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One-Pass Algorithms for MAP Inference of Nonsymmetric Determinantal Point Processes

Aravind Reddy, Ryan A. Rossi, Zhao Song, Anup B. Rao, Tung Mai, Nedim Lipka, Gang Wu, Eunyee Koh, Nesreen K. Ahmed
2022 International Conference on Machine Learning  
In this paper, we initiate the study of one-pass algorithms for solving the maximum-a-posteriori (MAP) inference problem for Non-symmetric Determinantal Point Processes (NDPPs).  ...  In particular, we formulate streaming and online versions of the problem and provide one-pass algorithms for solving these problems.  ...  Acknowledgments We would like to thank all the ICML 2022 reviewers of our paper and also the ICLR 2022 reviewers who reviewed an earlier version of this work, for their very valuable feedback.  ... 
dblp:conf/icml/ReddyR0RMLWKA22 fatcat:3qbaqayglfgmxojdvlfkka2vgm

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

From Sampling to Optimization on Discrete Domains with Applications to Determinant Maximization [article]

Nima Anari, Thuy-Duong Vuong
2021 arXiv   pre-print
As the main application of our result, we show a simple nearly-optimal k^O(k)-factor approximation algorithm for MAP inference on nonsymmetric DPPs.  ...  We show a connection between sampling and optimization on discrete domains.  ...  MAP Inference on Nonsymmetric DPPs Determinantal point processes (DPPs) have found many applications in machine learning, such as data summarization [Gon+14; LB12] , recommender systems [GPK16; Wil+18  ... 
arXiv:2102.05347v3 fatcat:fpirfdmpyfd5bn2hgzl45j4cke

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.  ...  k-NDPPs and NDPPs.  ...  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

Towards the next generation of high-fidelity simulators for online computing: adaptive modelling through the scales

Pierre Kerfriden
2019 Zenodo  
Models used for such applications require extreme robustness and swiftness of execution.  ...  and physically detailed numerical simulations, with a particular emphasis on reliability assessment for composite materials and fracture.  ...  The error bound, which should be sufficiently sharp for this approach to be successful, is usually constructed and calibrated as a preliminary step of the learning process [54, 55, 109, 110] .  ... 
doi:10.5281/zenodo.3404685 fatcat:qj3nv253bnhdrn366s2wowmud4