New particle-based VI algorithm expands function class and improves scalability.
problem Limited function class in particle-based VI algorithms restricts flexibility and scalability.
method Introduces a functional regularization term to expand the function class and proposes PFG algorithm.
result Proposed PFG algorithm has larger function class, improved scalability, better adaptation to ill-conditioned distributions, and provable convergence.
A new EVI framework improves ParVI methods by maintaining variational structure and reducing KL-divergence.
problem Improving variational inference methods for better approximation of target distributions.
method EVI framework that minimizes the VI objective function based on an energy-dissipation law, including a new 'Approximation-then-Variation' scheme.
result The new scheme significantly decreases KL-divergence and outperforms existing ParVI methods in fidelity.
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 new method for online VI in SSMs using asymptotic contrast.
problem Lack of functionality for streaming data in standard VI methods for SSMs.
method Propose maximising an IWAE-type variational lower bound on the asymptotic contrast function using stochastic approximation.
result OSIWAE allows for online learning of model parameters and latent states.
Optimal weights improve particle-based approximations of discrete distributions.
problem Improving particle-based approximations of discrete distributions.
method Proving optimality of weights and showing how to compute them efficiently.
result Optimal weights can be computed from existing particle-based methods without extra costs.
Real-life control tasks involve matters of various substances---rigid or soft bodies, liquid, gas---each with distinct physical behaviors. This poses challenges to traditional rigid-body physics engines. Particle-based simulators have been developed to model the dynamics of these complex scenes; however, relying on app…
A new ParVI framework improves particle-based variational inference methods.
problem Non-trivial kernel design in particle-based variational inference methods.
method Proposes a generalized Wasserstein gradient descent (GWG) framework with broader regularizers.
result Demonstrates strong convergence guarantees and effectiveness on simulated and real data.
PAPAL algorithm finds mixed Nash equilibria in continuous games.
problem Finding mixed Nash equilibria in non-convex, non-concave games.
method Particle-based Primal-Dual Algorithm (PAPAL) for weakly entropy-regularized min-max optimization.
result PAPAL offers non-asymptotic convergence guarantees for ε-mixed Nash equilibrium. New method for constrained sampling using gradient flows.
problem Sampling from constrained domains.
method Introducing a boundary condition for gradient flow to confine particles within the domain.
result Provable continuous-time convergence in total variation for constrained sampling.
A new method solves high-dimensional MFGs using particle-based flow matching.
problem Solving high-dimensional Mean-Field Games (MFGs) is computationally challenging.
method Proposes a particle-based deep Flow Matching (FM) method to update particles and train a flow neural network.
result Proves convergence of the scheme to a stationary point sublinearly and linearly under convexity assumptions.
BF-VI improves posterior approximation in complex models.
problem Inefficient posterior approximations in complex models.
method Combines normalizing flows and Bernstein polynomial transformations.
result BF-VI outperforms other VI methods in approximating complex multivariate posteriors.
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.
New coin sampling method for Bayesian inference without learning rates.
problem Scalable Bayesian inference with learning rate tuning issues.
method Coin sampling for gradient-based Bayesian inference.
result Comparable performance to other ParVI algorithms without learning rate tuning.
RVI accelerates encoderless VI for faster convergence.
problem Slow convergence in encoderless VI methods.
method Introduces Relay Variational Inference (RVI) for faster learning.
result RVI outperforms existing methods in convergence speed and performance.
A-VI can approximate F-VI under certain conditions, improving inference in some models.
problem Approximate Bayesian inference using factorized distributions.
method Amortized variational inference (A-VI) learns a common inference function for latent variables.
result A-VI can close the amortization gap in simple hierarchical models.
This paper reviews recent advancements in amortized Variational Inference.
problem Scalability and efficiency issues in traditional Variational Inference.
method Systematic review of various Variational Inference techniques, focusing on amortized approaches.
result Amortized Variational Inference improves scalability and efficiency for generative modeling tasks.
Automates VI divergence selection for efficient few-shot learning.
problem Efficiently selecting divergence measures for VI to improve performance.
method Meta-learning algorithm to learn optimal divergence metric and variational parameter initialization.
result Meta-learning approach outperforms standard VI methods across various tasks.
We develop a parallel variational inference (VI) procedure for use in data-distributed settings, where each machine only has access to a subset of data and runs VI independently, without communicating with other machines. This type of "embarrassingly parallel" procedure has recently been developed for MCMC inference al…
A new variational inference method using Gaussian score matching.
problem Approximating posterior distributions in Bayesian statistics.
method Score matching principle applied to variational inference.
result Gaussian score matching VI (GSM-VI) is faster and requires fewer gradient evaluations.
New algorithm trains latent diffusion models using interacting particles.
problem Training latent diffusion models efficiently and accurately.
method Reformulate training as minimizing a free energy functional, then approximate with interacting particles.
result The new algorithm outperforms previous methods in experiments.
New findings on Malgrange-Galois groupoid for Painlevé VI equation parameters.
problem Understanding transformations preserving specific forms for Painlevé VI equation.
method Computed Malgrange-Galois groupoid for Painlevé VI family with all parameters.
result Solutions of Painlevé VI do not satisfy new partial differential equations.
A new method interpolates between sampling and variational inference using stochastic mixtures.
problem Combining the strengths of sampling and variational inference methods.
method Develops a framework using stochastic mixtures of simple component distributions to interpolate between sampling and variational inference.
result Improves on both sampling and variational inference methods by reducing bias and variance.
Novel approach simplifies VI problems with faster performance.
problem Black-box VI optimization problems.
method Sample Average Approximation (SAA) combined with quasi-Newton methods and line search.
result Achieves faster performance than existing methods.
MWGraD solves multi-objective distributional optimization using particle-based gradient descent.
problem Simultaneously minimize multiple objective functionals over probability distributions.
method Iterative particle-based algorithm MWGraD, estimating and aggregating Wasserstein gradients.
result Demonstrates effectiveness on synthetic and real-world datasets.
Analyzes factors affecting flow VI performance.
problem Consistent performance of flow VI across studies.
method Step-by-step analysis of capacity, objectives, batchsize, estimators, and step-sizes.
result Specific recommendations and a flow VI recipe.
A new VIS approach improves log-likelihood estimation in latent variable models.
problem Challenges in achieving high log-likelihood with VI for complex posterior distributions.
method Uses forward χ2 divergence to optimize proposal distribution for better log-likelihood estimation. result Consistently outperforms state-of-the-art baselines in log-likelihood and parameter estimation.
Improved VI with Price's gradient estimator for target log-density.
problem Approximating target distributions from unnormalized log-densities.
method Stochastic gradient-based variational inference with Price's gradient estimator.
result Identifies Price's gradient as the key to WVI's superior performance.
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…
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.
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.
VI approximates complex densities faster than classical methods.
problem Approximating complex probability densities.
method Optimization of a family of probability density functions using KL divergence.
result VI converges faster than Markov Chain Monte Carlo.
This work proposes a new method for variational inference using Wasserstein gradient descent.
problem Optimizing variational parameters to match a true posterior distribution.
method Reinterpreting VI as an optimization problem over a variational parameter space, using Wasserstein gradient descent.
result The proposed Wasserstein gradient descent can be seen as a generalization of existing optimization techniques in VI.
New algorithms solve stochastic variational inequalities without bounded variance assumption.
problem Solving stochastic variational inequalities without bounded variance assumption.
method Developed algorithms for two classes of problems: monotone and structured nonmonotone VIs.
result Oracle complexity of O(ε^-4) for solving VIs with unbounded domains and possibly unbounded variance.
Simulation-free VI closes the approximation gap in latent SDEs
problem Recovering dynamical systems from noisy observations
method Helmholtz-SDE
result Recovers dynamics more faithfully than prior methods
This paper bridges statistical and machine learning approaches to variational inference.
problem Statisticians struggle to understand variational inference from a Frequentist perspective.
method Explains VI, VAEs, and DDMs from a Frequentist viewpoint, starting with EM.
result VI emerges as a scalable solution for intractable E-steps in VAEs and DDMs.
BSVGD improves sampling for multimodal distributions using branching.
problem Sampling from multimodal distributions.
method Random branching in Stein Variational Gradient Descent (SVGD).
result Theoretical convergence guarantee and empirical validation.
Develops possibilistic VI using maxitive Donsker-Varadhan formulation.
problem Adapting VI to possibilistic framework to handle uncertainty.
method Maxitive Donsker-Varadhan formulation for possibilistic VI.
result CBOpt optimizers achieve competitive performance in image classification.
AMF-VI uses adaptive mixtures of flows for robust VI across diverse distributions.
problem Inconsistent behavior of single-flow models across different distributions.
method Sequential expert training of individual flows and adaptive global weight estimation via likelihood-driven updates.
result AMF-VI achieves lower negative log-likelihood and stable gains in transport metrics across various posterior families.
One of the core problems of modern statistics is to approximate difficult-to-compute probability densities. This problem is especially important in Bayesian statistics, which frames all inference about unknown quantities as a calculation involving the posterior density. In this paper, we review variational inference (V…
Proposes PGPS for efficient Bayesian inference.
problem Efficient sampling from complex posterior distributions.
method Path-guided particle-based sampling with Log-weighted Shrinkage.
result PGPS generates samples closer to target distribution.
Solve Painleve VI to relate instanton bundles.
problem Relate instanton bundles to Painleve VI solutions.
method Generalize Hitchin's logarithmic connection to vector bundles with SL2 action.
result Identify Okamoto transformations as creation operators.
This paper introduces VI for physics-informed deep learning, enhancing uncertainty quantification.
problem Uncertainty quantification in physics-informed deep learning.
method Variational inference for generative and inverse problems.
result VI provides a flexible and scalable approach for physics-based inference.
Paper advances black-box VI using flows and Monte-Carlo methods.
problem Improving automatic posterior inference in black-box VI.
method Combines normalizing flows, Monte-Carlo methods, and optimization considerations.
result Significant improvement in state-of-the-art variational inference.
To obtain uncertainty estimates with real-world Bayesian deep learning models, practical inference approximations are needed. Dropout variational inference (VI) for example has been used for machine vision and medical applications, but VI can severely underestimates model uncertainty. Alpha-divergences are alternative …
New geometric insights reveal the persistence distribution in spin systems.
problem Determining the full persistence probability distribution in non-Markovian stochastic processes.
method Exact Fredholm Pfaffian structure and Painlevé VI system analysis.
result Recovery of the universal persistence exponent and its geometric interpretation.
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…
Particle-based variational inference methods (ParVIs) have gained attention in the Bayesian inference literature, for their capacity to yield flexible and accurate approximations. We explore ParVIs from the perspective of Wasserstein gradient flows, and make both theoretical and practical contributions. We unify variou…
Various standard texts on differential topology maintain that the level-preserving map defined by the track of an isotopy of embeddings is itself an embedding. This note describes a simple counterexample to this assertion.