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Particle methods for maximum likelihood estimation in latent variable models

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Abstract

Standard methods for maximum likelihood parameter estimation in latent variable models rely on the Expectation-Maximization algorithm and its Monte Carlo variants. Our approach is different and motivated by similar considerations to simulated annealing; that is we build a sequence of artificial distributions whose support concentrates itself on the set of maximum likelihood estimates. We sample from these distributions using a sequential Monte Carlo approach. We demonstrate state-of-the-art performance for several applications of the proposed approach.

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References

  • Amzal, B., Bois, F.Y., Parent, E., Robert, C.P.: Bayesian optimal design via interacting particle systems. J. Am. Stat. Assoc. 101(474), 773–785 (2006)

    Article  MATH  MathSciNet  Google Scholar 

  • Chopin, N.: Central limit theorem for sequential Monte Carlo methods and its applications to Bayesian inference. Ann. Stat. 32(6), 2385–2411 (2004)

    Article  MATH  MathSciNet  Google Scholar 

  • Del Moral, P.: Feynman-Kac Formulae: Genealogical and Interacting Particle Systems with Applications. Probability and its Applications. Springer, New York (2004)

    MATH  Google Scholar 

  • Del Moral, P., Doucet, A., Jasra, A.: Sequential Monte Carlo samplers. J. R. Stat. Soc. B 63(3), 411–436 (2006)

    Article  MathSciNet  Google Scholar 

  • Dempster, A.P., Laird, N.M., Rubin, D.B.: Maximum likelihood from incomplete data via the EM Algorithm. J. R. Stat. Soc. B 39, 2–38 (1977)

    MathSciNet  Google Scholar 

  • Doucet, A., de Freitas, N., Gordon, N. (eds.): Sequential Monte Carlo Methods in Practice. Statistics for Engineering and Information Science. Springer, New York (2001)

    MATH  Google Scholar 

  • Doucet, A., Godsill, S.J., Robert, C.P.: Marginal maximum a posteriori estimation using Markov chain Monte Carlo. Stat. Comput. 12, 77–84 (2002)

    Article  MathSciNet  Google Scholar 

  • Doucet, A., Briers, M., Sénécal, S.: Efficient block sampling strategies for sequential Monte Carlo methods. J. Comput. Graph. Stat. 15(3), 693–711 (2006)

    Article  Google Scholar 

  • Escobar, M.D., West, M.: Bayesian density estimation and inference using mixtures. J. Am. Stat. Assoc. 90(430), 577–588 (1995)

    Article  MATH  MathSciNet  Google Scholar 

  • Gaetan, C., Yao, J.-F.: A multiple-imputation Metropolis version of the EM algorithm. Biometrika 90(3), 643–654 (2003)

    Article  MathSciNet  Google Scholar 

  • Hwang, C.-R.: Laplace’s method revisited: weak convergence of probability measures. Ann. Probab. 8(6), 1177–1182 (1980)

    MATH  MathSciNet  Google Scholar 

  • Jacquier, E., Johannes, M., Polson, N.: MCMC maximum likelihood for latent state models. J. Econom. 137(2), 615–640 (2007)

    Article  Google Scholar 

  • Johansen, A.M.: Some non-standard sequential Monte Carlo methods with applications, Ph.D. thesis. University of Cambridge, Department of Engineering (2006)

  • Liu, J.S., Chen, R.: Sequential Monte Carlo methods for dynamic systems. J. Am. Stat. Assoc. 93(443), 1032–1044 (1998)

    Article  MATH  Google Scholar 

  • Müller, P., Sansó, B., de Iorio, M.: Optimum Bayesian design by inhomogeneous Markov chain simulation. J. Am. Stat. Assoc. 99(467), 788–798 (2004)

    Article  MATH  Google Scholar 

  • Robert, C.P., Casella, G.: Monte Carlo Statistical Methods, 2nd edn. Springer, New York (2004)

    MATH  Google Scholar 

  • Robert, C.P., Titterington, D.M.: Reparameterization strategies for hidden Markov models and Bayesian approaches to maximum likelihood estimation. Stat. Comput. 8, 145–158 (1998)

    Article  Google Scholar 

  • Roeder, K.: Density estimation with cofidence sets exemplified by superclusters and voids in galaxies. J. Am. Stat. Assoc. 85(411), 617–624 (1990)

    Article  MATH  Google Scholar 

  • Roeder, K., Wasserman, L.: Practical Bayesian density estimation using mixtures of normals. J. Am. Stat. Assoc. 92(439), 894–902 (1997)

    Article  MATH  MathSciNet  Google Scholar 

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Correspondence to Adam M. Johansen.

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Johansen, A.M., Doucet, A. & Davy, M. Particle methods for maximum likelihood estimation in latent variable models. Stat Comput 18, 47–57 (2008). https://doi.org/10.1007/s11222-007-9037-8

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  • DOI: https://doi.org/10.1007/s11222-007-9037-8

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