Max-margin learning with the Bayes factor

Rahul G. Krishnan, Arjun Khandelwal, Rajesh Ranganath, David Sontag
Proceedings of the 34th Conference on Uncertainty in Artificial Intelligence, PMLR R16:895-904, 2018.

Abstract

We propose a new way to answer probabilis- tic queries that span multiple datapoints. We formalize reasoning about the similarity of dif- ferent datapoints as the evaluation of the Bayes Factor within a hierarchical deep generative model that enforces a separation between the latent variables used for representation learning and those used for reasoning. Under this model, we derive an intuitive estimator for the Bayes Factor that represents similarity as the amount of overlap in representation space shared by dif- ferent points. The estimator we derive relies on a query-conditional latent reasoning network, that parameterizes a distribution over the latent space of the deep generative model. The latent reasoning network is trained to amortize the posterior-predictive distribution under a hierar- chical model using supervised data and a max- margin learning algorithm. We explore how the model may be used to focus the data variations captured in the latent space of the deep genera- tive model and how this may be used to build new algorithms for few-shot learning.

Cite this Paper

BibTeX
@InProceedings{pmlr-vR16-krishnan18a, title = {Max-margin learning with the {B}ayes factor}, author = {Krishnan, Rahul G. and Khandelwal, Arjun and Ranganath, Rajesh and Sontag, David}, booktitle = {Proceedings of the 34th Conference on Uncertainty in Artificial Intelligence}, pages = {895--904}, year = {2018}, editor = {Globerson, Amir and Silva, Ricardo}, volume = {R16}, series = {Proceedings of Machine Learning Research}, month = {06--10 Aug}, publisher = {PMLR}, pdf = {https://raw.githubusercontent.com/mlresearch/r16/main/assets/krishnan18a/krishnan18a.pdf}, url = {https://proceedings.mlr.press/r16/krishnan18a.html}, abstract = {We propose a new way to answer probabilis- tic queries that span multiple datapoints. We formalize reasoning about the similarity of dif- ferent datapoints as the evaluation of the Bayes Factor within a hierarchical deep generative model that enforces a separation between the latent variables used for representation learning and those used for reasoning. Under this model, we derive an intuitive estimator for the Bayes Factor that represents similarity as the amount of overlap in representation space shared by dif- ferent points. The estimator we derive relies on a query-conditional latent reasoning network, that parameterizes a distribution over the latent space of the deep generative model. The latent reasoning network is trained to amortize the posterior-predictive distribution under a hierar- chical model using supervised data and a max- margin learning algorithm. We explore how the model may be used to focus the data variations captured in the latent space of the deep genera- tive model and how this may be used to build new algorithms for few-shot learning.}, note = {Reissued by PMLR on 04 October 2026.} }
Endnote
%0 Conference Paper %T Max-margin learning with the Bayes factor %A Rahul G. Krishnan %A Arjun Khandelwal %A Rajesh Ranganath %A David Sontag %B Proceedings of the 34th Conference on Uncertainty in Artificial Intelligence %C Proceedings of Machine Learning Research %D 2018 %E Amir Globerson %E Ricardo Silva %F pmlr-vR16-krishnan18a %I PMLR %P 895--904 %U https://proceedings.mlr.press/r16/krishnan18a.html %V R16 %X We propose a new way to answer probabilis- tic queries that span multiple datapoints. We formalize reasoning about the similarity of dif- ferent datapoints as the evaluation of the Bayes Factor within a hierarchical deep generative model that enforces a separation between the latent variables used for representation learning and those used for reasoning. Under this model, we derive an intuitive estimator for the Bayes Factor that represents similarity as the amount of overlap in representation space shared by dif- ferent points. The estimator we derive relies on a query-conditional latent reasoning network, that parameterizes a distribution over the latent space of the deep generative model. The latent reasoning network is trained to amortize the posterior-predictive distribution under a hierar- chical model using supervised data and a max- margin learning algorithm. We explore how the model may be used to focus the data variations captured in the latent space of the deep genera- tive model and how this may be used to build new algorithms for few-shot learning. %Z Reissued by PMLR on 04 October 2026.
APA
Krishnan, R.G., Khandelwal, A., Ranganath, R. & Sontag, D.. (2018). Max-margin learning with the Bayes factor. Proceedings of the 34th Conference on Uncertainty in Artificial Intelligence, in Proceedings of Machine Learning Research R16:895-904 Available from https://proceedings.mlr.press/r16/krishnan18a.html. Reissued by PMLR on 04 October 2026.

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