Monotonically Overrelaxed EM Algorithms

References

• Betensky, R.A., and Finkelstein, D.M. (1999), “A Non-Parametric Maximum Likelihood Estimator for Bivariate Interval Censored Data,” Statistics in Medicine, 18, 3089–3100.
   PubMed Web of Science ®Google Scholar
• Bishop, Y. M.M., Fienberg, S.E., and Holland, P.W. (1975), Discrete Multivariate Analysis: Theory and Practice, Cambridge, MA: MIT Press.
   Google Scholar
• Böhning, D., Schlattmann, P., and Dietz, E. (1996), “Interval Censored Data: A Note on the Nonparametric Maximum Likelihood Estimator of the Distribution Function,” Biometrika, 83, 462–466.
   Web of Science ®Google Scholar
• Deming, W.E., and Stephan, F.F. (1940), “On a Least Squares Adjustment of a Sampled Frequency Table When the Expected Marginal Totals Are Known,” Annals of Mathematical Statistics, 11, 427–444.
   Google Scholar
• Dempster, A.P., Laird, N.M., and Rubin, D.B. (1977), “Maximum Likelihood Estimation From Incomplete Data via the EM Algorithm” (with discussion), Journal of the Royal Statistical Society, Series B, 39, 1–38.
   Google Scholar
• Dette, H., Pepelyshev, A., and Zhigljavsky, A. (2008), “Improving Updating Rules in Multiplicative Algorithms for Computing D-Optimal Designs,” Computational Statistics & Data Analysis, 53, 312–320.
   Web of Science ®Google Scholar
• Fessler, J.A., and Hero, A.O. (1994), “Space-Alternating Generalized Expectation-Maximisation Algorithm,” IEEE Transactions on Signal Processing, 42, 2664–2677.
   Web of Science ®Google Scholar
• Groeneboom, P., and Wellner, J. (1992), Information Bounds and Nonparametric Maximum Likelihood Estimation, Basel: Birkhäuser.
   Google Scholar
• Jamshidian, M., and Jennrich, R.I. (1993), “Conjugate Gradient Acceleration of the EM Algorithm,” Journal of the American Statistical Association, 88, 221–228.
   Web of Science ®Google Scholar
• ——— (1997), “Acceleration of the EM Algorithm by Using Quasi-Newton Methods,” Journal of the Royal Statistical Society, Series B, 59, 569–587.
   Google Scholar
• Kuroda, M., and Sakakihara, M. (2006), “Accelerating the Convergence of the EM Algorithm Using the Vector Epsilon Algorithm,” Computational Statistics and Data Analysis, 51, 1549–1561.
   Web of Science ®Google Scholar
• Laird, N., Lange, N., and Stram, D. (1987), “Maximizing Likelihood Computations With Repeated Measures: Application of the EM Algorithm,” Journal of the American Statistical Association, 82, 97–105.
   Web of Science ®Google Scholar
• Lange, K. (1995a), “A Gradient Algorithm Locally Equivalent to the EM Algorithm,” Journal of the Royal Statistical Society, Series B, 57, 425–438.
   Google Scholar
• ——— (1995b), “A Quasi-Newtonian Acceleration of the EM Algorithm,” Statistica Sinica, 5, 1–18.
   Web of Science ®Google Scholar
• Lange, K., Hunter, D.R., and Yang, I. (2000), “Optimization Transfer Using Surrogate Objective Functions” (with discussion), Journal of Computational and Graphical Statistics, 9, 1–59.
   Web of Science ®Google Scholar
• Liu, C.H., and Rubin, D.B. (1994), “The ECME Algorithm: A Simple Extension of EM and ECM With Faster Monotone Convergence,” Biometrika, 81, 633–648.
   Web of Science ®Google Scholar
• Liu, C.H., Rubin, D.B., and Wu, Y.N. (1998), “Parameter Expansion to Accelerate EM—The PX-EM Algorithm,” Biometrika, 85, 755–770.
   Web of Science ®Google Scholar
• Louis, T.A. (1982), “Finding the Observed Information Matrix When Using the EM Algorithm,” Journal of the Royal Statistical Society, Series B, 44, 226–233.
   Web of Science ®Google Scholar
• Maathuis, M. (2005), “Reduction Algorithm for the NPMLE for the Distribution Function of Bivariate Interval-Censored Data,” Journal of Computational and Graphical Statistics, 14, 352–362.
   Web of Science ®Google Scholar
• McLachlan, G.J., and Krishnan, T. (1997), The EM Algorithm and Extensions, New York: Wiley.
   Google Scholar
• Meng, X.-L., and Rubin, D.B. (1993), “Maximum Likelihood Estimation via the ECM Algorithm: A General Framework,” Biometrika, 80, 267–278.
   Web of Science ®Google Scholar
• Meng, X.-L., and van Dyk, D.A. (1997), “The EM Algorithm—An Old Folk-Song Sung to a Fast New Tune” (with discussion), Journal of the Royal Statistical Society, Series B, 59, 511–567.
   Google Scholar
• ——— (1998), “Fast EM-Type Implementations for Mixed Effects Models,” Journal of the Royal Statistical Society, Series B, 60, 559–578.
   Google Scholar
• ——— (1999), “Seeking Efficient Data Augmentation Schemes via Conditional and Marginal Augmentation,” Biometrika, 86, 301–320.
   Web of Science ®Google Scholar
• Pilla, R.S., and Lindsay, B.G. (2001), “Alternative EM Methods for Nonparametric Finite Mixture Models,” Biometrika, 88, 535–550.
   Web of Science ®Google Scholar
• Salakhutdinov, R., and Roweis, S. (2003), “Adaptive Overrelaxed Bound Optimization Methods,” in Proceedings of the Twentieth International Conference on Machine Learning (ICML-2003), Washington, DC, pp. 664–671.
   Google Scholar
• Schlossmacher, E.J. (1973), “An Iterative Technique for Absolute Deviations Curve Fitting,” Journal of the American Statistical Association, 68, 857–859.
   Web of Science ®Google Scholar
• Turnbull, B.W. (1976), “The Empirical Distribution Function With Arbitrarily Grouped, Censored and Truncated Data,” Journal of the Royal Statistical Society, Series B, 38, 290–295.
   Google Scholar
• Vaida, F. (2005), “Parameter Convergence for EM and MM Algorithms,” Statistica Sinica, 15, 831–840.
   Web of Science ®Google Scholar
• van Dyk, D.A., and Meng, X.-L. (2001), “The Art of Data Augmentation” (with discussion), Journal of Computational and Graphical Statistics, 10, 1–111.
   Web of Science ®Google Scholar
• Varadhan, R., and Roland, C. (2004), “Squared Extrapolation Methods (SQUAREM): A New Class of Simple and Efficient Numerical Schemes for Accelerating the Convergence of the EM Algorithm,” Working Paper 63, Department of Biostatistics, Johns Hopkins University, 1–70.
   Google Scholar
• Vardi, Y., Shepp, L.A., and Kaufman, L. (1985), “A Statistical Model for Positron Emission Tomography” (with discussion), Journal of the American Statistical Association, 80, 8–37.
   Web of Science ®Google Scholar
• Wellner, J.A., and Zhan, Y. (1997), “A Hybrid Algorithm for Computation of the Nonparametric Maximum Likelihood Estimator From Censored Data,” Journal of the American Statistical Association, 92, 945–959.
   Web of Science ®Google Scholar
• Wu, C. F.J. (1983), “On the Convergence Properties of the EM Algorithm,” The Annals of Statistics, 11, 95–103.
   Web of Science ®Google Scholar
• Young, D. (1971), Iterative Solutions of Large Linear Systems, New York: Academic Press.
   Google Scholar
• Yu, Y. (2010a), “Squeezing the Arimoto-Blahut Algorithm for Faster Convergence,” IEEE Transactions on Information Theory, 56, 3149–3157.
   Web of Science ®Google Scholar
• ——— (2010b), “Strict Monotonicity and Convergence Rate of Titterington’s Algorithm for Computing D-Optimal Designs,” Computational Statistics & Data Analysis, 54, 1419–1425.
   Web of Science ®Google Scholar
• ——— (2010c), “Improved EM for Mixture Proportions With Applications to Nonparametric ML Estimation for Censored Data,” Preprint, arXiv:1002.3640.
   Google Scholar