Adversarial Interpretation of Bayesian Inference

Hisham Husain, Jeremias Knoblauch
Proceedings of The 33rd International Conference on Algorithmic Learning Theory, PMLR 167:553-572, 2022.

Abstract

We build on the optimization-centric view on Bayesian inference advocated by Knoblauch et al. (2019). Thinking about Bayesian and generalized Bayesian posteriors as the solutions to a regularized minimization problem allows us to answer an intriguing question: If minimization is the primal problem, then what is its dual? By deriving the Fenchel dual of the problem, we demonstrate that this dual corresponds to an adversarial game: In the dual space, the prior becomes the cost function for an adversary that seeks to perturb the likelihood [loss] function targeted by standard [generalized] Bayesian inference. This implies that Bayes-like procedures are adversarially robust—providing another firm theoretical foundation for their empirical performance. Our contributions are foundational, and apply to a wide-ranging set of Machine Learning methods. This includes standard Bayesian inference, generalized Bayesian and Gibbs posteriors (Bissiri et al., 2016), as well as a diverse set of other methods including Generalized Variational Inference (Knoblauch et al., 2019) and the Wasserstein Autoencoder (Tolstikhin et al., 2017).

Cite this Paper

BibTeX
@InProceedings{pmlr-v167-husain22a, title = {Adversarial Interpretation of Bayesian Inference}, author = {Husain, Hisham and Knoblauch, Jeremias}, booktitle = {Proceedings of The 33rd International Conference on Algorithmic Learning Theory}, pages = {553--572}, year = {2022}, editor = {Dasgupta, Sanjoy and Haghtalab, Nika}, volume = {167}, series = {Proceedings of Machine Learning Research}, month = {29 Mar--01 Apr}, publisher = {PMLR}, pdf = {https://proceedings.mlr.press/v167/husain22a/husain22a.pdf}, url = {https://proceedings.mlr.press/v167/husain22a.html}, abstract = {We build on the optimization-centric view on Bayesian inference advocated by Knoblauch et al. (2019). Thinking about Bayesian and generalized Bayesian posteriors as the solutions to a regularized minimization problem allows us to answer an intriguing question: If minimization is the primal problem, then what is its dual? By deriving the Fenchel dual of the problem, we demonstrate that this dual corresponds to an adversarial game: In the dual space, the prior becomes the cost function for an adversary that seeks to perturb the likelihood [loss] function targeted by standard [generalized] Bayesian inference. This implies that Bayes-like procedures are adversarially robust—providing another firm theoretical foundation for their empirical performance. Our contributions are foundational, and apply to a wide-ranging set of Machine Learning methods. This includes standard Bayesian inference, generalized Bayesian and Gibbs posteriors (Bissiri et al., 2016), as well as a diverse set of other methods including Generalized Variational Inference (Knoblauch et al., 2019) and the Wasserstein Autoencoder (Tolstikhin et al., 2017).} }
Endnote
%0 Conference Paper %T Adversarial Interpretation of Bayesian Inference %A Hisham Husain %A Jeremias Knoblauch %B Proceedings of The 33rd International Conference on Algorithmic Learning Theory %C Proceedings of Machine Learning Research %D 2022 %E Sanjoy Dasgupta %E Nika Haghtalab %F pmlr-v167-husain22a %I PMLR %P 553--572 %U https://proceedings.mlr.press/v167/husain22a.html %V 167 %X We build on the optimization-centric view on Bayesian inference advocated by Knoblauch et al. (2019). Thinking about Bayesian and generalized Bayesian posteriors as the solutions to a regularized minimization problem allows us to answer an intriguing question: If minimization is the primal problem, then what is its dual? By deriving the Fenchel dual of the problem, we demonstrate that this dual corresponds to an adversarial game: In the dual space, the prior becomes the cost function for an adversary that seeks to perturb the likelihood [loss] function targeted by standard [generalized] Bayesian inference. This implies that Bayes-like procedures are adversarially robust—providing another firm theoretical foundation for their empirical performance. Our contributions are foundational, and apply to a wide-ranging set of Machine Learning methods. This includes standard Bayesian inference, generalized Bayesian and Gibbs posteriors (Bissiri et al., 2016), as well as a diverse set of other methods including Generalized Variational Inference (Knoblauch et al., 2019) and the Wasserstein Autoencoder (Tolstikhin et al., 2017).
APA
Husain, H. & Knoblauch, J.. (2022). Adversarial Interpretation of Bayesian Inference. Proceedings of The 33rd International Conference on Algorithmic Learning Theory, in Proceedings of Machine Learning Research 167:553-572 Available from https://proceedings.mlr.press/v167/husain22a.html.

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