Learning Determinantal Point Processes in Sublinear Time

Christophe Dupuy, Francis Bach
Proceedings of the Twenty-First International Conference on Artificial Intelligence and Statistics, PMLR 84:244-257, 2018.

Abstract

We propose a new class of determinantal point processes (DPPs) which can be manipulated for inference and parameter learning in potentially sublinear time in the number of items. This class, based on a specific low-rank factorization of the marginal kernel, is particularly suited to a subclass of continuous DPPs and DPPs defined on exponentially many items. We apply this new class to modelling text documents as sampling a DPP of sentences, and propose a conditional maximum likelihood formulation to model topic proportions, which is made possible with no approximation for our class of DPPs. We present an application to document summarization with a DPP on 2 to the power 500 items.

Cite this Paper

BibTeX
@InProceedings{pmlr-v84-dupuy18a, title = {Learning Determinantal Point Processes in Sublinear Time}, author = {Dupuy, Christophe and Bach, Francis}, booktitle = {Proceedings of the Twenty-First International Conference on Artificial Intelligence and Statistics}, pages = {244--257}, year = {2018}, editor = {Storkey, Amos and Perez-Cruz, Fernando}, volume = {84}, series = {Proceedings of Machine Learning Research}, month = {09--11 Apr}, publisher = {PMLR}, pdf = {http://proceedings.mlr.press/v84/dupuy18a/dupuy18a.pdf}, url = {https://proceedings.mlr.press/v84/dupuy18a.html}, abstract = {We propose a new class of determinantal point processes (DPPs) which can be manipulated for inference and parameter learning in potentially sublinear time in the number of items. This class, based on a specific low-rank factorization of the marginal kernel, is particularly suited to a subclass of continuous DPPs and DPPs defined on exponentially many items. We apply this new class to modelling text documents as sampling a DPP of sentences, and propose a conditional maximum likelihood formulation to model topic proportions, which is made possible with no approximation for our class of DPPs. We present an application to document summarization with a DPP on 2 to the power 500 items.} }
Endnote
%0 Conference Paper %T Learning Determinantal Point Processes in Sublinear Time %A Christophe Dupuy %A Francis Bach %B Proceedings of the Twenty-First International Conference on Artificial Intelligence and Statistics %C Proceedings of Machine Learning Research %D 2018 %E Amos Storkey %E Fernando Perez-Cruz %F pmlr-v84-dupuy18a %I PMLR %P 244--257 %U https://proceedings.mlr.press/v84/dupuy18a.html %V 84 %X We propose a new class of determinantal point processes (DPPs) which can be manipulated for inference and parameter learning in potentially sublinear time in the number of items. This class, based on a specific low-rank factorization of the marginal kernel, is particularly suited to a subclass of continuous DPPs and DPPs defined on exponentially many items. We apply this new class to modelling text documents as sampling a DPP of sentences, and propose a conditional maximum likelihood formulation to model topic proportions, which is made possible with no approximation for our class of DPPs. We present an application to document summarization with a DPP on 2 to the power 500 items.
APA
Dupuy, C. & Bach, F.. (2018). Learning Determinantal Point Processes in Sublinear Time. Proceedings of the Twenty-First International Conference on Artificial Intelligence and Statistics, in Proceedings of Machine Learning Research 84:244-257 Available from https://proceedings.mlr.press/v84/dupuy18a.html.

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