Fixed-point algorithms for learning determinantal point processes

Zelda Mariet, Suvrit Sra
Proceedings of the 32nd International Conference on Machine Learning, PMLR 37:2389-2397, 2015.

Abstract

Determinantal point processes (DPPs) offer an elegant tool for encoding probabilities over subsets of a ground set. Discrete DPPs are parametrized by a positive semidefinite matrix (called the DPP kernel), and estimating this kernel is key to learning DPPs from observed data. We consider the task of learning the DPP kernel, and develop for it a surprisingly simple yet effective new algorithm. Our algorithm offers the following benefits over previous approaches: (a) it is much simpler; (b) it yields equally good and sometimes even better local maxima; and (c) it runs an order of magnitude faster on large problems. We present experimental results on both real and simulated data to illustrate the numerical performance of our technique.

Cite this Paper

BibTeX
@InProceedings{pmlr-v37-mariet15, title = {Fixed-point algorithms for learning determinantal point processes}, author = {Mariet, Zelda and Sra, Suvrit}, booktitle = {Proceedings of the 32nd International Conference on Machine Learning}, pages = {2389--2397}, year = {2015}, editor = {Bach, Francis and Blei, David}, volume = {37}, series = {Proceedings of Machine Learning Research}, address = {Lille, France}, month = {07--09 Jul}, publisher = {PMLR}, pdf = {http://proceedings.mlr.press/v37/mariet15.pdf}, url = {https://proceedings.mlr.press/v37/mariet15.html}, abstract = {Determinantal point processes (DPPs) offer an elegant tool for encoding probabilities over subsets of a ground set. Discrete DPPs are parametrized by a positive semidefinite matrix (called the DPP kernel), and estimating this kernel is key to learning DPPs from observed data. We consider the task of learning the DPP kernel, and develop for it a surprisingly simple yet effective new algorithm. Our algorithm offers the following benefits over previous approaches: (a) it is much simpler; (b) it yields equally good and sometimes even better local maxima; and (c) it runs an order of magnitude faster on large problems. We present experimental results on both real and simulated data to illustrate the numerical performance of our technique.} }
Endnote
%0 Conference Paper %T Fixed-point algorithms for learning determinantal point processes %A Zelda Mariet %A Suvrit Sra %B Proceedings of the 32nd International Conference on Machine Learning %C Proceedings of Machine Learning Research %D 2015 %E Francis Bach %E David Blei %F pmlr-v37-mariet15 %I PMLR %P 2389--2397 %U https://proceedings.mlr.press/v37/mariet15.html %V 37 %X Determinantal point processes (DPPs) offer an elegant tool for encoding probabilities over subsets of a ground set. Discrete DPPs are parametrized by a positive semidefinite matrix (called the DPP kernel), and estimating this kernel is key to learning DPPs from observed data. We consider the task of learning the DPP kernel, and develop for it a surprisingly simple yet effective new algorithm. Our algorithm offers the following benefits over previous approaches: (a) it is much simpler; (b) it yields equally good and sometimes even better local maxima; and (c) it runs an order of magnitude faster on large problems. We present experimental results on both real and simulated data to illustrate the numerical performance of our technique.
RIS
TY - CPAPER TI - Fixed-point algorithms for learning determinantal point processes AU - Zelda Mariet AU - Suvrit Sra BT - Proceedings of the 32nd International Conference on Machine Learning DA - 2015/06/01 ED - Francis Bach ED - David Blei ID - pmlr-v37-mariet15 PB - PMLR DP - Proceedings of Machine Learning Research VL - 37 SP - 2389 EP - 2397 L1 - http://proceedings.mlr.press/v37/mariet15.pdf UR - https://proceedings.mlr.press/v37/mariet15.html AB - Determinantal point processes (DPPs) offer an elegant tool for encoding probabilities over subsets of a ground set. Discrete DPPs are parametrized by a positive semidefinite matrix (called the DPP kernel), and estimating this kernel is key to learning DPPs from observed data. We consider the task of learning the DPP kernel, and develop for it a surprisingly simple yet effective new algorithm. Our algorithm offers the following benefits over previous approaches: (a) it is much simpler; (b) it yields equally good and sometimes even better local maxima; and (c) it runs an order of magnitude faster on large problems. We present experimental results on both real and simulated data to illustrate the numerical performance of our technique. ER -
APA
Mariet, Z. & Sra, S.. (2015). Fixed-point algorithms for learning determinantal point processes. Proceedings of the 32nd International Conference on Machine Learning, in Proceedings of Machine Learning Research 37:2389-2397 Available from https://proceedings.mlr.press/v37/mariet15.html.

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