The Indian Chefs Process

Patrick Dallaire, Luca Ambrogioni, Ludovic Trottier, Umut Güçlü, Max Hinne, Philippe Giguère, Marcel Gerven, François Laviolette
Proceedings of the 36th Conference on Uncertainty in Artificial Intelligence (UAI), PMLR 124:600-608, 2020.

Abstract

This paper introduces the Indian chefs process (ICP) as a Bayesian nonparametric prior on the joint space of infinite directed acyclic graphs (DAGs) and orders that generalizes the Indian buffet process. As our construction shows, the proposed distribution relies on a latent Beta process controlling both the orders and outgoing connection probabilities of the nodes, and yields a probability distribution on sparse infinite graphs. The main advantage of the ICP over previously proposed Bayesian nonparametric priors for DAG structures is its greater flexibility. To the best of our knowledge, the ICP is the first Bayesian nonparametric model supporting every possible DAG involving latent nodes. We demonstrate the usefulness of the ICP on learning the structure of deep generative sigmoid networks as well as convolutional neural networks.

Cite this Paper

BibTeX
@InProceedings{pmlr-v124-dallaire20a, title = {The Indian Chefs Process}, author = {Dallaire, Patrick and Ambrogioni, Luca and Trottier, Ludovic and G\"{u}\c{c}l\"{u}, Umut and Hinne, Max and Gigu\`{e}re, Philippe and van Gerven, Marcel and Laviolette, Fran\c{c}ois}, booktitle = {Proceedings of the 36th Conference on Uncertainty in Artificial Intelligence (UAI)}, pages = {600--608}, year = {2020}, editor = {Peters, Jonas and Sontag, David}, volume = {124}, series = {Proceedings of Machine Learning Research}, month = {03--06 Aug}, publisher = {PMLR}, pdf = {http://proceedings.mlr.press/v124/dallaire20a/dallaire20a.pdf}, url = {https://proceedings.mlr.press/v124/dallaire20a.html}, abstract = {This paper introduces the Indian chefs process (ICP) as a Bayesian nonparametric prior on the joint space of infinite directed acyclic graphs (DAGs) and orders that generalizes the Indian buffet process. As our construction shows, the proposed distribution relies on a latent Beta process controlling both the orders and outgoing connection probabilities of the nodes, and yields a probability distribution on sparse infinite graphs. The main advantage of the ICP over previously proposed Bayesian nonparametric priors for DAG structures is its greater flexibility. To the best of our knowledge, the ICP is the first Bayesian nonparametric model supporting every possible DAG involving latent nodes. We demonstrate the usefulness of the ICP on learning the structure of deep generative sigmoid networks as well as convolutional neural networks. } }
Endnote
%0 Conference Paper %T The Indian Chefs Process %A Patrick Dallaire %A Luca Ambrogioni %A Ludovic Trottier %A Umut Güçlü %A Max Hinne %A Philippe Giguère %A Marcel Gerven %A François Laviolette %B Proceedings of the 36th Conference on Uncertainty in Artificial Intelligence (UAI) %C Proceedings of Machine Learning Research %D 2020 %E Jonas Peters %E David Sontag %F pmlr-v124-dallaire20a %I PMLR %P 600--608 %U https://proceedings.mlr.press/v124/dallaire20a.html %V 124 %X This paper introduces the Indian chefs process (ICP) as a Bayesian nonparametric prior on the joint space of infinite directed acyclic graphs (DAGs) and orders that generalizes the Indian buffet process. As our construction shows, the proposed distribution relies on a latent Beta process controlling both the orders and outgoing connection probabilities of the nodes, and yields a probability distribution on sparse infinite graphs. The main advantage of the ICP over previously proposed Bayesian nonparametric priors for DAG structures is its greater flexibility. To the best of our knowledge, the ICP is the first Bayesian nonparametric model supporting every possible DAG involving latent nodes. We demonstrate the usefulness of the ICP on learning the structure of deep generative sigmoid networks as well as convolutional neural networks.
APA
Dallaire, P., Ambrogioni, L., Trottier, L., Güçlü, U., Hinne, M., Giguère, P., Gerven, M. & Laviolette, F.. (2020). The Indian Chefs Process. Proceedings of the 36th Conference on Uncertainty in Artificial Intelligence (UAI), in Proceedings of Machine Learning Research 124:600-608 Available from https://proceedings.mlr.press/v124/dallaire20a.html.

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