@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}

}

@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}

}

@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}

}

@article{Martino2016b,

title = {Orthogonal Parallel MCMC Methods for Sampling and Optimization},

author = {Luca Martino and Victor Elvira and David Luengo and Jukka Corander and Francisco Louzada},

url = {http://www.sciencedirect.com/science/article/pii/S1051200416300987},

doi = {10.1016/j.dsp.2016.07.013},

issn = {10512004},

year  = {2016},

date = {2016-11-01},

journal = {Digital Signal Processing},

volume = {58},

pages = {64--84},

abstract = {Monte Carlo (MC) methods are widely used for Bayesian inference and optimization in statistics, signal processing and machine learning. A well-known class of MC methods are Markov Chain Monte Carlo (MCMC) algorithms. In order to foster better exploration of the state space, specially in high-dimensional applications, several schemes employing multiple parallel MCMC chains have been recently introduced. In this work, we describe a novel parallel interacting MCMC scheme, called orthogonal MCMC (O-MCMC), where a set of “vertical” parallel MCMC chains share information using some “horizontal” MCMC techniques working on the entire population of current states. More specifically, the vertical chains are led by random-walk proposals, whereas the horizontal MCMC techniques employ independent proposals, thus allowing an efficient combination of global exploration and local approximation. The interaction is contained in these horizontal iterations. Within the analysis of different implementations of O-MCMC, novel schemes in order to reduce the overall computational cost of parallel multiple try Metropolis (MTM) chains are also presented. Furthermore, a modified version of O-MCMC for optimization is provided by considering parallel simulated annealing (SA) algorithms. Numerical results show the advantages of the proposed sampling scheme in terms of efficiency in the estimation, as well as robustness in terms of independence with respect to initial values and the choice of the parameters.},

keywords = {Bayesian inference, Block Independent Metropolis, Journal, Optimization, Parallel Markov Chain Monte Carlo, Parallel Multiple Try Metropolis, Parallel Simulated Annealing, Recycling samples},

pubstate = {published},

tppubtype = {article}

}

@article{Nazabal2016b,

title = {Human Activity Recognition by Combining a Small Number of Classifiers.},

author = {Alfredo Naz\'{a}bal and Pablo Garcia-Moreno and Antonio Art\'{e}s-Rodr\'{i}guez and Zoubin Ghahramani},

url = {http://ieeexplore.ieee.org/articleDetails.jsp?arnumber=7161292},

doi = {10.1109/JBHI.2015.2458274},

issn = {2168-2208},

year  = {2016},

date = {2016-09-01},

journal = {IEEE journal of biomedical and health informatics},

volume = {20},

number = {5},

pages = {1342 -- 1351},

publisher = {IEEE},

abstract = {We consider the problem of daily Human Activity Recognition (HAR) using multiple wireless inertial sensors and, specifically, HAR systems with a very low number of sensors, each one providing an estimation of the performed activities. We propose new Bayesian models to combine the output of the sensors. The models are based on a soft outputs combination of individual classifiers to deal with the small number of sensors. We also incorporate the dynamic nature of human activities as a first order homogeneous Markov chain. We develop both inductive and transductive inference methods for each model to be employed in supervised and semi-supervised situations, respectively. Using different real HAR databases, we compare our classifiers combination models against a single classifier that employs all the signals from the sensors. Our models exhibit consistently a reduction of the error rate and an increase of robustness against sensor failures. Our models also outperform other classifiers combination models that do not consider soft outputs and a Markovian structure of the human activities.},

keywords = {Bayes methods, Bayesian inference, Biological system modeling, Classifier combination, Databases, Estimation, Hidden Markov models, Journal, Sensor systems},

pubstate = {published},

tppubtype = {article}

}

@article{Koblents2016,

title = {A Nonlinear Population Monte Carlo Scheme for the Bayesian Estimation of Parameters of α-stable Distributions},

author = {Eugenia Koblents and Joaqu\'{i}n M\'{i}guez and Marco A Rodr\'{i}guez and Alexandra M Schmidt},

url = {http://www.sciencedirect.com/science/article/pii/S0167947315002340},

doi = {10.1016/j.csda.2015.09.007},

issn = {01679473},

year  = {2016},

date = {2016-03-01},

journal = {Computational Statistics \& Data Analysis},

volume = {95},

pages = {57--74},

abstract = {The class of $alpha$-stable distributions enjoys multiple practical applications in signal processing, finance, biology and other areas because it allows to describe interesting and complex data patterns, such as asymmetry or heavy tails, in contrast with the simpler and widely used Gaussian distribution. The density associated with a general $alpha$-stable distribution cannot be obtained in closed form, which hinders the process of estimating its parameters. A nonlinear population Monte Carlo (NPMC) scheme is applied in order to approximate the posterior probability distribution of the parameters of an $alpha$-stable random variable given a set of random realizations of the latter. The approximate posterior distribution is computed by way of an iterative algorithm and it consists of a collection of samples in the parameter space with associated nonlinearly-transformed importance weights. A numerical comparison of the main existing methods to estimate the $alpha$-stable parameters is provided, including the traditional frequentist techniques as well as a Markov chain Monte Carlo (MCMC) and a likelihood-free Bayesian approach. It is shown by means of computer simulations that the NPMC method outperforms the existing techniques in terms of parameter estimation error and failure rate for the whole range of values of $alpha$, including the smaller values for which most existing methods fail to work properly. Furthermore, it is shown that accurate parameter estimates can often be computed based on a low number of observations. Additionally, numerical results based on a set of real fish displacement data are provided.},

keywords = {Animal movement, Bayesian inference, Importance sampling, L{\'{e}}vy process, α-stable distributions},

pubstate = {published},

tppubtype = {article}

}

@article{Nazabal2016bb,

title = {Human Activity Recognition by Combining a Small Number of Classifiers},

author = {Alfredo Nazabal and Pablo Garcia-Moreno and Antonio Artes-Rodriguez and Zoubin Ghahramani},

url = {http://ieeexplore.ieee.org/articleDetails.jsp?arnumber=7161292},

doi = {10.1109/JBHI.2015.2458274},

issn = {2168-2208},

year  = {2016},

date = {2016-01-01},

journal = {IEEE journal of biomedical and health informatics},

volume = {To appear},

publisher = {IEEE},

abstract = {We consider the problem of daily Human Activity Recognition (HAR) using multiple wireless inertial sensors and, specifically, HAR systems with a very low number of sensors, each one providing an estimation of the performed activities. We propose new Bayesian models to combine the output of the sensors. The models are based on a soft outputs combination of individual classifiers to deal with the small number of sensors. We also incorporate the dynamic nature of human activities as a first order homogeneous Markov chain. We develop both inductive and transductive inference methods for each model to be employed in supervised and semi-supervised situations, respectively. Using different real HAR databases, we compare our classifiers combination models against a single classifier that employs all the signals from the sensors. Our models exhibit consistently a reduction of the error rate and an increase of robustness against sensor failures. Our models also outperform other classifiers combination models that do not consider soft outputs and a Markovian structure of the human activities.},

keywords = {Bayes methods, Bayesian inference, Biological system modeling, Classifier combination, Databases, Estimation, Hidden Markov models, Sensor systems},

pubstate = {published},

tppubtype = {article}

}

@article{Impedovo2014b,

title = {Efficient Monte Carlo Methods for Multi-Dimensional Learning with Classifier Chains},

author = {Sebastiano Impedovo and Cheng-Lin Liu and Donato Impedovo and Giuseppe Pirlo and Jesse Read and Luca Martino and David Luengo},

url = {http://www.sciencedirect.com/science/article/pii/S0031320313004160},

year  = {2014},

date = {2014-01-01},

journal = {Pattern Recognition},

volume = {47},

number = {3},

pages = {1535--1546},

abstract = {Multi-dimensional classification (MDC) is the supervised learning problem where an instance is associated with multiple classes, rather than with a single class, as in traditional classification problems. Since these classes are often strongly correlated, modeling the dependencies between them allows MDC methods to improve their performance \textendash at the expense of an increased computational cost. In this paper we focus on the classifier chains (CC) approach for modeling dependencies, one of the most popular and highest-performing methods for multi-label classification (MLC), a particular case of MDC which involves only binary classes (i.e., labels). The original CC algorithm makes a greedy approximation, and is fast but tends to propagate errors along the chain. Here we present novel Monte Carlo schemes, both for finding a good chain sequence and performing efficient inference. Our algorithms remain tractable for high-dimensional data sets and obtain the best predictive performance across several real data sets.},

keywords = {Bayesian inference, Classifier chains, Monte Carlo methods, Multi-dimensional classification, Multi-label classification},

pubstate = {published},

tppubtype = {article}

}

@article{Salamanca2012b,

title = {Bayesian Equalization for LDPC Channel Decoding},

author = {Luis Salamanca and Juan Jose Murillo-Fuentes and Fernando Perez-Cruz},

url = {http://ieeexplore.ieee.org/lpdocs/epic03/wrapper.htm?arnumber=6129544},

issn = {1053-587X},

year  = {2012},

date = {2012-01-01},

journal = {IEEE Transactions on Signal Processing},

volume = {60},

number = {5},

pages = {2672--2676},

abstract = {We describe the channel equalization problem, and its prior estimate of the channel state information (CSI), as a joint Bayesian estimation problem to improve each symbol posterior estimates at the input of the channel decoder. Our approach takes into consideration not only the uncertainty due to the noise in the channel, but also the uncertainty in the CSI estimate. However, this solution cannot be computed in linear time, because it depends on all the transmitted symbols. Hence, we also put forward an approximation for each symbol's posterior, using the expectation propagation algorithm, which is optimal from the Kullback-Leibler divergence viewpoint and yields an equalization with a complexity identical to the BCJR algorithm. We also use a graphical model representation of the full posterior, in which the proposed approximation can be readily understood. The proposed posterior estimates are more accurate than those computed using the ML estimate for the CSI. In order to illustrate this point, we measure the error rate at the output of a low-density parity-check decoder, which needs the exact posterior for each symbol to detect the incoming word and it is sensitive to a mismatch in those posterior estimates. For example, for QPSK modulation and a channel with three taps, we can expect gains over 0.5 dB with same computational complexity as the ML receiver.},

keywords = {Approximation methods, Bayes methods, Bayesian equalization, Bayesian estimation problem, Bayesian inference, Bayesian methods, BCJR (Bahl\textendashCocke\textendashJelinek\textendashRaviv) algorithm, BCJR algorithm, Channel Coding, channel decoding, channel equalization, channel equalization problem, Channel estimation, channel state information, CSI, Decoding, equalisers, Equalizers, expectation propagation, expectation propagation algorithm, fading channels, graphical model representation, intersymbol interference, Kullback-Leibler divergence, LDPC, LDPC coding, low-density parity-check decoder, Modulation, parity check codes, symbol posterior estimates, Training},

pubstate = {published},

tppubtype = {article}

}