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 method speeds up optimization over probability measures.
problem High computational overhead in optimizing probability measures.
method Randomized coordinate descent on Wasserstein space.
result Significant speedups over full-gradient methods.
The paper analyzes rates for a modified gradient descent method using Stein variational gradients.
problem Improving the accuracy of gradient descent methods for complex target distributions.
method Derives finite-particle rates for regularized Stein variational gradient descent (R-SVGD).
result Establishes explicit non-asymptotic bounds for time-averaged empirical measures.
Error estimates found between SGD with momentum and Langevin diffusion.
problem Quantifying the difference between SGD with momentum and Langevin diffusion.
method Established error estimates using 1-Wasserstein and total variation distances.
result Quantitative error estimates between SGD with momentum and underdamped Langevin diffusion.
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.
A new method for Bayesian inference tackles high-dimensional problems.
problem Bayesian inference in high-dimensional settings with kernel density estimation issues.
method Projected Wasserstein gradient descent (pWGD) method to overcome curse of dimensionality.
result pWGD method effectively addresses high-dimensional Bayesian inference problems.
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.
We study the Wasserstein natural gradient in parametric statistical models with continuous sample spaces. Our approach is to pull back the L2-Wasserstein metric tensor in the probability density space to a parameter space, equipping the latter with a positive definite metric tensor, under which it becomes a Riemanni…
A new stochastic algorithm approximates optimal distributions without requiring propagation of chaos.
problem Optimizing functionals over probability distributions using finite particle systems.
method Virtual particle stochastic approximation, viewed as a form of stochastic gradient descent in the Wasserstein space.
result The algorithm's output converges to the optimal distribution and produces i.i.d. samples.
KSD Descent uses KSD to sample from a target distribution efficiently.
problem Sampling from complex target distributions efficiently.
method Wasserstein gradient flow of KSD, using L-BFGS optimization.
result KSD Descent can sample from a target distribution using a set of particles.
New algorithm approximates continuous Wasserstein barycenters efficiently.
problem Computing Wasserstein barycenters for continuous distributions.
method Stochastic algorithm using dual potentials and stochastic gradient descent.
result Efficient online approximation of continuous Wasserstein barycenters.
New algorithm for fitting Gaussian mixtures using Wasserstein-Fisher-Rao geometry.
problem Hard problem of fitting Gaussian mixture models to data computationally.
method Gradient descent over Wasserstein-Fisher-Rao geometry for probability measures.
result Established convergence guarantees for the proposed algorithm.
Improved convergence rates for Stein Variational Gradient Descent in finite-particle settings.
problem Improving convergence rates for Stein Variational Gradient Descent in finite-particle settings.
method Analyzing the time derivative of relative entropy and splitting it into dominant and smaller parts.
result Finite-particle convergence rates of order 1/\sqrt{N} for Kernelized Stein Discrepancy and Wasserstein-2 metrics.
Paper analyzes convergence of proximal algorithm in metric spaces without geodesic convexity.
problem Analyzing convergence of proximal algorithm in general metric spaces.
method Analysis of the Wasserstein proximal algorithm without geodesic convexity assumption.
result Establishes unbiased and linear convergence rate for proximal algorithm under natural Wasserstein inequality.
SGD handles label noise with bounds improving over SGLD.
problem Label noise in non-convex optimization.
method Stochastic gradient descent with uniform dissipativity and smoothness conditions, using Wasserstein distance and algorithmic stability.
result Generalization error bounds with a rate of n−2/3, better than SGLD's n−1/2. Improved sampling method using regularized Stein Variational Gradient Flow.
problem Improving the accuracy of sampling methods in machine learning.
method Proposed Regularized Stein Variational Gradient Flow to interpolate between SVGD and Wasserstein Gradient Flow.
result Established theoretical properties and provided preliminary numerical evidence of improved performance.
This paper analyzes neural networks for solving complex optimization problems.
problem Minimax optimization problems in infinite-dimensional function spaces.
method Mean-field analysis of stochastic gradient descent-ascent in neural networks.
result The algorithm converges to a stationary point at a sublinear rate.
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.
New bounds for M-SGD show its error distribution is nearly Gaussian.
problem Understanding the error distribution of M-SGD.
method Proved non-asymptotic bounds for M-SGD in Wasserstein distance.
result Error distribution of M-SGD is approximately Gaussian.
New method estimates rate-distortion function using optimal transport.
problem Estimating the fundamental performance limit of data compression.
method Wasserstein gradient descent to learn optimal reproduction distribution.
result Local convergence and sample complexity analysis of R-D estimator.
ASVGD accelerates SVGD for efficient sampling.
problem Slow SVGD in high-dimensional sampling.
method Accelerated gradient flow in a metric space of probability densities, using Nesterov's method and momentum-based updates.
result ASVGD outperforms SVGD and other methods in sampling efficiency.
Generative adversarial networks (GANs) are a widely used framework for learning generative models. Wasserstein GANs (WGANs), one of the most successful variants of GANs, require solving a minmax optimization problem to global optimality, but are in practice successfully trained using stochastic gradient descent-ascent.…
Proposes a new algorithm for robust learning in Schrödinger bridge problems.
problem Uncertainty in estimated learning signals in Schrödinger bridge problems.
method Variational Online Mirror Descent (OMD) framework for Schrödinger bridge problems.
result Formally proves convergence and a regret bound for the OMD formulation of Schrödinger bridge acquisition.
We develop a progressive training approach for neural networks which adaptively grows the network structure by splitting existing neurons to multiple off-springs. By leveraging a functional steepest descent idea, we derive a simple criterion for deciding the best subset of neurons to split and a splitting gradient for …
Improved stability for matrix recovery from rank-one measurements.
problem Phase retrieval problem of recovering rank-one positive semidefinite matrices.
method Developed a smoothing Newton method based on Bures-Wasserstein gradient descent.
result Superlinear convergence with rigorous guarantees and stable implementation.
A new method for learning gradient flows from population dynamics.
problem Reconstructing population dynamics from limited data.
method Residual approach to enforce continuity equations, combining with data-fitting divergence.
result Demonstrated state-of-the-art performance across trajectory inference benchmarks.
Wasserstein framework solves mixed linear regression problems.
problem Mixed linear regression with multi-modal distributions.
method Wasserstein distance minimization for nonconvex-concave minimax optimization.
result WMLR achieves global convergence and generalization guarantees for two linear models.
Study on deep matrix factorization with Bures-Wasserstein loss, focusing on critical points and convergence.
problem Analyzing critical points and convergence of generative deep linear networks trained with Bures-Wasserstein loss.
method Characterization of critical points and minimizers of Bures-Wasserstein distance, analysis of Hessian at low-rank matrices, convergence results for gradient flow and descent.
result Established convergence results for gradient flow and finite step size gradient descent under certain assumptions.
This work finds mixed equilibria in machine learning problems using measures and simultaneous gradient ascent-descent.
problem Finding pure equilibria in machine learning problems is computationally hard.
method Entropic regularization, simultaneous gradient ascent-descent, and particle discretization in the Wasserstein metric.
result Global convergence towards the global equilibrium in mixed equilibria problems.
Wasserstein gradient flows are continuous time dynamics that define curves of steepest descent to minimize an objective function over the space of probability measures (i.e., the Wasserstein space). This objective is typically a divergence w.r.t. a fixed target distribution. In recent years, these continuous time dynam…
Paper introduces a differentially private generative model using gradient flow and sliced Wasserstein distance.
problem Protecting privacy in sensitive training data for generative models.
method Gradient flow in the space of probability measures, Gaussian-smoothed Sliced Wasserstein Distance, and numerical scheme for SDE.
result Demonstrates higher-fidelity data generation at low privacy budget compared to existing methods.
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.
The paper provides convergence bounds for approximating a distribution using point clouds.
problem Approximating a distribution using discrete points with minimal Wasserstein distance.
method Lloyd's algorithm with Power cells, analyzed using gradient descent.
result Explicit upper bounds for the convergence speed of the Lloyd-type algorithm.
A new gradient flow framework for distributionally robust optimization.
problem Optimizing under uncertainty with worst-case distributional constraints.
method Gradient flow theory applied to distributionally robust optimization.
result Practical algorithms for sampling from worst-case distributions.
The paper studies properties of Sliced Wasserstein energy for discrete measures.
problem Optimizing discrete probability measures using Sliced Wasserstein loss.
method Investigates the regularity and optimisation properties of the Sliced Wasserstein energy and its Monte-Carlo approximation.
result Convergence results on the critical points of Monte-Carlo approximations to the Sliced Wasserstein energy.
New algorithm accelerates optimization on Riemannian manifolds, including Wasserstein space.
problem Accelerating optimization methods in Riemannian geometry.
method Dynamic stepsize algorithms on Riemannian manifolds with specific vector transport.
result First provable accelerated gradient method in Wasserstein space.
Uniform-in-time analysis for Stein Variational Gradient Descent across various metrics.
problem Understanding long-term behavior of finite-particle systems in relation to their mean-field limits.
method Developed uniform-in-time propagation-of-chaos results for continuous-time SVGD using cutoff strategies and finite-dimensional theories.
result Uniform-in-time propagation-of-chaos bounds in various metrics, including Langevin kernel Stein discrepancy, Wasserstein-1, and Wasserstein-2 distances.
Flow-based models generate data with improved theoretical guarantees.
problem Theoretical analysis of flow-based generative models.
method Proximal gradient descent in Wasserstein space for JKO flow model.
result KL guarantee of data generation by JKO flow model is O(ε2). Analyzed a generative model framework through Wasserstein Gradient Flow.
problem Generative modeling challenges.
method Wasserstein Gradient Flow (WGF) interpretation of Drifting Models (GMD).
result Different algorithms correspond to specific limiting points of WGFs on various divergences.
A new method for fast optimal transport using sliced Wasserstein generalized geodesics.
problem Computing optimal transport distances efficiently and accurately.
method Proposes a new proxy of squared Wasserstein distance based on one-dimensional projections.
result min-SWGG is an upper bound of Wasserstein distance with similar computational complexity.
We provide theoretical complexity analysis for new algorithms to compute the optimal transport (OT) distance between two discrete probability distributions, and demonstrate their favorable practical performance over state-of-art primal-dual algorithms and their capability in solving other problems in large-scale, such …
Proof of convergence for multi-objective optimization using inverse reinforcement learning.
problem Proving convergence in multi-objective optimization problems.
method Wasserstein inverse reinforcement learning with projective subgradient method and gradient descent.
result Convergence of inverse reinforcement learning for multi-objective optimization.
A new method de-randomizes MCMC dynamics using the Stein operator.
problem Estimating complex target distributions in Bayesian inference.
method De-randomized kernel-based particle samplers that discretize the fiber-gradient Hamiltonian flow.
result GSVGD de-randomizes complex MCMC dynamics, maintaining high sample quality.
New findings on optimal transport gradient for generative models, addressing numerical instabilities.
problem Numerical instabilities in training Wasserstein Generative Adversarial Networks (WGAN).
method Valid differentiation theorem for entropic regularized transport, semi-discrete gradient formulation, and optimization algorithm.
result Existence of optimal transport gradient for generative models under specified conditions.
The paper analyzes SGD with Richardson-Romberg extrapolation for convex optimization problems.
problem Solving strongly convex and smooth minimization problems efficiently.
method Combining SGD with Polyak-Ruppert averaging and Richardson-Romberg extrapolation.
result An expansion of the mean-squared error of the estimator with respect to the number of iterations.
New gradient flows improve high-dimensional sampling.
problem Sampling from high-dimensional target densities.
method Introducing Radon--Wasserstein gradient flows.
result Linear scaling in particles and dimensions.
Paper analyzes convergence rates of mean-field SVGD method.
problem Establishing quantitative rates of convergence for mean-field SVGD.
method Quantitative analysis of mean-field SVGD dynamics on torus.
result Explicit polynomial convergence rates in L2-norm for Riesz-type kernels.
Despite the growing prominence of generative adversarial networks (GANs), optimization in GANs is still a poorly understood topic. In this paper, we analyze the "gradient descent" form of GAN optimization i.e., the natural setting where we simultaneously take small gradient steps in both generator and discriminator par…