A Tree-Based Method for Fast Repeated Sampling of Determinantal Point Processes

Jennifer Gillenwater, Alex Kulesza, Zelda Mariet, Sergei Vassilvtiskii
Proceedings of the 36th International Conference on Machine Learning, PMLR 97:2260-2268, 2019.

Abstract

It is often desirable in recommender systems and other information retrieval applications to provide diverse results, and determinantal point processes (DPPs) have become a popular way to capture the trade-off between the quality of individual results and the diversity of the overall set. However, sampling from a DPP is inherently expensive: if the underlying collection contains N items, then generating each DPP sample requires time linear in N following a one-time preprocessing phase. Additionally, results often need to be personalized to a user, but standard approaches to personalization invalidate the preprocessing, making personalized samples especially expensive. In this work we address both of these shortcomings. First, we propose a new algorithm for generating DPP samples in time logarithmic in N, following a slightly more expensive preprocessing phase. We then extend the algorithm to support arbitrary query-time feature weights, allowing us to generate samples customized to individual users while still retaining logarithmic runtime; experiments show our approach runs over 300 times faster than traditional DPP sampling on collections of 100,000 items for samples of size 10.

Cite this Paper

BibTeX
@InProceedings{pmlr-v97-gillenwater19a, title = {A Tree-Based Method for Fast Repeated Sampling of Determinantal Point Processes}, author = {Gillenwater, Jennifer and Kulesza, Alex and Mariet, Zelda and Vassilvtiskii, Sergei}, booktitle = {Proceedings of the 36th International Conference on Machine Learning}, pages = {2260--2268}, year = {2019}, editor = {Chaudhuri, Kamalika and Salakhutdinov, Ruslan}, volume = {97}, series = {Proceedings of Machine Learning Research}, month = {09--15 Jun}, publisher = {PMLR}, pdf = {http://proceedings.mlr.press/v97/gillenwater19a/gillenwater19a.pdf}, url = {https://proceedings.mlr.press/v97/gillenwater19a.html}, abstract = {It is often desirable in recommender systems and other information retrieval applications to provide diverse results, and determinantal point processes (DPPs) have become a popular way to capture the trade-off between the quality of individual results and the diversity of the overall set. However, sampling from a DPP is inherently expensive: if the underlying collection contains N items, then generating each DPP sample requires time linear in N following a one-time preprocessing phase. Additionally, results often need to be personalized to a user, but standard approaches to personalization invalidate the preprocessing, making personalized samples especially expensive. In this work we address both of these shortcomings. First, we propose a new algorithm for generating DPP samples in time logarithmic in N, following a slightly more expensive preprocessing phase. We then extend the algorithm to support arbitrary query-time feature weights, allowing us to generate samples customized to individual users while still retaining logarithmic runtime; experiments show our approach runs over 300 times faster than traditional DPP sampling on collections of 100,000 items for samples of size 10.} }
Endnote
%0 Conference Paper %T A Tree-Based Method for Fast Repeated Sampling of Determinantal Point Processes %A Jennifer Gillenwater %A Alex Kulesza %A Zelda Mariet %A Sergei Vassilvtiskii %B Proceedings of the 36th International Conference on Machine Learning %C Proceedings of Machine Learning Research %D 2019 %E Kamalika Chaudhuri %E Ruslan Salakhutdinov %F pmlr-v97-gillenwater19a %I PMLR %P 2260--2268 %U https://proceedings.mlr.press/v97/gillenwater19a.html %V 97 %X It is often desirable in recommender systems and other information retrieval applications to provide diverse results, and determinantal point processes (DPPs) have become a popular way to capture the trade-off between the quality of individual results and the diversity of the overall set. However, sampling from a DPP is inherently expensive: if the underlying collection contains N items, then generating each DPP sample requires time linear in N following a one-time preprocessing phase. Additionally, results often need to be personalized to a user, but standard approaches to personalization invalidate the preprocessing, making personalized samples especially expensive. In this work we address both of these shortcomings. First, we propose a new algorithm for generating DPP samples in time logarithmic in N, following a slightly more expensive preprocessing phase. We then extend the algorithm to support arbitrary query-time feature weights, allowing us to generate samples customized to individual users while still retaining logarithmic runtime; experiments show our approach runs over 300 times faster than traditional DPP sampling on collections of 100,000 items for samples of size 10.
APA
Gillenwater, J., Kulesza, A., Mariet, Z. & Vassilvtiskii, S.. (2019). A Tree-Based Method for Fast Repeated Sampling of Determinantal Point Processes. Proceedings of the 36th International Conference on Machine Learning, in Proceedings of Machine Learning Research 97:2260-2268 Available from https://proceedings.mlr.press/v97/gillenwater19a.html.

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