Learning Markov Models Via Low-Rank Optimization
Published Online:23 Nov 2021https://doi.org/10.1287/opre.2021.2115
References
- (2014) Tensor decompositions for learning latent variable models. J. Mach. Learn. Res. 15(1):2773–2832.Google Scholar
- (2016) Reinforcement learning in rich-observation MDPs using spectral methods. Preprint, submitted November 11, 2016, https://arxiv.org/abs/1611.03907.Google Scholar
- (2017) The spacey random walk: A stochastic process for higher-order data. SIAM Rev. 59(2):321–345.Crossref, Google Scholar
- (1995) Dynamic Programming and Optimal Control, vol. 1. (Athena Scientific, Belmont, MA).Google Scholar
- (1995) Neuro-dynamic programming: an overview. Proceedings of the 34th IEEE Conference on Decision and Control, vol. 1 (IEEE), 560–564.Google Scholar
- (1999) Markov Chains: Gibbs fields, Monte Carlo Simulation, and Queues, vol. 31. (Springer Science & Business Media, Berlin, Germany).Crossref, Google Scholar
- (1994) Exact and ordinary lumpability in finite Markov chains. J. Appl. Probab. 31(1):59–75.Crossref, Google Scholar
- (2016) Poisson matrix recovery and completion. IEEE Trans. Signal Process. 64(6):1609–1620.Crossref, Google Scholar
- (2017) An efficient inexact symmetric Gauss–Seidel based majorized ADMM for high-dimensional convex composite conic programming. Math. Program. 161(1-2):237–270.Crossref, Google Scholar
- (2016) The direct extension of admm for multi-block convex minimization problems is not necessarily convergent. Math. Program. 155(1-2):57–79.Crossref, Google Scholar
- (2007) Automatic discovery of metastable states for the construction of Markov models of macromolecular conformational dynamics. J. Chem. Phys. 126(15), 155101.Crossref, Google Scholar
- (2008) Diffusion maps, reduction coordinates, and low dimensional representation of stochastic systems. Multiscale Model. Simul. 7(2):842–864.Crossref, Google Scholar
- (2012) Model reduction of Markov chains via low-rank approximation. American Control Conference (ACC), 2012, 2651–2656.Google Scholar
- (2011) Optimal Kullback-Leibler aggregation via spectral theory of Markov chains. IEEE Trans. Automat. Control. 56(12):2793–2808.Crossref, Google Scholar
- (2018) Semidefinite programming approach for the quadratic assignment problem with a sparse graph. Comput. Optim. Appl. 69:677–712.Crossref, Google Scholar
- (1991) Eigenvalue bounds on convergence to stationarity for nonreversible Markov chains, with an application to the exclusion process. Ann. Appl. Probab. 1(1):62–87.Crossref, Google Scholar
- (2010) A majorized penalty approach for calibrating rank constrained correlation matrix problems. Technical Report.Google Scholar
- (2016) Inference of high-dimensional autoregressive generalized linear models. Preprint, Submitted May 9, 2016, https://arxiv.org/abs/1605.02693.Google Scholar
- (2015) Minimax estimation of discrete distributions under ℓ1 loss. IEEE Trans. Inform. Theory. 61(11):6343–6354.Crossref, Google Scholar
- (2018) On learning Markov chains. Adv. Neural Inf. Process. Syst. Preprint, Submitted October 28, 2018, https://arxiv.org/abs/1810.11754.Google Scholar
- (2012) A spectral algorithm for learning hidden Markov models. J. Comput. System Sci. 78(5):1460–1480.Crossref, Google Scholar
- (2016) Recovering structured probability matrices. Preprint, Submitted February 21, 2016, https://arxiv.org/abs/1602.06586.Google Scholar
- (2018) Bernstein’s inequality for general markov chains. Preprint, Submitted May 28, 2018, https://arxiv.org/abs/1805.10721.Google Scholar
- (2015) Minimax optimal rates for poisson inverse problems with physical constraints. IEEE Trans. Inform. Theory. 61(8):4458–4474.Crossref, Google Scholar
- (2014) A partial proximal point algorithm for nuclear norm regularized matrix least squares problems. Math. Program. Comput. 6(3):281–325.Crossref, Google Scholar
- (2010) Matrix completion from a few entries. IEEE Trans. Inform. Theory. 56(6):2980–2998.Crossref, Google Scholar
- (2011) Nuclear-norm penalization and optimal rates for noisy low-rank matrix completion. Ann. Statist. 39(5):2302–2329.Crossref, Google Scholar
- (2007) Measure concentration of strongly mixing processes with applications. Ph.D. thesis, Carnegie Mellon University, School of Computer Science, Machine Learning.Google Scholar
- (2008) Concentration inequalities for dependent random variables via the martingale method. Ann. Probab. 36(6):2126–2158.Crossref, Google Scholar
- (2018) Fast algorithms for large-scale generalized distance weighted discrimination. J. Comput. Graph. Stat. 27(2):368–379.Crossref, Google Scholar
- (2018) DC programming and DCA: thirty years of developments. Math. Program. 169:5–68.Crossref, Google Scholar
- (2012) Exact penalty and error bounds in DC programming. J. Global Optim. 52(3):509–535.Crossref, Google Scholar
- (2017) Stochastic DCA for the large-sum of non-convex functions problem and its application to group variable selection in classification. International Conference on Machine Learning, 33 94–34 03.Google Scholar
- (2006) Theory of Point Estimation. (Springer Science & Business Media, Berlin, Germany).Google Scholar
- (2016a) A majorized ADMM with indefinite proximal terms for linearly constrained convex composite optimization. SIAM J. Optim. 26(2):922–950.Crossref, Google Scholar
- (2016b) A Schur complement based semi-proximal ADMM for convex quadratic conic programming and extensions. Math. Program. 155(1-2):333–373.Crossref, Google Scholar
- (2012) Understanding intra-urban trip patterns from taxi trajectory data. J. Geogr. Syst. 14(4):463–483.Crossref, Google Scholar
- (2015) Regularized m-estimators with nonconvexity: Statistical and algorithmic theory for local optima. J. Mach. Learn. Res. 16(1):559–616.Google Scholar
- (1996) Bounding d¯-distance by informational divergence: A method to prove measure concentration. Ann. Probab. 24(2):857–866.Crossref, Google Scholar
- (1991) Variable resolution dynamic programming: Efficiently learning action maps in multivariate real-valued state-spaces. Machine Learn. Proc. 1991:333–337.Google Scholar
- (2016) Rank centrality: Ranking from pairwise comparisons. Oper. Res. 65(1):266–287.Link, Google Scholar
- (2011) Estimation of (near) low-rank matrices with noise and high-dimensional scaling. Ann. Statist. 39(2):1069–1097.Crossref, Google Scholar
- (2013) Spectral methods for community detection and graph partitioning. Phys. Rev. E. 88(4):042822.Crossref, Google Scholar
- (2015) Concentration inequalities for markov chains by Marton couplings and spectral methods. Electron. J. Probab. 20:1–32.Google Scholar
- (1997) Convex analysis approach to DC programming: Theory, algorithms and applications. Acta Math. Vietnam. 22(1):289–355.Google Scholar
- (2005) The DC (difference of convex functions) programming and DCA revisited with DC models of real world nonconvex optimization problems. Ann. Oper. Res. 133(1-4):23–46.Crossref, Google Scholar
- (2015) Convex Analysis (Princeton University Press, Princeton, NJ).Google Scholar
- (2011) Determination of reaction coordinates via locally scaled diffusion map. J. Chem. Phys. 134(12):124116.Crossref, Google Scholar
- (1995) Reinforcement learning with soft state aggregation. Tesauro G, Touretzky D, Leen T, eds. Advances in Neural Information Processing Systems 7 (MIT Press, Cambridge, MA) 361–368.Google Scholar
- (1957) The problem of estimation. Ann. Math. Statist. 28(3):633–648.Crossref, Google Scholar
- (1998) Reinforcement Learning: An Introduction, vol. 1 (MIT Press, Cambridge, MA).Google Scholar
- (2011) Freedman’s inequality for matrix martingales. Electron. Commun. Probab. 16:262–270.Crossref, Google Scholar
- (2015) Convergence analysis of algorithms for DC programming. Preprint, Submitted August 17, 2015, https://arxiv.org/abs/1508.03899.Google Scholar
- (2018) Another look at distance-weighted discrimination. J. R. Stat. Soc. Ser. B. Stat. Methodol. 80(1):177–198.Crossref, Google Scholar
- (1993) On matrix approximation problems with Ky Fank norms. Numer. Algorithms. 5(5):263–272.Crossref, Google Scholar
- (2018) A proximal difference-of-convex algorithm with extrapolation. Comput. Optim. Appl. 69:297–324.Crossref, Google Scholar
- (2019a) Estimating the mixing time of ergodic Markov chains. Conf. Learn. Theory.Google Scholar
- (2019b) Minimax learning of ergodic Markov chains. International Conference on Algorithmic Learning Theory.Google Scholar
- (2017) Dynamic partition of complex networks. Preprint, Submitted May 23, 2017, arXiv:1705.07881.Google Scholar
- (2019) Spectral state compression of markov processes. IEEE Trans. Inform. Theory. 66:3202–3231.Google Scholar

