Stein Variational Gradient Descent as Gradient Flow

By Qiang Liu. 2017

319 citations recorded by the source corpus.

Stein variational gradient descent (SVGD) is a deterministic sampling algorithm that iteratively transports a set of particles to approximate given distributions, based on an efficient gradient-based update that guarantees to optimally decrease the KL divergence within a function space. This paper develops the first theoretical analysis on SVGD, discussing its weak convergence properties and showing that its asymptotic behavior is captured by a gradient flow of the KL divergence functional under a new metric structure induced by Stein operator. We also provide a number of results on Stein operator and Stein's identity using the notion of weak derivative, including a new proof of the distinguishability of Stein discrepancy under weak conditions.

Subfields: Applied Mathematics, Mathematical Physics, Statistics and Probability

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Applied Mathematics

In Mathematical Physics

In Statistics and Probability

Citations in the corpus

Improving Task-free Continual Learning by Distributionally Robust Memory Evolution (2022, background): “The probability measure in the kernelized Wasserstein space actually follows the kernelized WGF (Liu, 2017): Eq.”
Bayesian Deep Convolutional Encoder-Decoder Networks for Surrogate Modeling and Uncertainty Quantification (2018, methodology): “Here we adopt a recently proposed non-parametric variational inference method called stochastic variational gradient descent (SVGD) [30,59] that is similar to standard gradient descent while maintaining the efficiency of particle methods.”
Quantifying model form uncertainty in Reynolds-averaged turbulence models with Bayesian deep neural networks (2018, methodology): “[39, 40] along with the work of Zhu and Zabaras [31].”
SVGD as a kernelized Wasserstein gradient flow of the chi-squared divergence (2020, methodology): “Several works have studied theoretical properties of SVGD, including its interpretation as a gradient ﬂow under a modiﬁed geometry [Liu17,DNS19], and its asymptotic convergence [LLN19].”
Understanding MCMC Dynamics as Flows on the Wasserstein Space (2019, background): “Stein variational gradient descent (SVGD) (Liu & Wang, 2016) is the most famous representative, and the field is under an active development both in theory (Liu, 2017; Chen et al., 2018b;a; Liu et al., 2018) and application (Liu et al., 2017; Pu et al., 2017; Zhuo et al., 2018; Yoon et al., 2018).”
Interacting Particle Solutions of Fokker–Planck Equations Through Gradient–Log–Density Estimation (2020, methodology): “Relation to Stein Variational Gradient Descent Recently, Stein variational gradient descent (SVGD), a kernel based particle algorithm, has attracted considerable attention in the machine learning community [29,30].”
Refining Deep Generative Models via Discriminator Gradient Flow (2020, methodology): “, 2019), the Stein discrepancy (Liu, 2017), and the Sobolev discrepancy (Mroueh et al.”