An adaptive population importance sampler

Monte Carlo (MC) methods are widely used in signal processing, machine learning and communications for statistical inference and stochastic optimization. A well-known class of MC methods is composed of importance sampling and its adaptive extensions (e.g., population Monte Carlo). In this work, we introduce an adaptive importance sampler using a population of proposal densities. The novel algorithm provides a global estimation of the variables of interest iteratively, using all the samples generated. The cloud of proposals is adapted by learning from a subset of previously generated samples, in such a way that local features of the target density can be better taken into account compared to single global adaptation procedures. Numerical results show the advantages of the proposed sampling scheme in terms of mean absolute error and robustness to initialization.

[1]  A. Owen,et al.  Safe and Effective Importance Sampling , 2000 .

[2]  Petar M. Djuric,et al.  Gaussian particle filtering , 2003, IEEE Trans. Signal Process..

[3]  J. Skilling.  Nested sampling for general Bayesian computation , 2006 .

[4]  Xiaodong Wang,et al.  Monte Carlo methods for signal processing: a review in the statistical signal processing context , 2005, IEEE Signal Processing Magazine.

[5]  Jean-Marie Cornuet,et al.  Adaptive Multiple Importance Sampling , 2009, 0907.1254.

[6]  O. Cappé,et al.  Population Monte Carlo , 2004 .

[7]  Maurizio Dapor.  Monte Carlo Strategies , 2020, Transport of Energetic Electrons in Solids.

[8]  Jean-Michel Marin,et al.  Convergence of Adaptive Sampling Schemes , 2004 .

[9]  Mónica F. Bugallo,et al.  Marginalized population Monte Carlo , 2009, 2009 IEEE International Conference on Acoustics, Speech and Signal Processing.

[10]  R. Douc,et al.  Minimum variance importance sampling via Population Monte Carlo , 2007 .

[11]  Christian P. Robert,et al.  Monte Carlo Statistical Methods , 2005, Springer Texts in Statistics.

[12]  William J. Fitzgerald,et al.  Markov chain Monte Carlo methods with applications to signal processing , 2001, Signal Process..

[13]  Petar M. Djuric,et al.  Applications of particle filtering to communications: A review , 2002, 2002 11th European Signal Processing Conference.

[14]  J. Corander,et al.  Reconstructing population histories from single nucleotide polymorphism data. , 2011, Molecular biology and evolution.

[15]  H. Haario,et al.  An adaptive Metropolis algorithm , 2001 .

[16]  Petar M. Djuric,et al.  Gibbs sampling approach for generation of truncated multivariate Gaussian random variables , 1999, 1999 IEEE International Conference on Acoustics, Speech, and Signal Processing. Proceedings. ICASSP99 (Cat. No.99CH36258).

[17]  Luca Martino,et al.  Generalized rejection sampling schemes and applications in signal processing , 2009, Signal Process..

[18]  John W. Fisher,et al.  Nonparametric belief propagation for self-localization of sensor networks , 2005, IEEE Journal on Selected Areas in Communications.

[19]  C. Robert,et al.  Properties of nested sampling , 2008, 0801.3887.

[20]  Rong Chen,et al.  Monte Carlo Bayesian Signal Processing for Wireless Communications , 2002, J. VLSI Signal Process..

[21]  Xiaodong Wang,et al.  Monte Carlo methods for signal processing , 2005 .

[22]  Leonidas J. Guibas,et al.  Optimally combining sampling techniques for Monte Carlo rendering , 1995, SIGGRAPH.

[23]  Nando de Freitas,et al.  An Introduction to MCMC for Machine Learning , 2004, Machine Learning.

[24]  T. Hesterberg,et al.  Weighted Average Importance Sampling and Defensive Mixture Distributions , 1995 .

[25]  G. Parisi,et al.  Simulated tempering: a new Monte Carlo scheme , 1992, hep-lat/9205018.

[26]  C. Cornell,et al.  Adaptive Importance Sampling , 1990 .

[27]  Jun S. Liu,et al.  Monte Carlo strategies in scientific computing , 2001 .

[28]  Andreas M. Ali,et al.  An Empirical Study of Collaborative Acoustic Source Localization , 2007, 2007 6th International Symposium on Information Processing in Sensor Networks.

[29]  Luca Martino,et al.  Fully adaptive Gaussian mixture Metropolis-Hastings algorithm , 2012, 2013 IEEE International Conference on Acoustics, Speech and Signal Processing.

[30]  Joaquín Míguez,et al.  Robust mixture populationmonte Carlo scheme with adaptation of the number of components , 2013, 21st European Signal Processing Conference (EUSIPCO 2013).