2021
Pérez-Vieites, Sara; Míguez, Joaquín
Nested Gaussian filters for recursive Bayesian inference and nonlinear tracking in state space models Artículo de revista
En: Signal Processing, vol. 189, pp. 108295, 2021, ISSN: 0165-1684.
Resumen | Enlaces | BibTeX | Etiquetas: Bayesian inference, Filtering, Kalman, Monte Carlo, Parameter estimation
@article{PEREZVIEITES2021108295,
title = {Nested Gaussian filters for recursive Bayesian inference and nonlinear tracking in state space models},
author = {Sara P\'{e}rez-Vieites and Joaqu\'{i}n M\'{i}guez},
url = {https://www.sciencedirect.com/science/article/pii/S0165168421003327},
doi = {https://doi.org/10.1016/j.sigpro.2021.108295},
issn = {0165-1684},
year = {2021},
date = {2021-01-01},
urldate = {2021-01-01},
journal = {Signal Processing},
volume = {189},
pages = {108295},
abstract = {We introduce a new sequential methodology to calibrate the fixed parameters and track the stochastic dynamical variables of a state-space system. The proposed method is based on the nested hybrid filtering (NHF) framework of [1], that combines two layers of filters, one inside the other, to compute the joint posterior probability distribution of the static parameters and the state variables. In particular, we explore the use of deterministic sampling techniques for Gaussian approximation in the first layer of the algorithm, instead of the Monte Carlo methods employed in the original procedure. The resulting scheme reduces the computational cost and so makes the algorithms potentially better-suited for high-dimensional state and parameter spaces. We describe a specific instance of the new method and then study its performance and efficiency of the resulting algorithms for a stochastic Lorenz 63 model and for a stochastic volatility model with real data.},
keywords = {Bayesian inference, Filtering, Kalman, Monte Carlo, Parameter estimation},
pubstate = {published},
tppubtype = {article}
}
We introduce a new sequential methodology to calibrate the fixed parameters and track the stochastic dynamical variables of a state-space system. The proposed method is based on the nested hybrid filtering (NHF) framework of [1], that combines two layers of filters, one inside the other, to compute the joint posterior probability distribution of the static parameters and the state variables. In particular, we explore the use of deterministic sampling techniques for Gaussian approximation in the first layer of the algorithm, instead of the Monte Carlo methods employed in the original procedure. The resulting scheme reduces the computational cost and so makes the algorithms potentially better-suited for high-dimensional state and parameter spaces. We describe a specific instance of the new method and then study its performance and efficiency of the resulting algorithms for a stochastic Lorenz 63 model and for a stochastic volatility model with real data.
2018
Crisan, Dan; Míguez, Joaquín
Nested particle filters for online parameter estimation in discrete-time state-space Markov models Artículo de revista
En: Bernoulli, vol. 24, no 4A, pp. 3039 – 3086, 2018.
Enlaces | BibTeX | Etiquetas: error bounds, model inference, Monte Carlo, Parameter estimation, Particle filtering, recursive algorithms, State space models
@article{10.3150/17-BEJ954,
title = {Nested particle filters for online parameter estimation in discrete-time state-space Markov models},
author = {Dan Crisan and Joaqu\'{i}n M\'{i}guez},
url = {https://doi.org/10.3150/17-BEJ954},
doi = {10.3150/17-BEJ954},
year = {2018},
date = {2018-01-01},
urldate = {2018-01-01},
journal = {Bernoulli},
volume = {24},
number = {4A},
pages = {3039 -- 3086},
publisher = {Bernoulli Society for Mathematical Statistics and Probability},
keywords = {error bounds, model inference, Monte Carlo, Parameter estimation, Particle filtering, recursive algorithms, State space models},
pubstate = {published},
tppubtype = {article}
}
Míguez, Joaquín; Mariño, Inés P.; Vázquez, Manuel A
Analysis of a nonlinear importance sampling scheme for Bayesian parameter estimation in state-space models Artículo de revista
En: Signal Processing, vol. 142, pp. 281-291, 2018, ISSN: 0165-1684.
Resumen | Enlaces | BibTeX | Etiquetas: Adaptive importance sampling, Bayesian inference, Importance sampling, Parameter estimation, population Monte Carlo, State space models
@article{MIGUEZ2018281,
title = {Analysis of a nonlinear importance sampling scheme for Bayesian parameter estimation in state-space models},
author = {Joaqu\'{i}n M\'{i}guez and In\'{e}s P. Mari\~{n}o and Manuel A V\'{a}zquez},
url = {https://www.sciencedirect.com/science/article/pii/S0165168417302761},
doi = {https://doi.org/10.1016/j.sigpro.2017.07.030},
issn = {0165-1684},
year = {2018},
date = {2018-01-01},
urldate = {2018-01-01},
journal = {Signal Processing},
volume = {142},
pages = {281-291},
abstract = {The Bayesian estimation of the unknown parameters of state-space (dynamical) systems has received considerable attention over the past decade, with a handful of powerful algorithms being introduced. In this paper we tackle the theoretical analysis of the recently proposed nonlinear population Monte Carlo (NPMC). This is an iterative importance sampling scheme whose key features, compared to conventional importance samplers, are (i) the approximate computation of the importance weights (IWs) assigned to the Monte Carlo samples and (ii) the nonlinear transformation of these IWs in order to prevent the degeneracy problem that flaws the performance of conventional importance samplers. The contribution of the present paper is a rigorous proof of convergence of the nonlinear IS (NIS) scheme as the number of Monte Carlo samples, M, increases. Our analysis reveals that the NIS approximation errors converge to 0 almost surely and with the optimal Monte Carlo rate of M−12. Moreover, we prove that this is achieved even when the mean estimation error of the IWs remains constant, a property that has been termed exact approximation in the Markov chain Monte Carlo literature. We illustrate these theoretical results by means of a computer simulation example involving the estimation of the parameters of a state-space model typically used for target tracking.},
keywords = {Adaptive importance sampling, Bayesian inference, Importance sampling, Parameter estimation, population Monte Carlo, State space models},
pubstate = {published},
tppubtype = {article}
}
The Bayesian estimation of the unknown parameters of state-space (dynamical) systems has received considerable attention over the past decade, with a handful of powerful algorithms being introduced. In this paper we tackle the theoretical analysis of the recently proposed nonlinear population Monte Carlo (NPMC). This is an iterative importance sampling scheme whose key features, compared to conventional importance samplers, are (i) the approximate computation of the importance weights (IWs) assigned to the Monte Carlo samples and (ii) the nonlinear transformation of these IWs in order to prevent the degeneracy problem that flaws the performance of conventional importance samplers. The contribution of the present paper is a rigorous proof of convergence of the nonlinear IS (NIS) scheme as the number of Monte Carlo samples, M, increases. Our analysis reveals that the NIS approximation errors converge to 0 almost surely and with the optimal Monte Carlo rate of M−12. Moreover, we prove that this is achieved even when the mean estimation error of the IWs remains constant, a property that has been termed exact approximation in the Markov chain Monte Carlo literature. We illustrate these theoretical results by means of a computer simulation example involving the estimation of the parameters of a state-space model typically used for target tracking.
Míguez, Joaquín; Mariño, Inés P.; Vázquez, Manuel A
Analysis of a nonlinear importance sampling scheme for Bayesian parameter estimation in state-space models Artículo de revista
En: Signal Processing, vol. 142, pp. 281-291, 2018, ISSN: 0165-1684.
Resumen | Enlaces | BibTeX | Etiquetas: Adaptive importance sampling, Bayesian inference, Importance sampling, Parameter estimation, population Monte Carlo, State space models
@article{MIGUEZ2018281b,
title = {Analysis of a nonlinear importance sampling scheme for Bayesian parameter estimation in state-space models},
author = {Joaqu\'{i}n M\'{i}guez and In\'{e}s P. Mari\~{n}o and Manuel A V\'{a}zquez},
url = {https://www.sciencedirect.com/science/article/pii/S0165168417302761},
doi = {https://doi.org/10.1016/j.sigpro.2017.07.030},
issn = {0165-1684},
year = {2018},
date = {2018-01-01},
urldate = {2018-01-01},
journal = {Signal Processing},
volume = {142},
pages = {281-291},
abstract = {The Bayesian estimation of the unknown parameters of state-space (dynamical) systems has received considerable attention over the past decade, with a handful of powerful algorithms being introduced. In this paper we tackle the theoretical analysis of the recently proposed nonlinear population Monte Carlo (NPMC). This is an iterative importance sampling scheme whose key features, compared to conventional importance samplers, are (i) the approximate computation of the importance weights (IWs) assigned to the Monte Carlo samples and (ii) the nonlinear transformation of these IWs in order to prevent the degeneracy problem that flaws the performance of conventional importance samplers. The contribution of the present paper is a rigorous proof of convergence of the nonlinear IS (NIS) scheme as the number of Monte Carlo samples, M, increases. Our analysis reveals that the NIS approximation errors converge to 0 almost surely and with the optimal Monte Carlo rate of M−12. Moreover, we prove that this is achieved even when the mean estimation error of the IWs remains constant, a property that has been termed exact approximation in the Markov chain Monte Carlo literature. We illustrate these theoretical results by means of a computer simulation example involving the estimation of the parameters of a state-space model typically used for target tracking.},
keywords = {Adaptive importance sampling, Bayesian inference, Importance sampling, Parameter estimation, population Monte Carlo, State space models},
pubstate = {published},
tppubtype = {article}
}
The Bayesian estimation of the unknown parameters of state-space (dynamical) systems has received considerable attention over the past decade, with a handful of powerful algorithms being introduced. In this paper we tackle the theoretical analysis of the recently proposed nonlinear population Monte Carlo (NPMC). This is an iterative importance sampling scheme whose key features, compared to conventional importance samplers, are (i) the approximate computation of the importance weights (IWs) assigned to the Monte Carlo samples and (ii) the nonlinear transformation of these IWs in order to prevent the degeneracy problem that flaws the performance of conventional importance samplers. The contribution of the present paper is a rigorous proof of convergence of the nonlinear IS (NIS) scheme as the number of Monte Carlo samples, M, increases. Our analysis reveals that the NIS approximation errors converge to 0 almost surely and with the optimal Monte Carlo rate of M−12. Moreover, we prove that this is achieved even when the mean estimation error of the IWs remains constant, a property that has been termed exact approximation in the Markov chain Monte Carlo literature. We illustrate these theoretical results by means of a computer simulation example involving the estimation of the parameters of a state-space model typically used for target tracking.
2011
Tuia, D; Verrelst, J; Alonso, L; Perez-Cruz, Fernando; Camps-Valls, Gustavo
Multioutput Support Vector Regression for Remote Sensing Biophysical Parameter Estimation Artículo de revista
En: IEEE Geoscience and Remote Sensing Letters, vol. 8, no 4, pp. 804–808, 2011, ISSN: 1545-598X.
Resumen | Enlaces | BibTeX | Etiquetas: Biological system modeling, Biomedical imaging, Biophysical parameter estimation, chlorophyll content estimation, Estimation, fractional vegetation cover, geophysical image processing, hyperspectral compact high-resolution imaging spec, image resolution, leaf area index, model inversion, multioutput support vector regression method, nonparametric biophysical parameter estimation, Parameter estimation, regression, regression analysis, Remote sensing, remote sensing biophysical parameter estimation, remote sensing image, single-output support vector regression method, spectrometers, Support vector machines, support vector regression (SVR), Vegetation mapping
@article{Tuia2011,
title = {Multioutput Support Vector Regression for Remote Sensing Biophysical Parameter Estimation},
author = {D Tuia and J Verrelst and L Alonso and Fernando Perez-Cruz and Gustavo Camps-Valls},
url = {http://ieeexplore.ieee.org/lpdocs/epic03/wrapper.htm?arnumber=5735189},
issn = {1545-598X},
year = {2011},
date = {2011-01-01},
journal = {IEEE Geoscience and Remote Sensing Letters},
volume = {8},
number = {4},
pages = {804--808},
abstract = {This letter proposes a multioutput support vector regression (M-SVR) method for the simultaneous estimation of different biophysical parameters from remote sensing images. General retrieval problems require multioutput (and potentially nonlinear) regression methods. M-SVR extends the single-output SVR to multiple outputs maintaining the advantages of a sparse and compact solution by using an $epsilon$-insensitive cost function. The proposed M-SVR is evaluated in the estimation of chlorophyll content, leaf area index and fractional vegetation cover from a hyperspectral compact high-resolution imaging spectrometer images. The achieved improvement with respect to the single-output regression approach suggests that M-SVR can be considered a convenient alternative for nonparametric biophysical parameter estimation and model inversion.},
keywords = {Biological system modeling, Biomedical imaging, Biophysical parameter estimation, chlorophyll content estimation, Estimation, fractional vegetation cover, geophysical image processing, hyperspectral compact high-resolution imaging spec, image resolution, leaf area index, model inversion, multioutput support vector regression method, nonparametric biophysical parameter estimation, Parameter estimation, regression, regression analysis, Remote sensing, remote sensing biophysical parameter estimation, remote sensing image, single-output support vector regression method, spectrometers, Support vector machines, support vector regression (SVR), Vegetation mapping},
pubstate = {published},
tppubtype = {article}
}
This letter proposes a multioutput support vector regression (M-SVR) method for the simultaneous estimation of different biophysical parameters from remote sensing images. General retrieval problems require multioutput (and potentially nonlinear) regression methods. M-SVR extends the single-output SVR to multiple outputs maintaining the advantages of a sparse and compact solution by using an $epsilon$-insensitive cost function. The proposed M-SVR is evaluated in the estimation of chlorophyll content, leaf area index and fractional vegetation cover from a hyperspectral compact high-resolution imaging spectrometer images. The achieved improvement with respect to the single-output regression approach suggests that M-SVR can be considered a convenient alternative for nonparametric biophysical parameter estimation and model inversion.