New method improves convergence and reduces variance in noisy optimization problems.
problem Computing exact minimizers with noisy gradient information.
method Stochastic mirror descent with interacting particles.
result Interaction helps improve convergence and reduce variance.
This paper optimizes functions of probability measures using particle gradient descent for displacement convex functions.
problem Optimizing functions of probability measures with displacement convex properties.
method Particle gradient descent applied to displacement convex functions with theoretical guarantees.
result Finite number of particles and computations are sufficient to find optimal solutions for displacement convex functions.
Algorithm generates private continuous-time data for sensitive domains.
problem Private generation of continuous-time data for sensitive domains.
method Mean-field Langevin dynamics and noisy particle gradient descent.
result Strong privacy guarantees for one-time data contributions.
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.
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.
SVGD algorithm converges at rate 1/sqrt(log log n) for sub-Gaussian distributions.
problem Approximating a probability distribution with particles.
method Stein variational gradient descent (SVGD) with finite particles and sub-Gaussian target distribution.
result SVGD achieves a convergence rate of 1/sqrt(log log n) for sub-Gaussian distributions.
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.
Improves SVGD for high-dimensional Bayesian inference by reducing variance collapse.
problem Variance collapse in SVGD reduces accuracy and diversity of estimation.
method Augmented Message Passing SVGD (AUMP-SVGD) method, a two-stage optimization procedure.
result AUMP-SVGD achieves satisfactory accuracy and overcomes variance collapse in various benchmark problems.
Improved particle approximation for mean-field neural networks.
problem Particle approximation error for mean-field neural networks.
method Improved particle approximation error by leveraging the problem structure in risk minimization.
result Established an LSI-constant-free particle approximation error concerning the objective gap.
Improved convergence rates for MFLD in various gradient estimators.
problem Proving convergence rates for mean-field Langevin dynamics with stochastic gradient updates.
method General framework for propagation of chaos, including finite-particle approximation, time-discretization, and stochastic gradient approximation.
result Improved convergence rates for SGD and SVRG settings.
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 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 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.
Study on privacy leakage in noisy gradient descent algorithms.
problem Information leakage of iterative randomized learning algorithms about training data.
method Analyzes the dynamics of Rényi differential privacy loss in noisy gradient descent algorithms.
result Privacy loss converges exponentially fast for smooth and strongly convex loss functions.
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.
We consider the behavior of gradient flow and of discrete and noisy gradient descent. It is commonly noted that the addition of noise to the process of discrete gradient descent can affect the trajectory of gradient descent. In previous work, we observed such effects. There, we considered the case where the minima had …
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 explores SVGD for Bayesian inference, linking deterministic and stochastic dynamics.
problem Bayesian inference and Markov chain Monte Carlo methods.
method Stein variational gradient descent (SVGD) with deterministic and stochastic dynamics.
result Identifies Stein-Fisher information as the leading order contribution in the long-time and many-particle regime.
AGNES accelerates gradient descent with noisy gradients.
problem Minimizing smooth convex and strongly convex functions with noisy gradients.
method Generalization of Nesterov's accelerated gradient descent algorithm for noisy conditions.
result AGNES achieves acceleration for noisy gradients with a constant of proportionality up to 1.
Paper analyzes SVGD algorithm for non-asymptotic convergence.
problem Optimizing a set of particles to approximate a target probability distribution.
method Finite time analysis of SVGD algorithm, providing descent lemma and convergence rates.
result SVGD algorithm decreases the objective at each iteration and converges to the target distribution.
A new algorithm solves sparse optimization problems on measures efficiently.
problem Sparse optimization problems on measures.
method Over-parameterized Stochastic Gradient Descent with Random Features.
result Global convergence with rate O ( log ( K ) / K ) O(\log(K)/\sqrt{K}) O ( log ( K ) / K ) and bounded total variation norms. We study an interacting particle system in R d \mathbf{R}^d R d motivated by Stein variational gradient descent [Q. Liu and D. Wang, NIPS 2016], a deterministic algorithm for sampling from a given probability density with unknown normalization. We prove that in the large particle limit the empirical measure of the particle s…
FS&P uses birth-death process to ensure global convergence of stochastic conic particle gradient descent.
problem Global optimization of non-convex objective functions over measure space.
method Introduces Fast Spawn\&Prune (FS\&P) combining CPGD with birth-death process.
result First theoretical guarantee of global convergence for discrete-time stochastic algorithms.
New particle algorithms optimize latent variable models.
problem Optimizing latent variable models for maximum likelihood estimation.
method Identify gradient flows associated with free energy functional and discretize them to create particle-based algorithms.
result Novel particle algorithms scale to high-dimensional settings and perform well in experiments.
A new model for generating point processes with complex geometries.
problem Difficulties in modeling point processes with large numbers of particles and complex geometries.
method Gradient descent algorithm applied to a phase harmonic operator on wavelet transforms of point patterns.
result The model allows for fast sampling of new configurations that match the statistics of observed point processes.
DSVGD improves federated learning with fewer communication rounds.
problem Federated learning scalability and trustworthiness.
method Distributed Stein Variational Gradient Descent (DSVGD) for non-parametric Bayesian inference.
result DSVGD achieves comparable accuracy and scalability to other methods, with well-calibrated predictions.
Preconditioned non-convex gradient descent improves noisy matrix estimation.
problem Estimating low-rank matrices from noisy measurements.
method Preconditioned non-convex gradient descent for noisy measurements.
result Preconditioned method converges to minimax optimal estimate at a linear rate.
Deep learning with noisy gradient descent outperforms linear estimators in high dimensions.
problem Theoretical explanation of deep learning's superiority over linear methods.
method Theoretical analysis of excess risk of a deep learning estimator trained by noisy gradient descent.
result Deep learning achieves a faster learning rate than linear estimators, especially in high dimensions.
In this note, we observe the behavior of gradient flow and discrete and noisy gradient descent in some simple settings. It is commonly noted that addition of noise to gradient descent can affect the trajectory of gradient descent. Here, we run some computer experiments for gradient descent on some simple functions, and…
Improved PoC for MFLD reduces approximation error and provides model ensemble guarantees.
problem Quantifying optimization complexity in mean-field Langevin dynamics.
method Refined defective log-Sobolev inequality for neural network training.
result Improved PoC result with reduced approximation error and theoretical model ensemble guarantees.
Many tasks in machine learning and signal processing can be solved by minimizing a convex function of a measure. This includes sparse spikes deconvolution or training a neural network with a single hidden layer. For these problems, we study a simple minimization method: the unknown measure is discretized into a mixture…
CBO interprets as SGD, leading to global convergence for nonconvex functions.
problem Understanding and improving gradient-based learning algorithms.
method Interpreting CBO as a stochastic relaxation of SGD.
result CBO provably converges globally to minimizers for nonsmooth nonconvex functions.
Paper studies convergence of Mean-Field GDA dynamics for MNE of continuous games.
problem Finding mixed Nash equilibria in continuous games.
method Two-scale Mean-Field Gradient Descent Ascent dynamics.
result Two-scale Mean-Field GDA converges exponentially to MNE without convexity assumptions.
MT-SGD samples from multiple target distributions using gradient descent.
problem Sampling from multiple unnormalized target distributions.
method Proposes MT-SGD, a flow of intermediate distributions to sample from multiple target distributions.
result Asymptotic analysis shows MT-SGD reduces to multiple-gradient descent for multi-objective optimization.
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.
We propose in this work RBM-SVGD, a stochastic version of Stein Variational Gradient Descent (SVGD) method for efficiently sampling from a given probability measure and thus useful for Bayesian inference. The method is to apply the Random Batch Method (RBM) for interacting particle systems proposed by Jin et al to the …
Paper proposes LSVGD to stabilize GAN training via Langevin Stein Variational Gradient Descent.
problem Mode collapse and performance deterioration in GAN training.
method Langevin Stein Variational Gradient Descent (LSVGD) incorporating noise to stabilize training.
result LSVGD improves performance and stability of various GAN models.
Neural networks can interpolate noisy data and still generalize well.
problem Generalization of neural networks trained on noisy data.
method Two-layer neural networks trained to interpolation by gradient descent on corrupted labels.
result Neural networks can achieve zero training error and optimal test error.
Stein variational gradient descent (SVGD) is a recently proposed particle-based Bayesian inference method, which has attracted a lot of interest due to its remarkable approximation ability and particle efficiency compared to traditional variational inference and Markov Chain Monte Carlo methods. However, we observed th…
Gaussian-SVGD dynamics converge to Gaussian distributions under certain conditions.
problem Understanding the theoretical properties of SVGD, especially for Gaussian targets.
method Detailed theoretical study of Gaussian-SVGD dynamics, considering both mean-field PDE and discrete particle systems.
result Gaussian-SVGD dynamics converge linearly to the Gaussian distribution closest to the target in KL divergence.
A new algorithm learns model regimes and parameters efficiently.
problem Learning high-dimensional parameters with discontinuous jumps.
method Differentiable interacting multiple model particle filter with gradient descent.
result Superior numerical performance compared to previous methods.
FGD reduces noisy gradient variance in SGD for neural networks.
problem Noisy and unreliable gradient estimation in SGD for deep learning.
method Solves an adaptive filtering problem to consistently estimate the local gradient.
result Significantly reduces gradient variance and accelerates convergence.
USD algorithm transports distributions with or without mass conservation.
problem Transporting distributions with different masses.
method Particle descent algorithm using Sobolev-Fisher discrepancy.
result USD converges to target distribution in MMD sense.
SIFG uses noisy particles to efficiently sample from complex distributions.
problem Efficient sampling from complex distributions using particle-based methods.
method SIFG introduces a semi-implicit functional gradient flow with Gaussian noise to improve sampling efficiency and accuracy.
result SIFG achieves strong theoretical convergence guarantees and efficient sampling.
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.
Stochastic particle-optimization sampling (SPOS) is a recently-developed scalable Bayesian sampling framework that unifies stochastic gradient MCMC (SG-MCMC) and Stein variational gradient descent (SVGD) algorithms based on Wasserstein gradient flows. With a rigorous non-asymptotic convergence theory developed recently…
A new method for robust training under label noise using weighted gradient descent.
problem Overfitting to noisy examples in machine learning.
method Exponentiated gradient reweighting for flexible handling of noisy data.
result Improved generalization in noisy classification and PCA problems.
Paper develops unbiased gradient estimator for continuous-time models.
problem Estimating unbiased gradient of log-likelihood for continuous-time models.
method Doubly randomized scheme with coupled conditional particle filter (CCPF).
result Unbiased gradient estimate facilitates gradient-based algorithms.