Generative Particle Variational Inference via Estimation of Functional Gradients

Neale Ratzlaff, Qinxun Bai, Li Fuxin, Wei Xu
Proceedings of the 38th International Conference on Machine Learning, PMLR 139:8869-8879, 2021.

Abstract

Recently, particle-based variational inference (ParVI) methods have gained interest because they can avoid arbitrary parametric assumptions that are common in variational inference. However, many ParVI approaches do not allow arbitrary sampling from the posterior, and the few that do allow such sampling suffer from suboptimality. This work proposes a new method for learning to approximately sample from the posterior distribution. We construct a neural sampler that is trained with the functional gradient of the KL-divergence between the empirical sampling distribution and the target distribution, assuming the gradient resides within a reproducing kernel Hilbert space. Our generative ParVI (GPVI) approach maintains the asymptotic performance of ParVI methods while offering the flexibility of a generative sampler. Through carefully constructed experiments, we show that GPVI outperforms previous generative ParVI methods such as amortized SVGD, and is competitive with ParVI as well as gold-standard approaches like Hamiltonian Monte Carlo for fitting both exactly known and intractable target distributions.

Cite this Paper

BibTeX
@InProceedings{pmlr-v139-ratzlaff21a, title = {Generative Particle Variational Inference via Estimation of Functional Gradients}, author = {Ratzlaff, Neale and Bai, Qinxun and Fuxin, Li and Xu, Wei}, booktitle = {Proceedings of the 38th International Conference on Machine Learning}, pages = {8869--8879}, year = {2021}, editor = {Meila, Marina and Zhang, Tong}, volume = {139}, series = {Proceedings of Machine Learning Research}, month = {18--24 Jul}, publisher = {PMLR}, pdf = {http://proceedings.mlr.press/v139/ratzlaff21a/ratzlaff21a.pdf}, url = {https://proceedings.mlr.press/v139/ratzlaff21a.html}, abstract = {Recently, particle-based variational inference (ParVI) methods have gained interest because they can avoid arbitrary parametric assumptions that are common in variational inference. However, many ParVI approaches do not allow arbitrary sampling from the posterior, and the few that do allow such sampling suffer from suboptimality. This work proposes a new method for learning to approximately sample from the posterior distribution. We construct a neural sampler that is trained with the functional gradient of the KL-divergence between the empirical sampling distribution and the target distribution, assuming the gradient resides within a reproducing kernel Hilbert space. Our generative ParVI (GPVI) approach maintains the asymptotic performance of ParVI methods while offering the flexibility of a generative sampler. Through carefully constructed experiments, we show that GPVI outperforms previous generative ParVI methods such as amortized SVGD, and is competitive with ParVI as well as gold-standard approaches like Hamiltonian Monte Carlo for fitting both exactly known and intractable target distributions.} }
Endnote
%0 Conference Paper %T Generative Particle Variational Inference via Estimation of Functional Gradients %A Neale Ratzlaff %A Qinxun Bai %A Li Fuxin %A Wei Xu %B Proceedings of the 38th International Conference on Machine Learning %C Proceedings of Machine Learning Research %D 2021 %E Marina Meila %E Tong Zhang %F pmlr-v139-ratzlaff21a %I PMLR %P 8869--8879 %U https://proceedings.mlr.press/v139/ratzlaff21a.html %V 139 %X Recently, particle-based variational inference (ParVI) methods have gained interest because they can avoid arbitrary parametric assumptions that are common in variational inference. However, many ParVI approaches do not allow arbitrary sampling from the posterior, and the few that do allow such sampling suffer from suboptimality. This work proposes a new method for learning to approximately sample from the posterior distribution. We construct a neural sampler that is trained with the functional gradient of the KL-divergence between the empirical sampling distribution and the target distribution, assuming the gradient resides within a reproducing kernel Hilbert space. Our generative ParVI (GPVI) approach maintains the asymptotic performance of ParVI methods while offering the flexibility of a generative sampler. Through carefully constructed experiments, we show that GPVI outperforms previous generative ParVI methods such as amortized SVGD, and is competitive with ParVI as well as gold-standard approaches like Hamiltonian Monte Carlo for fitting both exactly known and intractable target distributions.
APA
Ratzlaff, N., Bai, Q., Fuxin, L. & Xu, W.. (2021). Generative Particle Variational Inference via Estimation of Functional Gradients. Proceedings of the 38th International Conference on Machine Learning, in Proceedings of Machine Learning Research 139:8869-8879 Available from https://proceedings.mlr.press/v139/ratzlaff21a.html.

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