TY - GEN
T1 - Bayesian low-rank determinantal point processes
AU - Gartrell, Mike
AU - Paquet, Ulrich
AU - Koenigstein, Noam
N1 - Publisher Copyright:
© 2016 Copyright held by the owner/author(s).
PY - 2016/9/7
Y1 - 2016/9/7
N2 - Determinantal point processes (DPPs) are an emerging model for encoding probabilities over subsets, such as shopping baskets, selected from a ground set, such as an item catalog. They have recently proved to be appealing models for a number of machine learning tasks, including product recommendation. DPPs are parametrized by a positive semi-definite kernel matrix. Prior work has shown that using a low-rank factorization of this kernel provides scalability improvements that open the door to training on large-scale datasets and computing online recommendations, both of which are infeasible with standard DPP models that use a full-rank kernel. A low-rank DPP model can be trained using an optimization-based method, such as stochastic gradient ascent, to find a point estimate of the kernel parameters, which can be performed efficiently on large-scale datasets. However, this approach requires careful tuning of regularization parameters to prevent overfitting and provide good predictive performance, which can be computationally expensive. In this paper we present a Bayesian method for learning a low-rank factorization of this kernel, which provides automatic control of regularization. We show that our Bayesian low-rank DPP model can be trained efficiently using stochastic gradient Hamiltonian Monte Carlo (SGHMC). Our Bayesian model generally provides better predictive performance on several real-world product recommendation datasets than optimization-based low-rank DPP models trained using stochastic gradient ascent, and better performance than several state-of-the art recommendation methods in many cases.
AB - Determinantal point processes (DPPs) are an emerging model for encoding probabilities over subsets, such as shopping baskets, selected from a ground set, such as an item catalog. They have recently proved to be appealing models for a number of machine learning tasks, including product recommendation. DPPs are parametrized by a positive semi-definite kernel matrix. Prior work has shown that using a low-rank factorization of this kernel provides scalability improvements that open the door to training on large-scale datasets and computing online recommendations, both of which are infeasible with standard DPP models that use a full-rank kernel. A low-rank DPP model can be trained using an optimization-based method, such as stochastic gradient ascent, to find a point estimate of the kernel parameters, which can be performed efficiently on large-scale datasets. However, this approach requires careful tuning of regularization parameters to prevent overfitting and provide good predictive performance, which can be computationally expensive. In this paper we present a Bayesian method for learning a low-rank factorization of this kernel, which provides automatic control of regularization. We show that our Bayesian low-rank DPP model can be trained efficiently using stochastic gradient Hamiltonian Monte Carlo (SGHMC). Our Bayesian model generally provides better predictive performance on several real-world product recommendation datasets than optimization-based low-rank DPP models trained using stochastic gradient ascent, and better performance than several state-of-the art recommendation methods in many cases.
UR - http://www.scopus.com/inward/record.url?scp=84991214776&partnerID=8YFLogxK
U2 - 10.1145/2959100.2959178
DO - 10.1145/2959100.2959178
M3 - ???researchoutput.researchoutputtypes.contributiontobookanthology.conference???
AN - SCOPUS:84991214776
T3 - RecSys 2016 - Proceedings of the 10th ACM Conference on Recommender Systems
SP - 349
EP - 356
BT - RecSys 2016 - Proceedings of the 10th ACM Conference on Recommender Systems
PB - Association for Computing Machinery, Inc
T2 - 10th ACM Conference on Recommender Systems, RecSys 2016
Y2 - 15 September 2016 through 19 September 2016
ER -