zbMATH — the first resource for mathematics

Adaptive low-nonnegative-rank approximation for state aggregation of Markov chains. (English) Zbl 07183945
65K05 Numerical mathematical programming methods
90C06 Large-scale problems in mathematical programming
90C40 Markov and semi-Markov decision processes
Full Text: DOI
[1] T. W. Anderson and L. A. Goodman, Statistical inference about Markov chains, Ann. Math. Stat., 28 (1957), pp. 89-110, http://www.jstor.org/stable/2237025. · Zbl 0087.14905
[2] D. P. Bertsekas, Dynamic Programming and Optimal Control, Vols. I and II, Athena Scientific, Belmont, MA, 1995.
[3] D. P. Bertsekas, Abstract Dynamic Programming, Athena Scientific, Belmont, MA, 2018. · Zbl 1394.90001
[4] J. Bolte, S. Sabach, and M. Teboulle, Proximal alternating linearized minimization for nonconvex and nonsmooth problems, Math. Program., 146 (2014), pp. 459-494, https://doi.org/10.1007/s10107-013-0701-9. · Zbl 1297.90125
[5] S. Burer and R. D. Monteiro, A nonlinear programming algorithm for solving semidefinite programs via low-rank factorization, Math. Program., 95 (2003), pp. 329-357. · Zbl 1030.90077
[6] E. J. Candès and B. Recht, Exact matrix completion via convex optimization, Found. Comput. Math., 9 (2009), 717. · Zbl 1219.90124
[7] V. Chandrasekaran, B. Recht, P. A. Parrilo, and A. S. Willsky, The convex geometry of linear inverse problems, Found. Comput. Math., 12 (2012), pp. 805-849, https://doi.org/10.1007/s10208-012-9135-7. · Zbl 1280.52008
[8] Y. Chen and X. Ye, Projection Onto a Simplex, preprint, https://arxiv.org/abs/1101.6081, 2011.
[9] J. E. Cohen and U. G. Rothblum, Nonnegative ranks, decompositions, and factorizations of nonnegative matrices, Linear Algebra Appl., 190 (1993), pp. 149-168, https://doi.org/10.1016/0024-3795(93)90224-C. · Zbl 0784.15001
[10] W. E, T. Li, and E. Vanden-Eijnden, Optimal partition and effective dynamics of complex networks, Proc. Natl. Acad. Sci. USA, 105 (2008), pp. 7907-7912. · Zbl 1205.68031
[11] B. D. Haeffele and R. Vidal, Global Optimality in Tensor Factorization, Deep Learning, and Beyond, preprint, https://arxiv.org/abs/1506.07540, 2015.
[12] M. Journée, F. Bach, P.-A. Absil, and R. Sepulchre, Low-rank optimization on the cone of positive semidefinite matrices, SIAM J. Optim., 20 (2010), pp. 2327-2351. · Zbl 1215.65108
[13] R. H. Keshavan and S. Oh, A Gradient Descent Algorithm on the Grassman Manifold for Matrix Completion, preprint, https://arxiv.org/abs/0910.5260, 2009.
[14] H. Kim and H. Park, Nonnegative matrix factorization based on alternating nonnegativity constrained least squares and active set method, SIAM J. Matrix Anal. Appl., 30 (2008), pp. 713-730. · Zbl 1162.65354
[15] J. Kim and H. Park, Fast nonnegative matrix factorization: An active-set-like method and comparisons, SIAM J. Sci. Comput., 33 (2011), pp. 3261-3281. · Zbl 1232.65068
[16] D. D. Lee and H. S. Seung, Algorithms for non-negative matrix factorization, Adv. Neural Inf. Process. Syst., 13 (2001), pp. 556-562. http://papers.nips.cc/paper/1861-algorithms-for-non-negative-matrix-factorization.pdf.
[17] X. Li, M. Wang, and A. Zhang, Estimation of Markov Chain via Rank-constrained Likelihood, Proc. Mach. Learn. Res., 80 (2018), pp. 3033-3042.
[18] C.-J. Lin, Projected gradient methods for nonnegative matrix factorization, Neural Comput., 19 (2007), pp. 2756-2779, https://doi.org/10.1162/neco.2007.19.10.2756. · Zbl 1173.90583
[19] B. Mishra, G. Meyer, F. Bach, and R. Sepulchre, Low-rank optimization with trace norm penalty, SIAM J. Optim., 23 (2013), pp. 2124-2149. · Zbl 1286.65078
[20] B. Recht, M. Fazel, and P. A. Parrilo, Guaranteed minimum-rank solutions of linear matrix equations via nuclear norm minimization, SIAM Rev., 52 (2010), pp. 471-501, https://doi.org/10.1137/070697835. · Zbl 1198.90321
[21] R. S. Sutton and A. G. Barto, Reinforcement Learning: An Introduction, MIT Press, Cambridge, MA, 2018. · Zbl 1407.68009
[22] N. TLC, NYC Taxi and Limousine Commission (TLC) Trip Record Data, http://www.nyc.gov/html/tlc/html/about/trip_record_data.shtml, 2018.
[23] S. A. Vavasis, On the complexity of nonnegative matrix factorization, SIAM J. Optim., 20 (2010), pp. 1364-1377, https://doi.org/10.1137/070709967. · Zbl 1206.65130
[24] Z. Wen, W. Yin, and Y. Zhang, Solving a low-rank factorization model for matrix completion by a nonlinear successive over-relaxation algorithm, Math. Program. Comput., 4 (2012), pp. 333-361. · Zbl 1271.65083
[25] L. F. Yang, V. Braverman, T. Zhao, and M. Wang, Online Factorization and Partition of Complex Networks From Random Walks, Proceedings of the Conference on Uncertainty in Artifical Intelligence, http://auai.org/uai2019/proceedings/papers/299.pdf, 2017.
[26] A. Zhang and M. Wang, Spectral State Compression of Markov Processes, IEEE Trans. Inform. Theory, to appear, 2019.
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.