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.
A spiking neural network model for probabilistic inference of binary Markov random fields.
problem Implementing probabilistic inference in spiking neural networks.
method Designing a spiking recurrent neural network and proving its equivalence to mean-field inference of binary Markov random fields.
result The spiking neural network model can implement inference of arbitrary binary Markov random fields.
The mean field algorithm is a widely used approximate inference algorithm for graphical models whose exact inference is intractable. In each iteration of mean field, the approximate marginals for each variable are updated by getting information from the neighbors. This process can be equivalently converted into a feedf…
Study shows mean field method's effectiveness in community detection.
problem Theoretical and practical guarantees for community detection using mean field variational inference.
method Iterative Coordinate Ascent Variational Inference algorithm for the Stochastic Block Model.
result The algorithm converges linearly to the minimax rate within log n iterations.
New algorithm improves mean field inference in probabilistic models.
problem Improving mean field inference in probabilistic models.
method DR-DoubleGreedy algorithm for continuous DR-submodular maximization with box-constraints.
result Achieves optimal 1/2 approximation ratio for continuous DR-submodular maximization.
Mean field Gaussian inference limits mutual information to regularize neural networks.
problem Understanding and quantifying the regularization effect of mean field Gaussian inference.
method Empirically observed and theoretically quantified mutual information limitation through noise.
result Bounding mutual information between parameters and data effectively regularizes neural networks.
Review of mean-field methods for neural network inference.
problem Understanding neural network learning from a theoretical perspective.
method Mean-field methods, high-temperature expansions, replica method, message passing algorithms.
result Equivalences and complementarities of mean-field methods.
The paper analyzes mean-field variational Bayes for complex models and proposes new uncertainty quantification methods.
problem Approximating posterior distributions in complex Bayesian models with latent variables.
method Non-asymptotic analysis on mean-field variational inference, showing that a normal distribution with the MLE center approximates the posterior well.
result The mean-field approximation matches the MLE up to higher-order terms and is essentially efficient for regular parametric models.
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.
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.
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…
New algorithm improves CRF inference and learning.
problem Efficient inference and learning for dense CRFs.
method Regularized Frank-Wolfe algorithm for nonconvex CRF optimization.
result Regularized Frank-Wolfe outperforms mean field and CNN baselines.
CoRMF uses RNNs to solve Ising models efficiently by ordering critical edges.
problem Solving Ising models efficiently and accurately.
method Criticality-ordered spin sequence and RNNs for mean-field factorization.
result Proves tighter error bounds than naive mean-field.
ALO-CV approximates leave-one-out error in proportional regime.
problem Estimating generalization error in high-dimensional settings.
method Developed new analysis for ALO-CV, showed consistency under strong convexity.
result ALO-CV approximates leave-one-out error up to negligible error.
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.
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.
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.
Study shows mean-field approximation fails to improve PAC-Bayes bounds for neural networks.
problem Understanding why overparametrized neural networks achieve low risk and zero empirical risk.
method Optimized PAC-Bayes bounds using variational inference (VI), investigating mean-field approximation.
result Mean-field approximation does not provide significant improvements in PAC-Bayes bounds for neural networks.
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…
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.
Nonnegative Boltzmann machines (NNBMs) are recurrent probabilistic neural network models that can describe multi-modal nonnegative data. NNBMs form rectified Gaussian distributions that appear in biological neural network models, positive matrix factorization, nonnegative matrix factorization, and so on. In this paper,…
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.
A Gaussian restricted Boltzmann machine (GRBM) is a Boltzmann machine defined on a bipartite graph and is an extension of usual restricted Boltzmann machines. A GRBM consists of two different layers: a visible layer composed of continuous visible variables and a hidden layer composed of discrete hidden variables. In th…
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 …
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 …
New method infers population dynamics from snapshots using path space optimization.
problem Recover dynamics of a population from its temporal marginals.
method Grid-free algorithm using Schrödinger bridges coupled via noisy gradient descent in mean-field limit.
result Global convergence to min-entropy estimator with end-to-end theoretical guarantees.
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.
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.
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. 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…
The paper offers streamlined algorithms for fitting complex linear mixed models.
problem Linear mixed models with crossed random effects in large dimensions.
method Mean field variational Bayes algorithms with various relaxations and storage strategies.
result Different inference strategies have varying trade-offs between accuracy and computational demands.
Compact parameterization improves Bayesian neural network performance.
problem Improving performance of Bayesian neural networks using variational methods.
method Restricting variational distribution to a k-tied Normal distribution with low-rank factorization.
result Compact parameterization improves signal-to-noise ratio and convergence speed.
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.
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).
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).
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.
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 new method eliminates miscalibration in Gaussian process models for dynamical systems.
problem Miscalibration and overestimation of transition function parameters in Gaussian process models.
method Explicitly models the dependence between state trajectories and Gaussian process posterior, eliminating factorization.
result Better predictive performance and more calibrated estimates of the transition function.
Inference of hidden classes in stochastic block model is a classical problem with important applications. Most commonly used methods for this problem involve naïve mean field approaches or heuristic spectral methods. Recently, belief propagation was proposed for this problem. In this contribution we perform a comparati…
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.
Variational inference simplifies Bayesian model approximations.
problem Approximating complex Bayesian posterior distributions.
method Solving optimization problems to approximate posterior distributions with simpler variational distributions.
result Variational inference has been successfully applied in various models and large-scale applications.
MGVI improves variational inference by accounting for correlations without mean-field simplifications.
problem Approximating Bayesian inference problems with variational methods, especially for high-dimensional models.
method Metric Gaussian Variational Inference (MGVI) iteratively approximates the posterior with Gaussian distributions, optimizing the KL-divergence and using natural gradient descent.
result MGVI achieves higher accuracy and significant speedup compared to traditional methods, scaling linearly in computational time and memory.
Unified theory for deep and recurrent networks using Gaussian processes.
problem Understanding capabilities and limitations of different network architectures.
method Unified derivation of mean-field theory from statistical physics of disordered systems.
result Gaussian processes yield identical Gaussian kernels for both architectures at a single time point or layer.
The paper models asset pricing in a partially observed market using mean field game theory and exponential quadratic Gaussian framework.
problem Asset pricing in a market with partial observation and heterogeneous agents.
method Mean field game theory, exponential quadratic Gaussian framework, Kalman-Bucy filtering theory.
result Characterization of equilibrium risk premium through mean field BSDE and construction of unobservable risk premium process.
Non-linear image reconstruction and signal analysis deal with complex inverse problems. To tackle such problems in a systematic way, I present information field theory (IFT) as a means of Bayesian, data based inference on spatially distributed signal fields. IFT is a statistical field theory, which permits the construc…
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.
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.
Reparameterization trick yields more accurate gradient estimates in variational inference.
problem Improving gradient estimates in variational inference.
method Idealized analysis of mean-field Gaussian approximations and quadratic log densities.
result Marginal variances of reparameterization gradient are smaller than score function gradient.