Recent work used importance sampling ideas for better variational bounds on likelihoods. We clarify the applicability of these ideas to pure probabilistic inference, by showing the resulting Importance Weighted Variational Inference (IWVI) technique is an instance of augmented variational inference, thus identifying th…
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48 results for “Importance Weighted Variational Inference”
U-statistics improve gradient estimation in importance-weighted variational inference.
problem High variance in gradient estimation for importance-weighted variational inference.
method Use U-statistics to average base gradient estimators on overlapping batches of size m, achieving lower variance.
result U-statistic variance reduction leads to modest to significant improvements in inference performance.
The Importance Weighted Auto Encoder (IWAE) objective has been shown to improve the training of generative models over the standard Variational Auto Encoder (VAE) objective. Here, we derive importance weighted extensions to AVB and AAE. These latent variable models use implicitly defined inference networks whose approx…
This paper compares gradient estimators in importance-weighted VI and justifies the superiority of DREP over REP.
problem Understanding the impact of gradient estimators on importance-weighted VI algorithms.
method Unified theoretical comparison of reparameterized and doubly-reparameterized gradient estimators tied to IWAE, VR, and VR-IWAE bounds.
result Formally justifies the superiority of doubly-reparameterized gradient estimators over reparameterized ones in importance-weighted VI.
VISA improves inference efficiency for complex models.
problem Efficient approximate inference in computationally intensive models.
method Sequential sample-average approximations within a trust region.
result VISA achieves comparable accuracy with computational savings.
Deep Gaussian processes (DGPs) can model complex marginal densities as well as complex mappings. Non-Gaussian marginals are essential for modelling real-world data, and can be generated from the DGP by incorporating uncorrelated variables to the model. Previous work on DGP models has introduced noise additively and use…
Nested Variational Inferencestat.ML
Develops a method for learning proposals in nested importance samplers.
problem Improving sampling quality in complex distributions.
method Nested Variational Inference (NVI) using forward or reverse KL divergence.
result Optimizing nested objectives leads to improved sample quality.
The recognition network in deep latent variable models such as variational autoencoders (VAEs) relies on amortized inference for efficient posterior approximation that can scale up to large datasets. However, this technique has also been demonstrated to select suboptimal variational parameters, often resulting in consi…
Paper improves REINFORCE for VI without restrictive assumptions.
problem Improves REINFORCE for VI without restrictive assumptions.
method Introduces VIMCO- gradient estimator to overcome SNR collapse.
result VIMCO- achieves SNR scaling, superior to existing VIMCO.
We provide theoretical and empirical evidence that using tighter evidence lower bounds (ELBOs) can be detrimental to the process of learning an inference network by reducing the signal-to-noise ratio of the gradient estimator. Our results call into question common implicit assumptions that tighter ELBOs are better vari…
Paper formalizes and analyzes a new bound for variational inference.
problem Lack of theoretical guarantees in variational algorithms.
method Introduces VR-IWAE bound, a generalization of IWAE.
result VR-IWAE bound leads to unbiased gradient estimators.
New insights into variational inference using Monte Carlo estimates.
problem Improving variational bounds in latent variable models.
method Analyzing properties of Monte Carlo estimates and their impact on variational gaps.
result Negative correlation reduces variational gaps, contrary to intuition.
We introduce overdispersed black-box variational inference, a method to reduce the variance of the Monte Carlo estimator of the gradient in black-box variational inference. Instead of taking samples from the variational distribution, we use importance sampling to take samples from an overdispersed distribution in the s…
New method improves inference for hierarchical models.
problem Challenges in inference for large hierarchical models.
method Locally enhanced variational bounds with subsampling.
result Better posterior approximations than baselines.
New methods improve gradient estimation in autoencoders, enhancing generative network performance.
problem Improving gradient estimation in autoencoders to enhance learning.
method Developed and studied three methods: PIWAE, MIWAE, CIWAE.
result Generated approximate posterior distributions closer to true posterior distribution.
DGPs with variational inference suffer from SNR issues that degrade gradient estimates, leading to unreliable training.
problem SNR issues in gradient estimates for DGPs with variational inference.
method Adapted doubly reparameterized gradient estimators for DGP training.
result Fix improves predictive performance of DGP models.
Importance weighted variational inference (Burda et al., 2015) uses multiple i.i.d. samples to have a tighter variational lower bound. We believe a joint proposal has the potential of reducing the number of redundant samples, and introduce a hierarchical structure to induce correlation. The hope is that the proposals w…
Paper introduces VDE, a variance-reduced determinant estimator.
problem Estimating determinants with low variance and efficiency.
method Combines variational inference and spherical normalizing flows.
result VDE achieves zero variance in ideal cases, requiring only one sample.
R2D2-Net improves Bayesian neural networks by preventing over-shrinkage of important weights.
problem Bayesian neural networks struggle with choosing appropriate priors, leading to over-shrinkage or poor predictive performance.
method Proposes R2D2-Net with an R^2-induced Dirichlet Decomposition prior and variational Gibbs inference algorithm.
result R2D2-Net effectively shrinks irrelevant coefficients while preventing key features from over-shrinkage.
Variational inference with α-divergences has been widely used in modern probabilistic machine learning. Compared to Kullback-Leibler (KL) divergence, a major advantage of using α-divergences (with positive α values) is their mass-covering property. However, estimating and optimizing α-divergences require to use importa…
Paper addresses variational inference issues in Bayesian neural networks.
problem Negative infinite ELBO for function-space priors in BNNs.
method Regularized KL divergence for well-defined function-space variational inference.
result Method provides competitive uncertainty estimates for BNNs.
DAIS minimizes symmetrized KL divergence between initial and target distributions.
problem Optimizing over initial distributions in importance sampling.
method Differentiable annealed importance sampling (DAIS) minimizing symmetrized KL divergence.
result DAIS minimizes symmetrized KL divergence between initial and target distributions.
New Holder bounds improve variational inference by flattening thermodynamic curves.
problem Improving variational inference by addressing performance gaps between theory and practice.
method Generalizing thermodynamic integration to weighted Holder mean, introducing Holder bounds.
result Holder bounds promise a one-step approximation of exact marginal log-likelihood.
Paper introduces f-divergence variational inference for broader application.
problem Variational inference limited to specific divergences.
method Generalizes variational inference to all f-divergences using f-divergence minimization.
result Unified framework for variational inference with arbitrary f-divergences.
Variational Inference is a powerful tool in the Bayesian modeling toolkit, however, its effectiveness is determined by the expressivity of the utilized variational distributions in terms of their ability to match the true posterior distribution. In turn, the expressivity of the variational family is largely limited by …
The paper uses Bayesian methods to infer hidden processes with unknown parameters.
problem Estimating hidden processes from noisy observations with unknown parameters.
method Variational Bayesian inference with autoregressive moving average (ARMA) and vector autoregressive (VAR) models, combined with sequential Monte Carlo (SMC) and importance sampling resampling (SISR).
result The proposed inference method accurately estimates hidden states from non-linear noisy observations.
Stacking for Non-mixing Bayesian Computations: The Curse and Blessing of Multimodal Posteriorsstat.ME
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.
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.
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.
We propose a simple and general variant of the standard reparameterized gradient estimator for the variational evidence lower bound. Specifically, we remove a part of the total derivative with respect to the variational parameters that corresponds to the score function. Removing this term produces an unbiased gradient …
The variational autoencoder (VAE; Kingma, Welling (2014)) is a recently proposed generative model pairing a top-down generative network with a bottom-up recognition network which approximates posterior inference. It typically makes strong assumptions about posterior inference, for instance that the posterior distributi…
Stochastic variational inference for Bayesian deep neural network (DNN) requires specifying priors and approximate posterior distributions over neural network weights. Specifying meaningful weight priors is a challenging problem, particularly for scaling variational inference to deeper architectures involving high dime…
Improved variational inference for GPLVMs using AIS.
problem Challenges in generating effective proposal distributions for high-dimensional or complex data.
method Annealed Importance Sampling (AIS) combined with reparameterization.
result Our method achieves tighter variational bounds and higher log-likelihoods.
Variational inference (VI) and Markov chain Monte Carlo (MCMC) are two main approximate approaches for learning deep generative models by maximizing marginal likelihood. In this paper, we propose using annealed importance sampling for learning deep generative models. Our proposed approach bridges VI with MCMC. It gener…
The importance weighted autoencoder (IWAE) (Burda et al., 2016) is a popular variational-inference method which achieves a tighter evidence bound (and hence a lower bias) than standard variational autoencoders by optimising a multi-sample objective, i.e. an objective that is expressible as an integral over Mont…
Optimal Variance Control of the Score Function Gradient Estimator for Importance Weighted Boundsstat.ML
Paper improves variance control in importance weighted variational bounds.
problem Improving the variance of gradient estimators for IWAE.
method Develops a novel control variate that grows SNR as √K for large K.
result Empirically, the method yields superior variance reduction for generative models.
Liberty or Depth: Deep Bayesian Neural Nets Do Not Need Complex Weight Posterior Approximationscs.LG
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.
Bayesian methods improve OoD detection in deep networks.
problem Detecting Out-of-Distribution (OoD) inputs in deep neural networks.
method Three Bayesian inference approaches applied to VAE weights.
result Improved OoD detection scores over benchmarks.
Variational inference approximates the posterior distribution of a probabilistic model with a parameterized density by maximizing a lower bound for the model evidence. Modern solutions fit a flexible approximation with stochastic gradient descent, using Monte Carlo approximation for the gradients. This enables variatio…
Boosting variational inference (BVI) approximates an intractable probability density by iteratively building up a mixture of simple component distributions one at a time, using techniques from sparse convex optimization to provide both computational scalability and approximation error guarantees. But the guarantees hav…
Paper presents a method to summarize HMC samples for neural networks, providing meaningful uncertainty estimates.
problem Lack of interpretable summary statistics for HMC samples in neural networks due to permutation symmetry.
method Introducing a transpositions metric to quantify permutations and using rebasin method to summarize HMC samples.
result Compact representation of HMC samples provides meaningful uncertainty estimates for each weight in a neural network.
We tackle causal inference under conditional moment restrictions using importance weighting.
problem Challenges in causal inference under conditional moment restrictions, especially in high-dimensional settings.
method Transform conditional moment restrictions to unconditional moment restrictions through importance weighting.
result Successfully estimate nonparametric functions defined under conditional moment restrictions.
Cross-validation under sample selection bias can, in principle, be done by importance-weighting the empirical risk. However, the importance-weighted risk estimator produces sub-optimal hyperparameter estimates in problem settings where large weights arise with high probability. We study its sampling variance as a funct…
Variational Laplace improves Bayesian neural networks performance.
problem Improving Bayesian neural networks performance.
method Develops variational Laplace for BNNs, exploiting curvature of likelihood.
result Variational Laplace outperforms other inference methods.
Variational Laplace improves Bayesian neural network performance without sampling.
problem Improving Bayesian neural network performance and calibration.
method Develops a new variational Laplace method for BNNs, exploiting curvature of likelihood.
result Variational Laplace outperforms standard VI methods in test performance and calibration.
Combines control variates and adaptive importance sampling for Monte Carlo integration.
problem Improving Monte Carlo integration accuracy with control variates and adaptive sampling.
method A quadrature rule combining control variates and adaptive importance sampling.
result Non-asymptotic bound on the probabilistic error of the procedure.
A new method combines VI and IS to improve Bayesian inference accuracy.
problem Bayesian inference often underestimates posterior tails, leading to miscalibration and degeneracy.
method Proposes a novel combination of optimization and sampling techniques using the forward KL divergence.
result The method guarantees asymptotic consistency and fast convergence to optimal IS and variational approximations.
Enhances mixture models with classifier-defined weights.
problem Density evaluation and sampling in mixture models.
method Introduces Classifier Weighted Mixtures (CWM) with functional weights.
result Improves expressivity in variational estimation without increasing complexity.