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Scalable Learning and MAP Inference for Nonsymmetric Determinantal Point Processes [article]

Mike Gartrell, Insu Han, Elvis Dohmatob, Jennifer Gillenwater, Victor-Emmanuel Brunel
2021 arXiv   pre-print
Determinantal point processes (DPPs) have attracted significant attention in machine learning for their ability to model subsets drawn from a large item collection.  ...  However, for an item collection of size M, existing NDPP learning and inference algorithms require memory quadratic in M and runtime cubic (for learning) or quadratic (for inference) in M, making them  ...  INTRODUCTION Determinantal point processes (DPPs) have proven useful for numerous machine learning tasks.  ... 
arXiv:2006.09862v2 fatcat:ij6tpkl6bnhhppfikvatyffitm

Scalable Sampling for Nonsymmetric Determinantal Point Processes [article]

Insu Han, Mike Gartrell, Jennifer Gillenwater, Elvis Dohmatob, Amin Karbasi
2022 arXiv   pre-print
A determinantal point process (DPP) on a collection of M items is a model, parameterized by a symmetric kernel matrix, that assigns a probability to every subset of those items.  ...  Recent work shows that removing the kernel symmetry constraint, yielding nonsymmetric DPPs (NDPPs), can lead to significant predictive performance gains for machine learning applications.  ...  For our experiments, all dataset processing steps, experimental procedures, and hyperparameter settings are described in Appendices A, B, and C, respectively. 10 ACKNOWLEDGEMENTS Amin Karbasi acknowledges  ... 
arXiv:2201.08417v2 fatcat:rskpiwmvz5b4xge2l4qhsizxmm

Scalable MCMC Sampling for Nonsymmetric Determinantal Point Processes [article]

Insu Han, Mike Gartrell, Elvis Dohmatob, Amin Karbasi
2022 arXiv   pre-print
A determinantal point process (DPP) is an elegant model that assigns a probability to every subset of a collection of n items.  ...  With both a theoretical analysis and experiments on real-world datasets, we verify that our scalable approximate sampling algorithms are orders of magnitude faster than existing sampling approaches for  ...  Amin Karbasi acknowledges funding in direct support of this work from NSF (IIS-1845032), ONR (N00014-19-1-2406), and the AI Institute for Learning-Enabled Optimization at Scale (TILOS).  ... 
arXiv:2207.00486v1 fatcat:4wdfyck74rfmxf3dqcfklibb7q

Nyström landmark sampling and regularized Christoffel functions [article]

Michaël Fanuel, Joachim Schreurs, Johan A.K. Suykens
2021 arXiv   pre-print
Beyond the known connection between Christoffel functions and leverage scores, a connection of our method with finite determinantal point processes (DPPs) is also explained.  ...  In this context, we propose a deterministic and a randomized adaptive algorithm for selecting landmark points within a training data set.  ...  SIAM Journal on Mathematics of Data Science 1(1):208–236 Gartrell M, Brunel VE, Dohmatob E, Krichene S (2019) Learning nonsymmetric determinantal point processes.  ... 
arXiv:1905.12346v4 fatcat:cy4nua5a7rfp3ma5khkxrks44m