing variational approximation by solving a sequence of optimization problems, allowing the practitioner to trad…
Variational inference has become an increasingly attractive fast alternative to Markov chain Monte Carlo methods for approximate Bayesian inference. However, a major obstacle to the widespread use of variational methods is the lack of post-hoc accuracy measures that are both theoretically justified and computationally …
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.
Variational autoencoders often collapse, showing latent variables are non-identifiable.
problem Posterior collapse in variational autoencoders due to non-identifiable latent variables.
method Proves latent variable non-identifiability causes posterior collapse. Proposes latent-identifiable models using Brenier maps and input convex neural networks.
result Latent-identifiable models resolve posterior collapse and provide meaningful representations.
Structured Nonparametric Variational Inference for Dependent Latent Modeling
problem Approximating posterior distributions with complex dependencies among latent variables
method Structured Nonparametric Variational Inference (SN-VI)
result Flexible and accurate posterior approximation with arbitrary shapes
Variational inference (VI) provides fast approximations of a Bayesian posterior in part because it formulates posterior approximation as an optimization problem: to find the closest distribution to the exact posterior over some family of distributions. For practical reasons, the family of distributions in VI is usually…
Self-reflective VAE improves inference and generative modeling without complex components.
problem Limitations of typical VAEs in inference and generative modeling.
method Introduces self-reflective inference, a new hierarchical structure that matches variational posterior to exact posterior.
result Self-reflective inference achieves state-of-the-art performance on binarized MNIST without autoregressive layers.
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.