Bibliography¶
- AKFT13
Raja Hafiz Affandi, Alex Kulesza, Emily B Fox, and Ben Taskar. Nyström Approximation for Large-Scale Determinantal Processes. In International Conference on Artificial Intelligence and Statistics (AISTATS), volume 31, 85–98. 2013. URL: http://proceedings.mlr.press/v31/affandi13a.
- AM15
Ahmed El Alaoui and Michael W. Mahoney. Fast randomized kernel ridge regression with statistical guarantees. In Proceedings of the 28th International Conference on Neural Information Processing Systems, 775–783. Montreal, Canada, December 2015.
- Ald90
David J Aldous. The Random Walk Construction of Uniform Spanning Trees and Uniform Labelled Trees. SIAM Journal on Discrete Mathematics, 3(4):450–465, nov 1990. URL: http://epubs.siam.org/doi/10.1137/0403039, doi:10.1137/0403039.
- AGR16
Nima Anari, Shayan Oveis Gharan, and Alireza Rezaei. Monte Carlo Markov Chain Algorithms for Sampling Strongly Rayleigh Distributions and Determinantal Point Processes. In Conference on Learning Theory (COLT), 103–115. New York, USA, 2016. PMLR. URL: http://proceedings.mlr.press/v49/anari16, arXiv:1602.05242.
- AGaudilliere13
Luca Avena and Alexandre Gaudillière. On some random forests with determinantal roots. e-prints, 2013. URL: http://citeseerx.ist.psu.edu/viewdoc/download?doi=10.1.1.740.6173{\&}rep=rep1{\&}type=pdf.
- BT05
Adrian Baddeley and Rolf Turner. spatstat : An R Package for Analyzing Spatial Point Patterns. Journal of Statistical Software, 12(6):1–42, jan 2005. URL: http://www.jstatsoft.org/v12/i06/, doi:10.18637/jss.v012.i06.
- BH16
Rémi Bardenet and Adrien Hardy. Monte Carlo with Determinantal Point Processes. ArXiv e-prints, 2016. URL: http://arxiv.org/abs/1605.00361, arXiv:1605.00361.
- Bor09
Alexei Borodin. Determinantal point processes. ArXiv e-prints, 2009. URL: http://arxiv.org/abs/0911.1153, arXiv:0911.1153.
- BDF10
Alexei Borodin, Persi Diaconis, and Jason Fulman. On adding a list of numbers (and other one-dependent determinantal processes). Bulletin of the American Mathematical Society, 47(4):639–670, 2010. URL: http://www.ams.org/journals/bull/2010-47-04/S0273-0979-2010-01306-9/S0273-0979-2010-01306-9.pdf, arXiv:0904.3740.
- BRW19
David Burt, Carl Edward Rasmussen, and Mark Van Der Wilk. Rates of Convergence for Sparse Variational Gaussian Process Regression. In International Conference on Machine Learning (ICML), 862–871. may 2019. URL: http://proceedings.mlr.press/v97/burt19a.html, arXiv:1903.03571.
- CDerezinskiV20
Daniele Calandriello, Michal Dereziński, and Michal Valko. Sampling from a k-DPP without looking at all items. In Advances in Neural Information Processing Systems. 2020.
- CLV17
Daniele Calandriello, Alessandro Lazaric, and Michal Valko. Distributed adaptive sampling for kernel matrix approximation. In Artificial Intelligence and Statistics, 1421–1429. 2017.
- DVJ03
Daryl J. Daley and David Vere-Jones. An Introduction to the Theory of Point Processes. Volume I: Elementary Theory and Methods. Probability and its Applications. Springer-Verlag New York, New York, USA, 2 edition, 2003. ISBN 0-387-95541-0. URL: http://link.springer.com/10.1007/b97277, doi:10.1007/b97277.
- DFL13
Laurent Decreusefond, Ian Flint, and Kah Choon Low. Perfect Simulation of Determinantal Point Processes. ArXiv e-prints, 2013. URL: http://arxiv.org/abs/1311.1027, arXiv:1311.1027.
- DWH18
Michal Derezinski, Manfred K Warmuth, and Daniel J Hsu. Leveraged volume sampling for linear regression. In S. Bengio, H. Wallach, H. Larochelle, K. Grauman, N. Cesa-Bianchi, and R. Garnett, editors, Advances in Neural Information Processing Systems 31, pages 2505–2514. Curran Associates, Inc., 2018. URL: http://papers.nips.cc/paper/7517-leveraged-volume-sampling-for-linear-regression.pdf.
- Derezinski19
Michał Dereziński. Fast determinantal point processes via distortion-free intermediate sampling. In Alina Beygelzimer and Daniel Hsu, editors, Proceedings of the Thirty-Second Conference on Learning Theory, volume 99 of Proceedings of Machine Learning Research, 1029–1049. Phoenix, USA, 25–28 Jun 2019. PMLR. URL: http://proceedings.mlr.press/v99/derezinski19a.html.
- DerezinskiCV19
Michal Dereziński, Daniele Calandriello, and Michal Valko. Exact sampling of determinantal point processes with sublinear time preprocessing. In Advances in Neural Information Processing Systems. 2019.
- DE15
Alexander Dubbs and Alan Edelman. Infinite Random Matrix Theory, Tridiagonal Bordered Toeplitz Matrices, and the Moment Problem. Linear Algebra and its Applications, 467:188–201, 2015. arXiv:1502.04931, doi:10.1016/j.laa.2014.11.006.
- DE02
Ioana Dumitriu and Alan Edelman. Matrix Models for Beta Ensembles. Journal of Mathematical Physics, 43(11):5830–5847, 2002. URL: https://sites.math.washington.edu/{~}dumitriu/JMathPhys{\_}43{\_}5830.pdf, arXiv:0206043, doi:10.1063/1.1507823.
- DB18
Christophe Dupuy and Francis Bach. Learning Determinantal Point Processes in Sublinear Time. In International Conference on Artificial Intelligence and Statistics (AISTATS), volume 84, 244–257. Lanzarote, Spain, 2018. PMLR. URL: http://proceedings.mlr.press/v84/dupuy18a, arXiv:1610.05925.
- GBDK19
Mike Gartrell, Victor-Emmanuel Brunel, Elvis Dohmatob, and Syrine Krichene. Learning Nonsymmetric Determinantal Point Processes. ArXiv e-prints, may 2019. URL: http://arxiv.org/abs/1905.12962, arXiv:1905.12962.
- GPK16
Mike Gartrell, Ulrich Paquet, and Noam Koenigstein. Low-Rank Factorization of Determinantal Point Processes for Recommendation. In AAAI Conference on Artificial Intelligence, 1912–1918. 2016. URL: https://www.aaai.org/ocs/index.php/AAAI/AAAI17/paper/download/14657/14354, arXiv:1602.05436.
- GBV17
Guillaume Gautier, Rémi Bardenet, and Michal Valko. Zonotope hit-and-run for efficient sampling from projection DPPs. International Conference on Machine Learning (ICML), pages 1223–1232, may 2017. URL: http://proceedings.mlr.press/v70/gautier17a, arXiv:1705.10498.
- GBV19
Guillaume Gautier, Rémi Bardenet, and Michal Valko. On two ways to use determinantal point processes for Monte Carlo integration. In Neural Information Processing Systems (NeurIPS). 2019. URL:.
- GPBV19
Guillaume Gautier, Guillermo Polito, Rémi Bardenet, and Michal Valko. DPPy: DPP Sampling with Python. Journal of Machine Learning Research - Machine Learning Open Source Software (JMLR-MLOSS), in press, 2019.
- Gau09
Walter Gautschi. How sharp is Bernstein’s Inequality for Jacobi polynomials? Electronic Transactions on Numerical Analysis, 36:1–8, 2009. URL: http://emis.ams.org/journals/ETNA/vol.36.2009-2010/pp1-8.dir/pp1-8.pdf.
- Gil14
Jennifer Gillenwater. Approximate inference for determinantal point processes. PhD thesis, University of Pennsylvania, 2014. URL: https://repository.upenn.edu/edissertations/1285.
- HKPVirag06
J. Ben Hough, Manjunath Krishnapur, Yuval Peres, and Bálint Virág. Determinantal Processes and Independence. In Probability Surveys, volume 3, 206–229. The Institute of Mathematical Statistics and the Bernoulli Society, 2006. URL: http://arxiv.org/abs/math/0503110, arXiv:0503110, doi:10.1214/154957806000000078.
- Joh06
Kurt Johansson. Random matrices and determinantal processes. Les Houches Summer School Proceedings, 83(C):1–56, 2006. arXiv:0510038, doi:10.1016/S0924-8099(06)80038-7.
- Kam18
Mohamed Slim Kammoun. Monotonous subsequences and the descent process of invariant random permutations. Electronic Journal of Probability, 2018. URL: https://projecteuclid.org/euclid.ejp/1543287754, arXiv:1805.05253, doi:10.1214/18-EJP244.
- KDK16
Tarun Kathuria, Amit Deshpande, and Pushmeet Kohli. Batched Gaussian Process Bandit Optimization via Determinantal Point Processes. In Neural Information Processing Systems (NIPS), 4206–4214. 2016. URL: http://papers.nips.cc/paper/6452-batched-gaussian-process-bandit-optimization-via-determinantal-point-processes, arXiv:1611.04088.
- Ker96
Sergei Kerov. A Differential Model Of Growth Of Young Diagrams. Proceedings of St.Petersburg Mathematical Society, 1996. URL: http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.30.7744.
- KN04
Rowan Killip and Irina Nenciu. Matrix models for circular ensembles. International Mathematics Research Notices, 2004(50):2665, 2004. URL: https://academic.oup.com/imrn/article-lookup/doi/10.1155/S1073792804141597, arXiv:0410034, doi:10.1155/S1073792804141597.
- KT12
Alex Kulesza and Ben Taskar. Determinantal Point Processes for Machine Learning. Foundations and Trends in Machine Learning, 5(2-3):123–286, 2012. URL: http://arxiv.org/abs/1207.6083, arXiv:1207.6083, doi:10.1561/2200000044.
- Konig04
Wolfgang König. Orthogonal polynomial ensembles in probability theory. Probab. Surveys, 2:385–447, 2004. URL: http://arxiv.org/abs/math/0403090, arXiv:0403090, doi:10.1214/154957805100000177.
- LGD18
Claire Launay, Bruno Galerne, and Agnès Desolneux. Exact Sampling of Determinantal Point Processes without Eigendecomposition. ArXiv e-prints, feb 2018. URL: http://arxiv.org/abs/1802.08429, arXiv:1802.08429.
- LMollerR12
Frédéric Lavancier, Jesper Møller, and Ege Rubak. Determinantal point process models and statistical inference : Extended version. Journal of the Royal Statistical Society. Series B: Statistical Methodology, 77(4):853–877, may 2012. URL: https://rss.onlinelibrary.wiley.com/doi/abs/10.1111/rssb.12096, arXiv:1205.4818, doi:10.1111/rssb.12096.
- LJS16a
Chengtao Li, Stefanie Jegelka, and Suvrit Sra. Efficient Sampling for k-Determinantal Point Processes. In International Conference on Artificial Intelligence and Statistics (AISTATS), 1328–1337. Cadiz, Spain, 2016. URL: http://proceedings.mlr.press/v51/li16f, arXiv:1509.01618.
- LJS16b
Chengtao Li, Stefanie Jegelka, and Suvrit Sra. Fast DPP Sampling for Nyström with Application to Kernel Methods. In International Conference on Machine Learning (ICML), 2061–2070. New York, USA, 2016. URL: http://proceedings.mlr.press/v48/lih16, arXiv:1603.06052.
- LJS16c
Chengtao Li, Stefanie Jegelka, and Suvrit Sra. Fast Mixing Markov Chains for Strongly Rayleigh Measures, DPPs, and Constrained Sampling. In Neural Information Processing Systems (NIPS), 4188–4196. Barcelona, Spain, 2016. URL: https://papers.nips.cc/paper/6182-fast-mixing-markov-chains-for-strongly-rayleigh-measures-dpps-and-constrained-sampling, arXiv:1608.01008.
- LJS16d
Chengtao Li, Stefanie Jegelka, and Suvrit Sra. Fast Sampling for Strongly Rayleigh Measures with Application to Determinantal Point Processes. ArXiv e-prints, 2016. URL: http://arxiv.org/abs/1607.03559, arXiv:1607.03559.
- Lyo02
Russell Lyons. Determinantal probability measures. Publications mathématiques de l’IHÉS, 98(1):167–212, apr 2002. URL: http://link.springer.com/10.1007/s10240-003-0016-0, arXiv:0204325, doi:10.1007/s10240-003-0016-0.
- Mac75
Odile Macchi. The coincidence approach to stochastic point processes. Advances in Applied Probability, 7(01):83–122, 1975. URL: https://www.cambridge.org/core/product/identifier/S0001867800040313/type/journal{\_}article, doi:10.2307/1425855.
- MCA19
Adrien Mazoyer, Jean-François Coeurjolly, and Pierre-Olivier Amblard. Projections of determinantal point processes. ArXiv e-prints, 2019. URL: https://arxiv.org/pdf/1901.02099.pdf, arXiv:1901.02099v3.
- Mez06
Francesco Mezzadri. How to generate random matrices from the classical compact groups. Notices of the American Mathematical Society, 54:592–604, sep 2006. URL: http://arxiv.org/abs/math-ph/0609050, arXiv:0609050.
- MollerW04
Jesper. Møller and Rasmus Plenge. Waagepetersen. Statistical inference and simulation for spatial point processes. Volume 23. Chapman & Hall/CRC, 2004. ISBN 1584882654. URL: https://www.crcpress.com/Statistical-Inference-and-Simulation-for-Spatial-Point-Processes/Moller-Waagepetersen/p/book/9781584882657, doi:10.1201/9780203496930.
- PB11
Raj K. Pathria and Paul D. Beale. Statistical Mechanics. Academic Press, 2011. ISBN 0123821894. URL: http://linkinghub.elsevier.com/retrieve/pii/B9780123821881000207, doi:10.1016/B978-0-12-382188-1.00020-7.
- Pou19
Jack Poulson. High-performance sampling of generic Determinantal Point Processes. ArXiv e-prints, apr 2019. URL: http://arxiv.org/abs/1905.00165, arXiv:1905.00165.
- PW98
James Gary Propp and David Bruce Wilson. How to Get a Perfectly Random Sample from a Generic Markov Chain and Generate a Random Spanning Tree of a Directed Graph. Journal of Algorithms, 27(2):170–217, may 1998. URL: https://www.sciencedirect.com/science/article/pii/S0196677497909172, doi:10.1006/JAGM.1997.0917.
- RW06
Carl Edward. Rasmussen and Christopher K. I. Williams. Gaussian processes for machine learning. MIT Press, 2006. ISBN 026218253X. URL: http://www.gaussianprocess.org/gpml/.
- RCCR18
Alessandro Rudi, Daniele Calandriello, Luigi Carratino, and Lorenzo Rosasco. On fast leverage score sampling and optimal learning. In Advances in Neural Information Processing Systems 31, pages 5672–5682. 2018.
- Sos00
Alexander Soshnikov. Determinantal random point fields. Russian Mathematical Surveys, 55(5):923–975, feb 2000. URL: http://dx.doi.org/10.1070/RM2000v055n05ABEH000321, arXiv:0002099, doi:10.1070/RM2000v055n05ABEH000321.
- TAB17
Nicolas Tremblay, Pierre-Olivier Amblard, and Simon Barthelme. Graph sampling with determinantal processes. In European Signal Processing Conference (EUSIPCO), 1674–1678. IEEE, aug 2017. URL: http://ieeexplore.ieee.org/document/8081494/, arXiv:1703.01594, doi:10.23919/EUSIPCO.2017.8081494.
- TBA18
Nicolas Tremblay, Simon Barthelme, and Pierre-Olivier Amblard. Optimized Algorithms to Sample Determinantal Point Processes. ArXiv e-prints, feb 2018. URL: http://arxiv.org/abs/1802.08471, arXiv:1802.08471.
- Wig67
Eugene P. Wigner. Random Matrices in Physics. SIAM Review, 9(1):1–23, 1967. doi:10.1137/1009001.