%0 Journal Article %1 chu2020equivalence %A Chu, Casey %A Minami, Kentaro %A Fukumizu, Kenji %D 2020 %K bayesian optimization readings variational %T The equivalence between Stein variational gradient descent and black-box variational inference %U http://arxiv.org/abs/2004.01822 %X We formalize an equivalence between two popular methods for Bayesian inference: Stein variational gradient descent (SVGD) and black-box variational inference (BBVI). In particular, we show that BBVI corresponds precisely to SVGD when the kernel is the neural tangent kernel. Furthermore, we interpret SVGD and BBVI as kernel gradient flows; we do this by leveraging the recent perspective that views SVGD as a gradient flow in the space of probability distributions and showing that BBVI naturally motivates a Riemannian structure on that space. We observe that kernel gradient flow also describes dynamics found in the training of generative adversarial networks (GANs). This work thereby unifies several existing techniques in variational inference and generative modeling and identifies the kernel as a fundamental object governing the behavior of these algorithms, motivating deeper analysis of its properties.

@article{chu2020equivalence, abstract = {We formalize an equivalence between two popular methods for Bayesian inference: Stein variational gradient descent (SVGD) and black-box variational inference (BBVI). In particular, we show that BBVI corresponds precisely to SVGD when the kernel is the neural tangent kernel. Furthermore, we interpret SVGD and BBVI as kernel gradient flows; we do this by leveraging the recent perspective that views SVGD as a gradient flow in the space of probability distributions and showing that BBVI naturally motivates a Riemannian structure on that space. We observe that kernel gradient flow also describes dynamics found in the training of generative adversarial networks (GANs). This work thereby unifies several existing techniques in variational inference and generative modeling and identifies the kernel as a fundamental object governing the behavior of these algorithms, motivating deeper analysis of its properties.}, added-at = {2020-04-07T12:33:10.000+0200}, author = {Chu, Casey and Minami, Kentaro and Fukumizu, Kenji}, biburl = {https://www.bibsonomy.org/bibtex/24e059dc4bc61836969192bcfbdf8345b/kirk86}, description = {[2004.01822] The equivalence between Stein variational gradient descent and black-box variational inference}, interhash = {c24b50dee82c51ff321bc5034c42538b}, intrahash = {4e059dc4bc61836969192bcfbdf8345b}, keywords = {bayesian optimization readings variational}, note = {cite arxiv:2004.01822Comment: ICLR 2020, Workshop on Integration of Deep Neural Models and Differential Equations}, timestamp = {2020-04-07T12:33:10.000+0200}, title = {The equivalence between Stein variational gradient descent and black-box variational inference}, url = {http://arxiv.org/abs/2004.01822}, year = 2020 }