Switching nonparametric regression models

References

• Baum, L., Petrie, T., Soules, G., and Weiss, N. (1970), ‘A Maximization Technique Occurring in the Statistical Analysis of Probabilistic Functions of Markov Chains’, The Annals of Mathematical Statistics, 41, 164–171. doi: 10.1214/aoms/1177697196
   Google Scholar
• Bilmes, J. (1998), ‘A Gentle Tutorial of the EM Algorithm and its Application to Parameter Estimation for Gaussian Mixture and Hidden Markov Models’, Technical Report TR-97-021, ICSI.
   Google Scholar
• Cappé, O., Moulines, E., and Rydén, T. (2005), Inference in Hidden Markov Models, New York: Springer Verlag.
   Google Scholar
• Chiou, J. (2012), ‘Dynamical Functional Prediction and Classification, with Application to Traffic Flow Prediction’, The Annals of Applied Statistics, 6, 1588–1614. doi: 10.1214/12-AOAS595
   Web of Science ®Google Scholar
• Dempster, A.P., Laird, N.M., and Rubin, D.B. (1977), ‘Maximum Likelihood from Incomplete Data via the EM Algorithm’, Journal of the Royal Statistical Society Series B, 39, 1–38.
   Google Scholar
• Fan, J., and Gijbels, I. (1992), ‘Variable Bandwidth and Local Linear Regression Smoothers’, Annals of Statistics, 20, 2008–2036. doi: 10.1214/aos/1176348900
   Web of Science ®Google Scholar
• Gijbels, I., and Goderniaux, A. (2004), ‘Bootstrap Test for Change-Points in Nonparametric Regression’, Journal of Nonparametric Statistics, 16, 591–611. doi: 10.1080/10485250310001626088
   Web of Science ®Google Scholar
• Härdle, W. (1990), Applied Nonparametric Regression, Cambridge: Cambridge University Press.
   Google Scholar
• Härdle, W., and Marron, J. (1995), ‘Fast and Simple Scatterplot Smoothing’, Computational Statistics & Data Analysis, 20, 1–17. doi: 10.1016/0167-9473(94)00031-D
   Web of Science ®Google Scholar
• Heckman, N. (2012), ‘Reproducing Kernel Hilbert Spaces Made Easy’, Statistics Surveys, 6, 113–141. doi: 10.1214/12-SS101
   Google Scholar
• Lázaro-Gredilla, M., Van Vaerenbergh, S., and Lawrence, N.D. (2012), ‘Overlapping Mixtures of Gaussian Processes for the Data Association Problem’, Pattern Recognition, 45, 1386–1395. doi: 10.1016/j.patcog.2011.10.004
   Web of Science ®Google Scholar
• Louis, T. (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
• McLachlan, G., and Krishnan, T. (2008), The EM Algorithm and Extensions (2nd ed.), 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. doi: 10.1093/biomet/80.2.267
   Web of Science ®Google Scholar
• Ou, X., and Martin, E. (2008), ‘Batch Process Modelling with Mixtures of Gaussian Processes’, Neural Computing & Applications, 17, 471–479. doi: 10.1007/s00521-007-0144-4
   Web of Science ®Google Scholar
• Rabiner, L. (1989), ‘A Tutorial on Hidden Markov Models and Selected Applications in Speech Recognition’, Proceedings of the IEEE, 77, 257–286. doi: 10.1109/5.18626
   Web of Science ®Google Scholar
• Rasmussen, C., and Ghahramani, Z. (2002), ‘Infinite Mixtures of Gaussian Process Experts’, in Advances in Neural Information Processing Systems 14: Proceedings of the 2001 Conference, Vol. 2, Cambridge, MA: The MIT Press, pp. 881–888.
   Google Scholar
• Rasmussen, C.E., and Williams, C.K.I. (2006), Gaussian Processes for Machine Learning, Cambridge, MA: The MIT Press.
   Google Scholar
• Ruppert, D., Wand, M.P., and Carroll, R.J. (2003), Semiparametric Regression, Cambridge: Cambridge University Press.
   Google Scholar
• Schiegg, M., Neumann, M., and Kersting, K. (2012), ‘Markov Logic Mixtures of Gaussian Processes: Towards Machines Reading Regression Data’, in Proceedings of the 15th International Conference on Artificial Intelligence and Statistics, Vol. 22.
   Google Scholar
• Schmidt, G., Mattern, R., and Schüler, F. (1981), ‘Biomechanical Investigation to Determine Physical and Traumatological Differentiation Criteria for the Maximum Load Capacity of Head and Vertebral Column with and without Protective Helmet under the Effects of Impact’, EEC Research Program on Biomechanics of Impacts. Final report Phase III, Project G5, Institut für Rechtsmedizin, Universität Heidelberg.
   Google Scholar
• Shi, J., Murray-Smith, R., and Titterington, D. (2005), ‘Hierarchical Gaussian Process Mixtures for Regression’, Statistics and Computing, 15, 31–41. doi: 10.1007/s11222-005-4787-7
   Web of Science ®Google Scholar
• Silverman, B. (1985), ‘Some Aspects of the Spline Smoothing Approach to Non-Parametric Regression Curve Fitting’, Journal of the Royal Statistical Society Series B, 47, 1–52.
   Google Scholar
• Tresp, V. (2001), ‘Mixtures of Gaussian Processes’, in Advances in Neural Information Processing Systems 13: Proceedings of the 2000 Conference, Cambridge, MA: The MIT Press, pp. 654–660.
   Google Scholar
• Wahba, G. (1983), ‘Bayesian “Confidence Intervals" for the Cross-Validated Smoothing Spline’, Journal of the Royal Statistical Society Series B, 45, 133–150.
   Google Scholar
• Wood, S.N. (2011), ‘Fast Stable Restricted Maximum Likelihood and Marginal Likelihood Estimation of Semiparametric Generalized Linear Models’, Journal of the Royal Statistical Society Series B, 73, 3–36. doi: 10.1111/j.1467-9868.2010.00749.x
   Google Scholar
• Yang, Y., and Ma, J. (2011), ‘An Efficient EM Approach to Parameter Learning of the Mixture of Gaussian Processes’, in Proceedings of the 8th International Conference on Advances in Neural Networks, Berlin: Springer-Verlag, pp. 165–174.
   Google Scholar