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 approximate inference for Bayesian models.
problem Approximate inference for high-dimensional Bayesian models.
method Entropic regularization of mean-field variational inference.
result Improved recovery of true posterior dependency.
The paper studies stability of mean-field variational inference for log-concave distributions.
problem Stability of mean-field variational inference for log-concave distributions.
method Novel approach via linearized optimal transport, lifting non-convex problem to convex optimization over transport maps.
result Dimension-free Lipschitz continuity of the MFVI optimizer with respect to the target distribution, measured in 2-Wasserstein distance.
The mean field variational Bayes method is becoming increasingly popular in statistics and machine learning. Its iterative Coordinate Ascent Variational Inference algorithm has been widely applied to large scale Bayesian inference. See Blei et al. (2017) for a recent comprehensive review. Despite the popularity of the …
Beta process is the standard nonparametric Bayesian prior for latent factor model. In this paper, we derive a structured mean-field variational inference algorithm for a beta process non-negative matrix factorization (NMF) model with Poisson likelihood. Unlike the linear Gaussian model, which is well-studied in the non…
We conduct non-asymptotic analysis on the mean-field variational inference for approximating posterior distributions in complex Bayesian models that may involve latent variables. We show that the mean-field approximation to the posterior can be well-approximated relative to the Kullback-Leibler divergence discrepancy m…
Develops a new framework for analyzing MFVI algorithms.
problem Analyzes mean field variational inference (MFVI) formulations.
method Inspired by variational Bayesian formulations, represents MFVI problem in three ways: gradient flow, Fokker-Planck-like equations, and diffusion process.
result Establishes rigorous guarantees for convergence of time-discretized coordinate ascent variational inference algorithms.
The paper introduces structured variational families to improve scalability in black-box variational inference.
problem Scalability issues in black-box variational inference, especially for large datasets and hierarchical models.
method Developed structured variational families that achieve better iteration complexity of O(N) compared to full-rank families.
result Structured variational families can achieve better scaling with respect to dataset size N, improving iteration complexity from O(N^2) to O(N).
We develop a general variational inference method that preserves dependency among the latent variables. Our method uses copulas to augment the families of distributions used in mean-field and structured approximations. Copulas model the dependency that is not captured by the original variational distribution, and thus …
New method for variational inference without conjugacy constraints.
problem Efficient variational inference with flexible prior and approximation families.
method Wasserstein gradient flow for mean-field approximation.
result Improved convergence and efficiency of variational inference.
Mean-field variational methods are widely used for approximate posterior inference in many probabilistic models. In a typical application, mean-field methods approximately compute the posterior with a coordinate-ascent optimization algorithm. When the model is conditionally conjugate, the coordinate updates are easily …
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.
New algorithm speeds up large-scale statistical inference.
problem Efficiently solving large-scale mean-field variational inference problems.
method Developed a novel primal-dual algorithm (PD-VI) and a block-preconditioned extension (P2D-VI) for mean-field variational inference. result PD-VI and P2D-VI achieve faster convergence and better solution quality compared to existing methods. 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.
Many modern unsupervised or semi-supervised machine learning algorithms rely on Bayesian probabilistic models. These models are usually intractable and thus require approximate inference. Variational inference (VI) lets us approximate a high-dimensional Bayesian posterior with a simpler variational distribution by solv…
This work introduces a fixed-point optimization for variational inference.
problem Improving quantified uncertainty in predictions by optimizing a simplified distribution over parameters.
method Projective integral updates for high-dimensional variational inference.
result Efficient quasirandom quadrature sequence for mean-field distributions, leading to quasi-Newton variational Bayes (QNVB).
We challenge the longstanding assumption that the mean-field approximation for variational inference in Bayesian neural networks is severely restrictive, and show this is not the case in deep networks. We prove several results indicating that deep mean-field variational weight posteriors can induce similar distribution…
MFVI mode collapse explained; RoVI proposed to mitigate.
problem Mode collapse in MFVI for mixture distributions.
method Introducing ε-separateness, deriving bounds, proposing RoVI.
result MFVI optimizers collapse to a single component when components are ε-separated.
Bayesian model selection via mean-field variational approximation improves efficiency and accuracy.
problem Bayesian model selection under model mis-specification and latent variables.
method Mean-field variational approximation with non-asymptotic properties and geometric convergence.
result ELBO tends to select models closer to the true model than BIC as sample size increases.
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.
An autonomous variational inference algorithm for arbitrary graphical models requires the ability to optimize variational approximations over the space of model parameters as well as over the choice of tractable families used for the variational approximation. In this paper, we present a novel combination of graph part…
Develops methods for structured variational inference with star-structured models.
problem Inference in models with interdependent variables.
method Star-structured variational inference, existence, uniqueness, self-consistency proofs, approximation error bounds, gradient-based algorithm.
result First results for existence, uniqueness, and self-consistency of variational approximations in star-structured models.
Rotates MFVI for better Gaussian approximations.
problem Improving variational approximations for complex distributions.
method Rotated coordinate system, PCA-based rotation, iterative Gaussianization.
result Significantly more accurate approximations with lower computational cost.
Ensemble Kalman Filter improves GPSSM inference for online learning.
problem Non-mean-field variational inference issues in GPSSM.
method Combining EnKF with NMF variational inference.
result Improved online learning performance and data-fitting accuracy.
A tutorial on variational inference for high-dimensional models.
problem Approximating marginal likelihood and posterior in Bayesian models.
method Parametric approach to variational inference.
result Variational inference is now preferred for high-dimensional models and large datasets.
Improved Bayesian uncertainty quantification using variational bagging.
problem Inefficient and underestimating uncertainty in mean-field variational Bayes.
method Integrates bagging with variational Bayes for improved inference.
result Bagged variational posterior provides proper uncertainty quantification.
This paper analyzes MFVBI for GMM using statistical mechanics.
problem Approximate fast computation of Gaussian Mixture Model.
method Statistical mechanics and MFVBI applied to GMM.
result Rigorous analysis and mathematical foundation for MFVBI applied to GMM.
A scalable method for accurate inference of low-dimensional parameters in high-dimensional linear regression.
problem Statistical inference for low-dimensional parameters in high-dimensional linear regression models.
method Mean-field variational Bayes approach, focusing on nuisance parameters and conditional distributions.
result Competitive numerical performance and theoretical guarantees for estimation and uncertainty quantification.
Wide BNNs with odd activations fail to approximate data under mean-field inference.
problem Theoretical limitations of mean-field variational inference in wide, deep Bayesian neural networks.
method Analysis of mean-field variational inference in fully-connected BNNs with odd activation functions and Gaussian likelihood.
result The optimal mean-field variational posterior predictive distribution converges to the prior predictive distribution as network width increases.
BBVI converges nearly dimensionally independent for log-concave targets.
problem Efficiently optimizing variational parameters in high-dimensional spaces.
method Proved convergence rate of BBVI with reparametrization gradient for log-concave targets.
result BBVI converges with nearly independent dimension dependence for log-concave targets.
The mean field methods, which entail approximating intractable probability distributions variationally with distributions from a tractable family, enjoy high efficiency, guaranteed convergence, and provide lower bounds on the true likelihood. But due to requirement for model-specific derivation of the optimization equa…
We derive streamlined mean field variational Bayes algorithms for fitting linear mixed models with crossed random effects. In the most general situation, where the dimensions of the crossed groups are arbitrarily large, streamlining is hindered by lack of sparseness in the underlying least squares system. Because of th…
New method improves uncertainty estimation in complex statistical models.
problem Challenges in estimating high-dimensional mixed models due to computational complexity.
method Partially factorized variational inference to relax mean-field assumption.
result Relaxed variational inference provides accurate uncertainty quantification without high computational cost.
Study shows TAP free energy minimization provides better posterior inference in high-dimensional linear models.
problem Deviation from true posterior mean and underestimation of posterior uncertainty in variational inference.
method Minimization of TAP free energy in a high-dimensional asymptotic framework, showing geometric and statistical properties.
result Local minimizer of TAP free energy provides consistent estimate of posterior marginals and correctly calibrated posterior inference.
Variational Bayesian Inference is a popular methodology for approximating posterior distributions over Bayesian neural network weights. Recent work developing this class of methods has explored ever richer parameterizations of the approximate posterior in the hope of improving performance. In contrast, here we share a …
CAVI converges for log-concave measures via optimal transport.
problem Finding the closest product measure to a log-concave measure via CAVI.
method Adapting coordinate descent techniques from Euclidean space to optimal transport for log-concave densities.
result Proves convergence of CAVI for log-concave densities and provides rates of convergence under additional conditions.
Optimizes variational inference for dynamic network models.
problem Estimating pairwise inner products and intercepts in dynamic latent space models.
method Structured mean-field variational inference with block coordinate ascent algorithm.
result Variational risk attains minimax optimal rate with logarithmic factor under certain conditions.
New method for high-dimensional linear regression using empirical Bayes.
problem Estimating prior in high-dimensional linear regression.
method Variational empirical Bayes approach with NPMLE and mean field approximation.
result Established asymptotic consistency and computational efficiency of the method.
A mean field variational Bayes approach to support vector machines (SVMs) using the latent variable representation on Polson & Scott (2012) is presented. This representation allows circumvention of many of the shortcomings associated with classical SVMs including automatic penalty parameter selection, the ability to ha…
Improves variational inference for sparse models using mixtures of exponential families.
problem Intractability of posterior distributions in Bayesian sparse models.
method Flexible mean field variational inference using mixtures of non-overlapping exponential families.
result Mixtures of exponential families with non-overlapping support form an exponential family, enabling analytical updates.
New bounds show BBVI's gradient variance matches SGD conditions, improving parameterization efficiency.
problem Understanding and improving the convergence of black-box variational inference (BBVI).
method Showed BBVI satisfies matching gradient variance bounds corresponding to the ABC condition for smooth and quadratically-growing log-likelihoods.
result Proven BBVI's gradient variance matches SGD conditions, with superior dimensional dependence for mean-field parameterization.
Dynamic trees are mixtures of tree structured belief networks. They solve some of the problems of fixed tree networks at the cost of making exact inference intractable. For this reason approximate methods such as sampling or mean field approaches have been used. However, mean field approximations assume a factorized di…
We present a general method for deriving collapsed variational inference algo- rithms for probabilistic models in the conjugate exponential family. Our method unifies many existing approaches to collapsed variational inference. Our collapsed variational inference leads to a new lower bound on the marginal likelihood. W…
I propose a variational approach to maximum pseudolikelihood inference of the Ising model. The variational algorithm is more computationally efficient, and does a better job predicting out-of-sample correlations than L2 regularized maximum pseudolikelihood inference as well as mean field and isolated spin pair appro…
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 present a new algorithm for approximate inference in probabilistic programs, based on a stochastic gradient for variational programs. This method is efficient without restrictions on the probabilistic program; it is particularly practical for distributions which are not analytically tractable, including highly struc…
DADVI improves ADVI by using deterministic approximation for faster, more accurate posterior estimation.
problem Intractable posterior uncertainty estimates and lack of clear convergence criteria in ADVI.
method Replaces stochastic MFVB objective with deterministic Monte Carlo approximation (SAA) and uses second-order optimization.
result DADVI provides faster and more accurate posterior estimates with default settings.
Paper optimizes approximating high-dimensional diffusions by independent coordinates.
problem Optimizing approximations of high-dimensional diffusions by independent coordinates.
method Introduces independent projection as optimal for two criteria.
result Independent projection is optimal for two criteria related to entropy and convergence.