1. | Nazábal, Alfredo; Garcia-Moreno, Pablo; Artés-Rodríguez, Antonio; Ghahramani, Zoubin: Human Activity Recognition by Combining a Small Number of Classifiers.. In: IEEE journal of biomedical and health informatics, 20 (5), pp. 1342 – 1351, 2016, ISSN: 2168-2208. (Type: Journal Article | Abstract | Links | BibTeX) @article{Nazabal2016b, title = {Human Activity Recognition by Combining a Small Number of Classifiers.}, author = {Alfredo Nazábal and Pablo Garcia-Moreno and Antonio Artés-Rodríguez 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 = {}, pubstate = {published}, tppubtype = {article} } 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. |

2. | Nazabal, Alfredo; Garcia-Moreno, Pablo; Artes-Rodriguez, Antonio; Ghahramani, Zoubin: Human Activity Recognition by Combining a Small Number of Classifiers. In: IEEE journal of biomedical and health informatics, To appear , 2016, ISSN: 2168-2208. (Type: Journal Article | Abstract | Links | BibTeX) @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 = {}, pubstate = {published}, tppubtype = {article} } 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. |

3. | Luengo, David; Martino, Luca; Elvira, Victor; Bugallo, Monica F: Bias correction for distributed Bayesian estimators. In: 2015 IEEE 6th International Workshop on Computational Advances in Multi-Sensor Adaptive Processing (CAMSAP), pp. 253–256, IEEE, Cancun, 2015, ISBN: 978-1-4799-1963-5. (Type: Inproceedings | Abstract | Links | BibTeX) @inproceedings{Luengo2015a, title = {Bias correction for distributed Bayesian estimators}, author = {David Luengo and Luca Martino and Victor Elvira and Monica F Bugallo}, url = {http://ieeexplore.ieee.org/lpdocs/epic03/wrapper.htm?arnumber=7383784}, doi = {10.1109/CAMSAP.2015.7383784}, isbn = {978-1-4799-1963-5}, year = {2015}, date = {2015-12-01}, booktitle = {2015 IEEE 6th International Workshop on Computational Advances in Multi-Sensor Adaptive Processing (CAMSAP)}, pages = {253--256}, publisher = {IEEE}, address = {Cancun}, abstract = {Dealing with the whole dataset in big data estimation problems is usually unfeasible. A common solution then consists of dividing the data into several smaller sets, performing distributed Bayesian estimation and combining these partial estimates to obtain a global estimate. A major problem of this approach is the presence of a non-negligible bias in the partial estimators, due to the mismatch between the unknown true prior and the prior assumed in the estimation. A simple method to mitigate the effect of this bias is proposed in this paper. Essentially, the approach is based on using a reference data set to obtain a rough estimation of the parameter of interest, i.e., a reference parameter. This information is then communicated to the partial filters that handle the smaller data sets, which can thus use a refined prior centered around this parameter. Simulation results confirm the good performance of this scheme.}, keywords = {}, pubstate = {published}, tppubtype = {inproceedings} } Dealing with the whole dataset in big data estimation problems is usually unfeasible. A common solution then consists of dividing the data into several smaller sets, performing distributed Bayesian estimation and combining these partial estimates to obtain a global estimate. A major problem of this approach is the presence of a non-negligible bias in the partial estimators, due to the mismatch between the unknown true prior and the prior assumed in the estimation. A simple method to mitigate the effect of this bias is proposed in this paper. Essentially, the approach is based on using a reference data set to obtain a rough estimation of the parameter of interest, i.e., a reference parameter. This information is then communicated to the partial filters that handle the smaller data sets, which can thus use a refined prior centered around this parameter. Simulation results confirm the good performance of this scheme. |

4. | Martino, Luca; Elvira, Victor; Luengo, David; Corander, Jukka: An Adaptive Population Importance Sampler: Learning From Uncertainty. In: IEEE Transactions on Signal Processing, 63 (16), pp. 4422–4437, 2015, ISSN: 1053-587X. (Type: Journal Article | Abstract | Links | BibTeX) @article{Martino2015bbb, title = {An Adaptive Population Importance Sampler: Learning From Uncertainty}, author = {Luca Martino and Victor Elvira and David Luengo and Jukka Corander}, url = {http://ieeexplore.ieee.org/articleDetails.jsp?arnumber=7117437}, doi = {10.1109/TSP.2015.2440215}, issn = {1053-587X}, year = {2015}, date = {2015-08-01}, journal = {IEEE Transactions on Signal Processing}, volume = {63}, number = {16}, pages = {4422--4437}, publisher = {IEEE}, abstract = {Monte Carlo (MC) methods are well-known computational techniques, widely used in different fields such as signal processing, communications and machine learning. An important class of MC methods is composed of importance sampling (IS) and its adaptive extensions, such as population Monte Carlo (PMC) and adaptive multiple IS (AMIS). In this paper, we introduce a novel adaptive and iterated importance sampler using a population of proposal densities. The proposed algorithm, named adaptive population importance sampling (APIS), provides a global estimation of the variables of interest iteratively, making use of all the samples previously generated. APIS combines a sophisticated scheme to build the IS estimators (based on the deterministic mixture approach) with a simple temporal adaptation (based on epochs). In this way, APIS is able to keep all the advantages of both AMIS and PMC, while minimizing their drawbacks. Furthermore, APIS is easily parallelizable. The cloud of proposals is adapted in such a way that local features of the target density can be better taken into account compared to single global adaptation procedures. The result is a fast, simple, robust, and high-performance algorithm applicable to a wide range of problems. Numerical results show the advantages of the proposed sampling scheme in four synthetic examples and a localization problem in a wireless sensor network.}, keywords = {}, pubstate = {published}, tppubtype = {article} } Monte Carlo (MC) methods are well-known computational techniques, widely used in different fields such as signal processing, communications and machine learning. An important class of MC methods is composed of importance sampling (IS) and its adaptive extensions, such as population Monte Carlo (PMC) and adaptive multiple IS (AMIS). In this paper, we introduce a novel adaptive and iterated importance sampler using a population of proposal densities. The proposed algorithm, named adaptive population importance sampling (APIS), provides a global estimation of the variables of interest iteratively, making use of all the samples previously generated. APIS combines a sophisticated scheme to build the IS estimators (based on the deterministic mixture approach) with a simple temporal adaptation (based on epochs). In this way, APIS is able to keep all the advantages of both AMIS and PMC, while minimizing their drawbacks. Furthermore, APIS is easily parallelizable. The cloud of proposals is adapted in such a way that local features of the target density can be better taken into account compared to single global adaptation procedures. The result is a fast, simple, robust, and high-performance algorithm applicable to a wide range of problems. Numerical results show the advantages of the proposed sampling scheme in four synthetic examples and a localization problem in a wireless sensor network. |

5. | Luengo, David; Martino, Luca; Elvira, Victor; Bugallo, Monica F: Efficient Linear Combination of Partial Monte Carlo Estimators. In: 2015 IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP), pp. 4100–4104, IEEE, Brisbane, 2015, ISBN: 978-1-4673-6997-8. (Type: Inproceedings | Abstract | Links | BibTeX) @inproceedings{Luengo2015bb, title = {Efficient Linear Combination of Partial Monte Carlo Estimators}, author = {David Luengo and Luca Martino and Victor Elvira and Monica F Bugallo}, url = {http://ieeexplore.ieee.org/lpdocs/epic03/wrapper.htm?arnumber=7178742 http://www.tsc.uc3m.es/~velvira/papers/ICASSP2015_luengo.pdf}, doi = {10.1109/ICASSP.2015.7178742}, isbn = {978-1-4673-6997-8}, year = {2015}, date = {2015-04-01}, booktitle = {2015 IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP)}, pages = {4100--4104}, publisher = {IEEE}, address = {Brisbane}, abstract = {In many practical scenarios, including those dealing with large data sets, calculating global estimators of unknown variables of interest becomes unfeasible. A common solution is obtaining partial estimators and combining them to approximate the global one. In this paper, we focus on minimum mean squared error (MMSE) estimators, introducing two efficient linear schemes for the fusion of partial estimators. The proposed approaches are valid for any type of partial estimators, although in the simulated scenarios we concentrate on the combination of Monte Carlo estimators due to the nature of the problem addressed. Numerical results show the good performance of the novel fusion methods with only a fraction of the cost of the asymptotically optimal solution.}, keywords = {}, pubstate = {published}, tppubtype = {inproceedings} } In many practical scenarios, including those dealing with large data sets, calculating global estimators of unknown variables of interest becomes unfeasible. A common solution is obtaining partial estimators and combining them to approximate the global one. In this paper, we focus on minimum mean squared error (MMSE) estimators, introducing two efficient linear schemes for the fusion of partial estimators. The proposed approaches are valid for any type of partial estimators, although in the simulated scenarios we concentrate on the combination of Monte Carlo estimators due to the nature of the problem addressed. Numerical results show the good performance of the novel fusion methods with only a fraction of the cost of the asymptotically optimal solution. |

6. | Taborda, Camilo G; Perez-Cruz, Fernando; Guo, Dongning: New Information-Estimation Results for Poisson, Binomial and Negative Binomial Models. In: 2014 IEEE International Symposium on Information Theory, pp. 2207–2211, IEEE, Honolulu, 2014, ISBN: 978-1-4799-5186-4. (Type: Inproceedings | Abstract | Links | BibTeX) @inproceedings{Taborda2014, title = {New Information-Estimation Results for Poisson, Binomial and Negative Binomial Models}, author = {Camilo G Taborda and Fernando Perez-Cruz and Dongning Guo}, url = {http://ieeexplore.ieee.org/articleDetails.jsp?arnumber=6875225}, doi = {10.1109/ISIT.2014.6875225}, isbn = {978-1-4799-5186-4}, year = {2014}, date = {2014-06-01}, booktitle = {2014 IEEE International Symposium on Information Theory}, pages = {2207--2211}, publisher = {IEEE}, address = {Honolulu}, abstract = {In recent years, a number of mathematical relationships have been established between information measures and estimation measures for various models, including Gaussian, Poisson and binomial models. In this paper, it is shown that the second derivative of the input-output mutual information with respect to the input scaling can be expressed as the expectation of a certain Bregman divergence pertaining to the conditional expectations of the input and the input power. This result is similar to that found for the Gaussian model where the Bregman divergence therein is the square distance. In addition, the Poisson, binomial and negative binomial models are shown to be similar in the small scaling regime in the sense that the derivative of the mutual information and the derivative of the relative entropy converge to the same value.}, keywords = {}, pubstate = {published}, tppubtype = {inproceedings} } In recent years, a number of mathematical relationships have been established between information measures and estimation measures for various models, including Gaussian, Poisson and binomial models. In this paper, it is shown that the second derivative of the input-output mutual information with respect to the input scaling can be expressed as the expectation of a certain Bregman divergence pertaining to the conditional expectations of the input and the input power. This result is similar to that found for the Gaussian model where the Bregman divergence therein is the square distance. In addition, the Poisson, binomial and negative binomial models are shown to be similar in the small scaling regime in the sense that the derivative of the mutual information and the derivative of the relative entropy converge to the same value. |

7. | Taborda, Camilo G; Perez-Cruz, Fernando: Derivative of the Relative Entropy over the Poisson and Binomial Channel. In: 2012 IEEE Information Theory Workshop, pp. 386–390, IEEE, Lausanne, 2012, ISBN: 978-1-4673-0223-4. (Type: Inproceedings | Abstract | Links | BibTeX) @inproceedings{Taborda2012, title = {Derivative of the Relative Entropy over the Poisson and Binomial Channel}, author = {Camilo G Taborda and Fernando Perez-Cruz}, url = {http://ieeexplore.ieee.org/lpdocs/epic03/wrapper.htm?arnumber=6404699}, isbn = {978-1-4673-0223-4}, year = {2012}, date = {2012-01-01}, booktitle = {2012 IEEE Information Theory Workshop}, pages = {386--390}, publisher = {IEEE}, address = {Lausanne}, abstract = {In this paper it is found that, regardless of the statistics of the input, the derivative of the relative entropy over the Binomial channel can be seen as the expectation of a function that has as argument the mean of the conditional distribution that models the channel. Based on this relationship we formulate a similar expression for the mutual information concept. In addition to this, using the connection between the Binomial and Poisson distribution we develop similar results for the Poisson channel. Novelty of the results presented here lies on the fact that, expressions obtained can be applied to a wide range of scenarios.}, keywords = {}, pubstate = {published}, tppubtype = {inproceedings} } In this paper it is found that, regardless of the statistics of the input, the derivative of the relative entropy over the Binomial channel can be seen as the expectation of a function that has as argument the mean of the conditional distribution that models the channel. Based on this relationship we formulate a similar expression for the mutual information concept. In addition to this, using the connection between the Binomial and Poisson distribution we develop similar results for the Poisson channel. Novelty of the results presented here lies on the fact that, expressions obtained can be applied to a wide range of scenarios. |

8. | Florentino-Liaño, Blanca; O'Mahony, Niamh; Artés-Rodríguez, Antonio: Long Term Human Activity Recognition with Automatic Orientation Estimation. In: 2012 IEEE International Workshop on Machine Learning for Signal Processing, pp. 1–6, IEEE, Santander, 2012, ISSN: 1551-2541. (Type: Inproceedings | Abstract | Links | BibTeX) @inproceedings{Florentino-Liano2012b, title = {Long Term Human Activity Recognition with Automatic Orientation Estimation}, author = {Blanca Florentino-Liaño and Niamh O'Mahony and Antonio Artés-Rodríguez}, url = {http://ieeexplore.ieee.org/lpdocs/epic03/wrapper.htm?arnumber=6349789}, issn = {1551-2541}, year = {2012}, date = {2012-01-01}, booktitle = {2012 IEEE International Workshop on Machine Learning for Signal Processing}, pages = {1--6}, publisher = {IEEE}, address = {Santander}, abstract = {This work deals with the elimination of sensitivity to sensor orientation in the task of human daily activity recognition using a single miniature inertial sensor. The proposed method detects time intervals of walking, automatically estimating the orientation in these intervals and transforming the observed signals to a “virtual” sensor orientation. Classification results show that excellent performance, in terms of both precision and recall (up to 100%), is achieved, for long-term recordings in real-life settings.}, keywords = {}, pubstate = {published}, tppubtype = {inproceedings} } This work deals with the elimination of sensitivity to sensor orientation in the task of human daily activity recognition using a single miniature inertial sensor. The proposed method detects time intervals of walking, automatically estimating the orientation in these intervals and transforming the observed signals to a “virtual” sensor orientation. Classification results show that excellent performance, in terms of both precision and recall (up to 100%), is achieved, for long-term recordings in real-life settings. |

9. | Taborda, Camilo G; Perez-Cruz, Fernando: Mutual Information and Relative Entropy over the Binomial and Negative Binomial Channels. In: 2012 IEEE International Symposium on Information Theory Proceedings, pp. 696–700, IEEE, Cambridge, MA, 2012, ISSN: 2157-8095. (Type: Inproceedings | Abstract | Links | BibTeX) @inproceedings{Taborda2012a, title = {Mutual Information and Relative Entropy over the Binomial and Negative Binomial Channels}, author = {Camilo G Taborda and Fernando Perez-Cruz}, url = {http://ieeexplore.ieee.org/lpdocs/epic03/wrapper.htm?arnumber=6284304}, issn = {2157-8095}, year = {2012}, date = {2012-01-01}, booktitle = {2012 IEEE International Symposium on Information Theory Proceedings}, pages = {696--700}, publisher = {IEEE}, address = {Cambridge, MA}, abstract = {We study the relation of the mutual information and relative entropy over the Binomial and Negative Binomial channels with estimation theoretical quantities, in which we extend already known results for Gaussian and Poisson channels. We establish general expressions for these information theory concepts with a direct connection with estimation theory through the conditional mean estimation and a particular loss function.}, keywords = {}, pubstate = {published}, tppubtype = {inproceedings} } We study the relation of the mutual information and relative entropy over the Binomial and Negative Binomial channels with estimation theoretical quantities, in which we extend already known results for Gaussian and Poisson channels. We establish general expressions for these information theory concepts with a direct connection with estimation theory through the conditional mean estimation and a particular loss function. |

10. | Leiva-Murillo, Jose M; Artés-Rodríguez, Antonio: Information-Theoretic Linear Feature Extraction Based on Kernel Density Estimators: A Review. In: IEEE Transactions on Systems, Man, and Cybernetics, Part C (Applications and Reviews), 42 (6), pp. 1180–1189, 2012, ISSN: 1094-6977. (Type: Journal Article | Abstract | Links | BibTeX) @article{Leiva-Murillo2012a, title = {Information-Theoretic Linear Feature Extraction Based on Kernel Density Estimators: A Review}, author = {Jose M Leiva-Murillo and Antonio Artés-Rodríguez}, url = {http://www.tsc.uc3m.es/~antonio/papers/P44_2012_Information Theoretic Linear Feature Extraction Based on Kernel Density Estimators A Review.pdf http://ieeexplore.ieee.org/lpdocs/epic03/wrapper.htm?arnumber=6185689}, issn = {1094-6977}, year = {2012}, date = {2012-01-01}, journal = {IEEE Transactions on Systems, Man, and Cybernetics, Part C (Applications and Reviews)}, volume = {42}, number = {6}, pages = {1180--1189}, abstract = {In this paper, we provide a unified study of the application of kernel density estimators to supervised linear feature extraction by means of criteria inspired by information and detection theory. We enrich this study by the incorporation of two novel criteria to the study, i.e., the mutual information and the likelihood ratio test, and perform both a theoretical and an experimental comparison between the new methods and other ones previously described in the literature. The impact of the bandwidth selection of the density estimator in the classification performance is discussed. Some theoretical results that bound classification performance as a function or mutual information are also compiled. A set of experiments on different real-world datasets allows us to perform an empirical comparison of the methods, in terms of both accuracy and computational complexity. We show the suitability of these methods to determine the dimension of the subspace that contains the discriminative information.}, keywords = {}, pubstate = {published}, tppubtype = {article} } In this paper, we provide a unified study of the application of kernel density estimators to supervised linear feature extraction by means of criteria inspired by information and detection theory. We enrich this study by the incorporation of two novel criteria to the study, i.e., the mutual information and the likelihood ratio test, and perform both a theoretical and an experimental comparison between the new methods and other ones previously described in the literature. The impact of the bandwidth selection of the density estimator in the classification performance is discussed. Some theoretical results that bound classification performance as a function or mutual information are also compiled. A set of experiments on different real-world datasets allows us to perform an empirical comparison of the methods, in terms of both accuracy and computational complexity. We show the suitability of these methods to determine the dimension of the subspace that contains the discriminative information. |

11. | Maiz, Cristina S; Miguez, Joaquin: On the Optimization of Transportation Routes with Multiple Destinations in Random Networks. In: 2011 IEEE Statistical Signal Processing Workshop (SSP), pp. 349–352, IEEE, Nice, 2011, ISBN: 978-1-4577-0569-4. (Type: Inproceedings | Abstract | Links | BibTeX) @inproceedings{Maiz2011, title = {On the Optimization of Transportation Routes with Multiple Destinations in Random Networks}, author = {Cristina S Maiz and Joaquin Miguez}, url = {http://ieeexplore.ieee.org/lpdocs/epic03/wrapper.htm?arnumber=5967701}, isbn = {978-1-4577-0569-4}, year = {2011}, date = {2011-01-01}, booktitle = {2011 IEEE Statistical Signal Processing Workshop (SSP)}, pages = {349--352}, publisher = {IEEE}, address = {Nice}, abstract = {Various practical problems in transportation research and routing in communication networks can be reduced to the computation of the best path that traverses a certain graph and visits a set of D specified destination nodes. Simple versions of this problem have received attention in the literature. Optimal solutions exist for the cases in which (a) D >; 1 and the graph is deterministic or (b) D = 1 and the graph is stochastic (and possibly time-dependent). Here, we address the general problem in which both D >; 1 and the costs of the edges in the graph are stochastic and time-varying. We tackle this complex global optimization problem by first converting it into an equivalent estimation problem and then computing a numerical solution using a sequential Monte Carlo algorithm. The advantage of the proposed technique over some standard methods (devised for graphs with time-invariant statistics) is illustrated by way of computer simulations.}, keywords = {}, pubstate = {published}, tppubtype = {inproceedings} } Various practical problems in transportation research and routing in communication networks can be reduced to the computation of the best path that traverses a certain graph and visits a set of D specified destination nodes. Simple versions of this problem have received attention in the literature. Optimal solutions exist for the cases in which (a) D >; 1 and the graph is deterministic or (b) D = 1 and the graph is stochastic (and possibly time-dependent). Here, we address the general problem in which both D >; 1 and the costs of the edges in the graph are stochastic and time-varying. We tackle this complex global optimization problem by first converting it into an equivalent estimation problem and then computing a numerical solution using a sequential Monte Carlo algorithm. The advantage of the proposed technique over some standard methods (devised for graphs with time-invariant statistics) is illustrated by way of computer simulations. |

12. | Tuia, D; Verrelst, J; Alonso, L; Perez-Cruz, Fernando; Camps-Valls, Gustavo: Multioutput Support Vector Regression for Remote Sensing Biophysical Parameter Estimation. In: IEEE Geoscience and Remote Sensing Letters, 8 (4), pp. 804–808, 2011, ISSN: 1545-598X. (Type: Journal Article | Abstract | Links | BibTeX) @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 = {}, 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. |

13. | Vazquez, Manuel A; Miguez, Joaquin: Adaptive MLSD for MIMO Transmission Systems with Unknown Subchannel Orders. In: 2010 7th International Symposium on Wireless Communication Systems, pp. 451–455, IEEE, York, 2010, ISSN: 2154-0217. (Type: Inproceedings | Abstract | Links | BibTeX) @inproceedings{Vazquez2010, title = {Adaptive MLSD for MIMO Transmission Systems with Unknown Subchannel Orders}, author = {Manuel A Vazquez and Joaquin Miguez}, url = {http://ieeexplore.ieee.org/lpdocs/epic03/wrapper.htm?arnumber=5624335}, issn = {2154-0217}, year = {2010}, date = {2010-01-01}, booktitle = {2010 7th International Symposium on Wireless Communication Systems}, pages = {451--455}, publisher = {IEEE}, address = {York}, abstract = {In the equalization of frequency-selective multiple-input multiple-output (MIMO) channels it is usually assumed that the length of the channel impulse response (CIR), also referred to as the channel order, is known. However, this is not true in most practical situations and, in order to avoid the serious performance degradation that occurs when the CIR length is underestimated, a channel with "more than enough" taps is usually considered. This very frequently leads to overestimating the channel order, which increases the computational complexity of any maximum likelihood sequence detection (MLSD) algorithm, while degrading its performance at the same time. The problem of estimating a single channel order for a time and frequency selective MIMO channel has recently been tackled. However, this is an idealized approach, since a MIMO channel comprises multiple subchannels (as many as the number of inputs times that of the outputs), each of them possibly with its own order. In this paper, we introduce an algorithm for MLSD that incorporates the full estimation of the MIMO CIR parameters, including one channel order per output. The proposed technique is based on the per survivor processing (PSP) methodology, it admits both blind and semiblind implementations, depending on the availability of pilot data, and it is designed to work with time-selective channels. Besides the analytical derivation of the algorithm, we provide computer simulation results that illustrate the effectiveness of the resulting receiver.}, keywords = {}, pubstate = {published}, tppubtype = {inproceedings} } In the equalization of frequency-selective multiple-input multiple-output (MIMO) channels it is usually assumed that the length of the channel impulse response (CIR), also referred to as the channel order, is known. However, this is not true in most practical situations and, in order to avoid the serious performance degradation that occurs when the CIR length is underestimated, a channel with "more than enough" taps is usually considered. This very frequently leads to overestimating the channel order, which increases the computational complexity of any maximum likelihood sequence detection (MLSD) algorithm, while degrading its performance at the same time. The problem of estimating a single channel order for a time and frequency selective MIMO channel has recently been tackled. However, this is an idealized approach, since a MIMO channel comprises multiple subchannels (as many as the number of inputs times that of the outputs), each of them possibly with its own order. In this paper, we introduce an algorithm for MLSD that incorporates the full estimation of the MIMO CIR parameters, including one channel order per output. The proposed technique is based on the per survivor processing (PSP) methodology, it admits both blind and semiblind implementations, depending on the availability of pilot data, and it is designed to work with time-selective channels. Besides the analytical derivation of the algorithm, we provide computer simulation results that illustrate the effectiveness of the resulting receiver. |

## 2016 |

## Journal Articles |

Nazábal, Alfredo; Garcia-Moreno, Pablo; Artés-Rodríguez, Antonio; Ghahramani, Zoubin Human Activity Recognition by Combining a Small Number of Classifiers. Journal Article IEEE journal of biomedical and health informatics, 20 (5), pp. 1342 – 1351, 2016, ISSN: 2168-2208. Abstract | Links | BibTeX | Tags: Bayes methods, Bayesian inference, Biological system modeling, Classifier combination, Databases, Estimation, Hidden Markov models, Journal, Sensor systems @article{Nazabal2016b, title = {Human Activity Recognition by Combining a Small Number of Classifiers.}, author = {Alfredo Nazábal and Pablo Garcia-Moreno and Antonio Artés-Rodríguez 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} } 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. |

Nazabal, Alfredo; Garcia-Moreno, Pablo; Artes-Rodriguez, Antonio; Ghahramani, Zoubin Human Activity Recognition by Combining a Small Number of Classifiers Journal Article IEEE journal of biomedical and health informatics, To appear , 2016, ISSN: 2168-2208. Abstract | Links | BibTeX | Tags: Bayes methods, Bayesian inference, Biological system modeling, Classifier combination, Databases, Estimation, Hidden Markov models, Sensor systems @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} } |

## 2015 |

## Journal Articles |

Martino, Luca; Elvira, Victor; Luengo, David; Corander, Jukka An Adaptive Population Importance Sampler: Learning From Uncertainty Journal Article IEEE Transactions on Signal Processing, 63 (16), pp. 4422–4437, 2015, ISSN: 1053-587X. Abstract | Links | BibTeX | Tags: Adaptive importance sampling, adaptive multiple IS, adaptive population importance sampler, AMIS, APIS, Estimation, Importance sampling, IS estimators, iterative estimation, iterative methods, Journal, MC methods, Monte Carlo (MC) methods, Monte Carlo methods, population Monte Carlo, Proposals, Signal processing algorithms, simple temporal adaptation, Sociology, Standards, Wireless sensor network, Wireless Sensor Networks @article{Martino2015bbb, title = {An Adaptive Population Importance Sampler: Learning From Uncertainty}, author = {Luca Martino and Victor Elvira and David Luengo and Jukka Corander}, url = {http://ieeexplore.ieee.org/articleDetails.jsp?arnumber=7117437}, doi = {10.1109/TSP.2015.2440215}, issn = {1053-587X}, year = {2015}, date = {2015-08-01}, journal = {IEEE Transactions on Signal Processing}, volume = {63}, number = {16}, pages = {4422--4437}, publisher = {IEEE}, abstract = {Monte Carlo (MC) methods are well-known computational techniques, widely used in different fields such as signal processing, communications and machine learning. An important class of MC methods is composed of importance sampling (IS) and its adaptive extensions, such as population Monte Carlo (PMC) and adaptive multiple IS (AMIS). In this paper, we introduce a novel adaptive and iterated importance sampler using a population of proposal densities. The proposed algorithm, named adaptive population importance sampling (APIS), provides a global estimation of the variables of interest iteratively, making use of all the samples previously generated. APIS combines a sophisticated scheme to build the IS estimators (based on the deterministic mixture approach) with a simple temporal adaptation (based on epochs). In this way, APIS is able to keep all the advantages of both AMIS and PMC, while minimizing their drawbacks. Furthermore, APIS is easily parallelizable. The cloud of proposals is adapted in such a way that local features of the target density can be better taken into account compared to single global adaptation procedures. The result is a fast, simple, robust, and high-performance algorithm applicable to a wide range of problems. Numerical results show the advantages of the proposed sampling scheme in four synthetic examples and a localization problem in a wireless sensor network.}, keywords = {Adaptive importance sampling, adaptive multiple IS, adaptive population importance sampler, AMIS, APIS, Estimation, Importance sampling, IS estimators, iterative estimation, iterative methods, Journal, MC methods, Monte Carlo (MC) methods, Monte Carlo methods, population Monte Carlo, Proposals, Signal processing algorithms, simple temporal adaptation, Sociology, Standards, Wireless sensor network, Wireless Sensor Networks}, pubstate = {published}, tppubtype = {article} } Monte Carlo (MC) methods are well-known computational techniques, widely used in different fields such as signal processing, communications and machine learning. An important class of MC methods is composed of importance sampling (IS) and its adaptive extensions, such as population Monte Carlo (PMC) and adaptive multiple IS (AMIS). In this paper, we introduce a novel adaptive and iterated importance sampler using a population of proposal densities. The proposed algorithm, named adaptive population importance sampling (APIS), provides a global estimation of the variables of interest iteratively, making use of all the samples previously generated. APIS combines a sophisticated scheme to build the IS estimators (based on the deterministic mixture approach) with a simple temporal adaptation (based on epochs). In this way, APIS is able to keep all the advantages of both AMIS and PMC, while minimizing their drawbacks. Furthermore, APIS is easily parallelizable. The cloud of proposals is adapted in such a way that local features of the target density can be better taken into account compared to single global adaptation procedures. The result is a fast, simple, robust, and high-performance algorithm applicable to a wide range of problems. Numerical results show the advantages of the proposed sampling scheme in four synthetic examples and a localization problem in a wireless sensor network. |

## Inproceedings |

Luengo, David; Martino, Luca; Elvira, Victor; Bugallo, Monica F Bias correction for distributed Bayesian estimators Inproceedings 2015 IEEE 6th International Workshop on Computational Advances in Multi-Sensor Adaptive Processing (CAMSAP), pp. 253–256, IEEE, Cancun, 2015, ISBN: 978-1-4799-1963-5. Abstract | Links | BibTeX | Tags: Bayes methods, Big data, Distributed databases, Estimation, Probability density function, Wireless Sensor Networks @inproceedings{Luengo2015a, title = {Bias correction for distributed Bayesian estimators}, author = {David Luengo and Luca Martino and Victor Elvira and Monica F Bugallo}, url = {http://ieeexplore.ieee.org/lpdocs/epic03/wrapper.htm?arnumber=7383784}, doi = {10.1109/CAMSAP.2015.7383784}, isbn = {978-1-4799-1963-5}, year = {2015}, date = {2015-12-01}, booktitle = {2015 IEEE 6th International Workshop on Computational Advances in Multi-Sensor Adaptive Processing (CAMSAP)}, pages = {253--256}, publisher = {IEEE}, address = {Cancun}, abstract = {Dealing with the whole dataset in big data estimation problems is usually unfeasible. A common solution then consists of dividing the data into several smaller sets, performing distributed Bayesian estimation and combining these partial estimates to obtain a global estimate. A major problem of this approach is the presence of a non-negligible bias in the partial estimators, due to the mismatch between the unknown true prior and the prior assumed in the estimation. A simple method to mitigate the effect of this bias is proposed in this paper. Essentially, the approach is based on using a reference data set to obtain a rough estimation of the parameter of interest, i.e., a reference parameter. This information is then communicated to the partial filters that handle the smaller data sets, which can thus use a refined prior centered around this parameter. Simulation results confirm the good performance of this scheme.}, keywords = {Bayes methods, Big data, Distributed databases, Estimation, Probability density function, Wireless Sensor Networks}, pubstate = {published}, tppubtype = {inproceedings} } Dealing with the whole dataset in big data estimation problems is usually unfeasible. A common solution then consists of dividing the data into several smaller sets, performing distributed Bayesian estimation and combining these partial estimates to obtain a global estimate. A major problem of this approach is the presence of a non-negligible bias in the partial estimators, due to the mismatch between the unknown true prior and the prior assumed in the estimation. A simple method to mitigate the effect of this bias is proposed in this paper. Essentially, the approach is based on using a reference data set to obtain a rough estimation of the parameter of interest, i.e., a reference parameter. This information is then communicated to the partial filters that handle the smaller data sets, which can thus use a refined prior centered around this parameter. Simulation results confirm the good performance of this scheme. |

Luengo, David; Martino, Luca; Elvira, Victor; Bugallo, Monica F Efficient Linear Combination of Partial Monte Carlo Estimators Inproceedings 2015 IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP), pp. 4100–4104, IEEE, Brisbane, 2015, ISBN: 978-1-4673-6997-8. Abstract | Links | BibTeX | Tags: covariance matrices, efficient linear combination, Estimation, fusion, Global estimator, global estimators, least mean squares methods, linear combination, minimum mean squared error estimators, Monte Carlo estimation, Monte Carlo methods, partial estimator, partial Monte Carlo estimators, Xenon @inproceedings{Luengo2015bb, title = {Efficient Linear Combination of Partial Monte Carlo Estimators}, author = {David Luengo and Luca Martino and Victor Elvira and Monica F Bugallo}, url = {http://ieeexplore.ieee.org/lpdocs/epic03/wrapper.htm?arnumber=7178742 http://www.tsc.uc3m.es/~velvira/papers/ICASSP2015_luengo.pdf}, doi = {10.1109/ICASSP.2015.7178742}, isbn = {978-1-4673-6997-8}, year = {2015}, date = {2015-04-01}, booktitle = {2015 IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP)}, pages = {4100--4104}, publisher = {IEEE}, address = {Brisbane}, abstract = {In many practical scenarios, including those dealing with large data sets, calculating global estimators of unknown variables of interest becomes unfeasible. A common solution is obtaining partial estimators and combining them to approximate the global one. In this paper, we focus on minimum mean squared error (MMSE) estimators, introducing two efficient linear schemes for the fusion of partial estimators. The proposed approaches are valid for any type of partial estimators, although in the simulated scenarios we concentrate on the combination of Monte Carlo estimators due to the nature of the problem addressed. Numerical results show the good performance of the novel fusion methods with only a fraction of the cost of the asymptotically optimal solution.}, keywords = {covariance matrices, efficient linear combination, Estimation, fusion, Global estimator, global estimators, least mean squares methods, linear combination, minimum mean squared error estimators, Monte Carlo estimation, Monte Carlo methods, partial estimator, partial Monte Carlo estimators, Xenon}, pubstate = {published}, tppubtype = {inproceedings} } In many practical scenarios, including those dealing with large data sets, calculating global estimators of unknown variables of interest becomes unfeasible. A common solution is obtaining partial estimators and combining them to approximate the global one. In this paper, we focus on minimum mean squared error (MMSE) estimators, introducing two efficient linear schemes for the fusion of partial estimators. The proposed approaches are valid for any type of partial estimators, although in the simulated scenarios we concentrate on the combination of Monte Carlo estimators due to the nature of the problem addressed. Numerical results show the good performance of the novel fusion methods with only a fraction of the cost of the asymptotically optimal solution. |

## 2014 |

## Inproceedings |

Taborda, Camilo G; Perez-Cruz, Fernando; Guo, Dongning New Information-Estimation Results for Poisson, Binomial and Negative Binomial Models Inproceedings 2014 IEEE International Symposium on Information Theory, pp. 2207–2211, IEEE, Honolulu, 2014, ISBN: 978-1-4799-5186-4. Abstract | Links | BibTeX | Tags: Bregman divergence, Estimation, estimation measures, Gaussian models, Gaussian processes, information measures, information theory, information-estimation results, negative binomial models, Poisson models, Stochastic processes @inproceedings{Taborda2014, title = {New Information-Estimation Results for Poisson, Binomial and Negative Binomial Models}, author = {Camilo G Taborda and Fernando Perez-Cruz and Dongning Guo}, url = {http://ieeexplore.ieee.org/articleDetails.jsp?arnumber=6875225}, doi = {10.1109/ISIT.2014.6875225}, isbn = {978-1-4799-5186-4}, year = {2014}, date = {2014-06-01}, booktitle = {2014 IEEE International Symposium on Information Theory}, pages = {2207--2211}, publisher = {IEEE}, address = {Honolulu}, abstract = {In recent years, a number of mathematical relationships have been established between information measures and estimation measures for various models, including Gaussian, Poisson and binomial models. In this paper, it is shown that the second derivative of the input-output mutual information with respect to the input scaling can be expressed as the expectation of a certain Bregman divergence pertaining to the conditional expectations of the input and the input power. This result is similar to that found for the Gaussian model where the Bregman divergence therein is the square distance. In addition, the Poisson, binomial and negative binomial models are shown to be similar in the small scaling regime in the sense that the derivative of the mutual information and the derivative of the relative entropy converge to the same value.}, keywords = {Bregman divergence, Estimation, estimation measures, Gaussian models, Gaussian processes, information measures, information theory, information-estimation results, negative binomial models, Poisson models, Stochastic processes}, pubstate = {published}, tppubtype = {inproceedings} } In recent years, a number of mathematical relationships have been established between information measures and estimation measures for various models, including Gaussian, Poisson and binomial models. In this paper, it is shown that the second derivative of the input-output mutual information with respect to the input scaling can be expressed as the expectation of a certain Bregman divergence pertaining to the conditional expectations of the input and the input power. This result is similar to that found for the Gaussian model where the Bregman divergence therein is the square distance. In addition, the Poisson, binomial and negative binomial models are shown to be similar in the small scaling regime in the sense that the derivative of the mutual information and the derivative of the relative entropy converge to the same value. |

## 2012 |

## Journal Articles |

Leiva-Murillo, Jose M; Artés-Rodríguez, Antonio Information-Theoretic Linear Feature Extraction Based on Kernel Density Estimators: A Review Journal Article IEEE Transactions on Systems, Man, and Cybernetics, Part C (Applications and Reviews), 42 (6), pp. 1180–1189, 2012, ISSN: 1094-6977. Abstract | Links | BibTeX | Tags: Bandwidth, Density, detection theory, Entropy, Estimation, Feature extraction, Feature extraction (FE), information theoretic linear feature extraction, information theory, information-theoretic learning (ITL), Kernel, Kernel density estimation, kernel density estimators, Machine learning @article{Leiva-Murillo2012a, title = {Information-Theoretic Linear Feature Extraction Based on Kernel Density Estimators: A Review}, author = {Jose M Leiva-Murillo and Antonio Artés-Rodríguez}, url = {http://www.tsc.uc3m.es/~antonio/papers/P44_2012_Information Theoretic Linear Feature Extraction Based on Kernel Density Estimators A Review.pdf http://ieeexplore.ieee.org/lpdocs/epic03/wrapper.htm?arnumber=6185689}, issn = {1094-6977}, year = {2012}, date = {2012-01-01}, journal = {IEEE Transactions on Systems, Man, and Cybernetics, Part C (Applications and Reviews)}, volume = {42}, number = {6}, pages = {1180--1189}, abstract = {In this paper, we provide a unified study of the application of kernel density estimators to supervised linear feature extraction by means of criteria inspired by information and detection theory. We enrich this study by the incorporation of two novel criteria to the study, i.e., the mutual information and the likelihood ratio test, and perform both a theoretical and an experimental comparison between the new methods and other ones previously described in the literature. The impact of the bandwidth selection of the density estimator in the classification performance is discussed. Some theoretical results that bound classification performance as a function or mutual information are also compiled. A set of experiments on different real-world datasets allows us to perform an empirical comparison of the methods, in terms of both accuracy and computational complexity. We show the suitability of these methods to determine the dimension of the subspace that contains the discriminative information.}, keywords = {Bandwidth, Density, detection theory, Entropy, Estimation, Feature extraction, Feature extraction (FE), information theoretic linear feature extraction, information theory, information-theoretic learning (ITL), Kernel, Kernel density estimation, kernel density estimators, Machine learning}, pubstate = {published}, tppubtype = {article} } In this paper, we provide a unified study of the application of kernel density estimators to supervised linear feature extraction by means of criteria inspired by information and detection theory. We enrich this study by the incorporation of two novel criteria to the study, i.e., the mutual information and the likelihood ratio test, and perform both a theoretical and an experimental comparison between the new methods and other ones previously described in the literature. The impact of the bandwidth selection of the density estimator in the classification performance is discussed. Some theoretical results that bound classification performance as a function or mutual information are also compiled. A set of experiments on different real-world datasets allows us to perform an empirical comparison of the methods, in terms of both accuracy and computational complexity. We show the suitability of these methods to determine the dimension of the subspace that contains the discriminative information. |

## Inproceedings |

Taborda, Camilo G; Perez-Cruz, Fernando Derivative of the Relative Entropy over the Poisson and Binomial Channel Inproceedings 2012 IEEE Information Theory Workshop, pp. 386–390, IEEE, Lausanne, 2012, ISBN: 978-1-4673-0223-4. Abstract | Links | BibTeX | Tags: binomial channel, binomial distribution, Channel estimation, conditional distribution, Entropy, Estimation, function expectation, Mutual information, mutual information concept, Poisson channel, Poisson distribution, Random variables, relative entropy derivative, similar expression @inproceedings{Taborda2012, title = {Derivative of the Relative Entropy over the Poisson and Binomial Channel}, author = {Camilo G Taborda and Fernando Perez-Cruz}, url = {http://ieeexplore.ieee.org/lpdocs/epic03/wrapper.htm?arnumber=6404699}, isbn = {978-1-4673-0223-4}, year = {2012}, date = {2012-01-01}, booktitle = {2012 IEEE Information Theory Workshop}, pages = {386--390}, publisher = {IEEE}, address = {Lausanne}, abstract = {In this paper it is found that, regardless of the statistics of the input, the derivative of the relative entropy over the Binomial channel can be seen as the expectation of a function that has as argument the mean of the conditional distribution that models the channel. Based on this relationship we formulate a similar expression for the mutual information concept. In addition to this, using the connection between the Binomial and Poisson distribution we develop similar results for the Poisson channel. Novelty of the results presented here lies on the fact that, expressions obtained can be applied to a wide range of scenarios.}, keywords = {binomial channel, binomial distribution, Channel estimation, conditional distribution, Entropy, Estimation, function expectation, Mutual information, mutual information concept, Poisson channel, Poisson distribution, Random variables, relative entropy derivative, similar expression}, pubstate = {published}, tppubtype = {inproceedings} } In this paper it is found that, regardless of the statistics of the input, the derivative of the relative entropy over the Binomial channel can be seen as the expectation of a function that has as argument the mean of the conditional distribution that models the channel. Based on this relationship we formulate a similar expression for the mutual information concept. In addition to this, using the connection between the Binomial and Poisson distribution we develop similar results for the Poisson channel. Novelty of the results presented here lies on the fact that, expressions obtained can be applied to a wide range of scenarios. |

Florentino-Liaño, Blanca; O'Mahony, Niamh; Artés-Rodríguez, Antonio Long Term Human Activity Recognition with Automatic Orientation Estimation Inproceedings 2012 IEEE International Workshop on Machine Learning for Signal Processing, pp. 1–6, IEEE, Santander, 2012, ISSN: 1551-2541. Abstract | Links | BibTeX | Tags: Acceleration, Activity recognition, automatic orientation estimation, biomedical equipment, Estimation, Gravity, Hidden Markov models, human daily activity recognition, Humans, Legged locomotion, long term human activity recognition, medical signal processing, object recognition, orientation estimation, sensors, single miniature inertial sensor, time intervals, Vectors, virtual sensor orientation, wearable sensors @inproceedings{Florentino-Liano2012b, title = {Long Term Human Activity Recognition with Automatic Orientation Estimation}, author = {Blanca Florentino-Liaño and Niamh O'Mahony and Antonio Artés-Rodríguez}, url = {http://ieeexplore.ieee.org/lpdocs/epic03/wrapper.htm?arnumber=6349789}, issn = {1551-2541}, year = {2012}, date = {2012-01-01}, booktitle = {2012 IEEE International Workshop on Machine Learning for Signal Processing}, pages = {1--6}, publisher = {IEEE}, address = {Santander}, abstract = {This work deals with the elimination of sensitivity to sensor orientation in the task of human daily activity recognition using a single miniature inertial sensor. The proposed method detects time intervals of walking, automatically estimating the orientation in these intervals and transforming the observed signals to a “virtual” sensor orientation. Classification results show that excellent performance, in terms of both precision and recall (up to 100%), is achieved, for long-term recordings in real-life settings.}, keywords = {Acceleration, Activity recognition, automatic orientation estimation, biomedical equipment, Estimation, Gravity, Hidden Markov models, human daily activity recognition, Humans, Legged locomotion, long term human activity recognition, medical signal processing, object recognition, orientation estimation, sensors, single miniature inertial sensor, time intervals, Vectors, virtual sensor orientation, wearable sensors}, pubstate = {published}, tppubtype = {inproceedings} } This work deals with the elimination of sensitivity to sensor orientation in the task of human daily activity recognition using a single miniature inertial sensor. The proposed method detects time intervals of walking, automatically estimating the orientation in these intervals and transforming the observed signals to a “virtual” sensor orientation. Classification results show that excellent performance, in terms of both precision and recall (up to 100%), is achieved, for long-term recordings in real-life settings. |

Taborda, Camilo G; Perez-Cruz, Fernando Mutual Information and Relative Entropy over the Binomial and Negative Binomial Channels Inproceedings 2012 IEEE International Symposium on Information Theory Proceedings, pp. 696–700, IEEE, Cambridge, MA, 2012, ISSN: 2157-8095. Abstract | Links | BibTeX | Tags: Channel estimation, conditional mean estimation, Entropy, Estimation, estimation theoretical quantity, estimation theory, Gaussian channel, Gaussian channels, information theory concept, loss function, mean square error methods, Mutual information, negative binomial channel, Poisson channel, Random variables, relative entropy @inproceedings{Taborda2012a, title = {Mutual Information and Relative Entropy over the Binomial and Negative Binomial Channels}, author = {Camilo G Taborda and Fernando Perez-Cruz}, url = {http://ieeexplore.ieee.org/lpdocs/epic03/wrapper.htm?arnumber=6284304}, issn = {2157-8095}, year = {2012}, date = {2012-01-01}, booktitle = {2012 IEEE International Symposium on Information Theory Proceedings}, pages = {696--700}, publisher = {IEEE}, address = {Cambridge, MA}, abstract = {We study the relation of the mutual information and relative entropy over the Binomial and Negative Binomial channels with estimation theoretical quantities, in which we extend already known results for Gaussian and Poisson channels. We establish general expressions for these information theory concepts with a direct connection with estimation theory through the conditional mean estimation and a particular loss function.}, keywords = {Channel estimation, conditional mean estimation, Entropy, Estimation, estimation theoretical quantity, estimation theory, Gaussian channel, Gaussian channels, information theory concept, loss function, mean square error methods, Mutual information, negative binomial channel, Poisson channel, Random variables, relative entropy}, pubstate = {published}, tppubtype = {inproceedings} } We study the relation of the mutual information and relative entropy over the Binomial and Negative Binomial channels with estimation theoretical quantities, in which we extend already known results for Gaussian and Poisson channels. We establish general expressions for these information theory concepts with a direct connection with estimation theory through the conditional mean estimation and a particular loss function. |

## 2011 |

## Journal Articles |

Tuia, D; Verrelst, J; Alonso, L; Perez-Cruz, Fernando; Camps-Valls, Gustavo Multioutput Support Vector Regression for Remote Sensing Biophysical Parameter Estimation Journal Article IEEE Geoscience and Remote Sensing Letters, 8 (4), pp. 804–808, 2011, ISSN: 1545-598X. Abstract | Links | BibTeX | Tags: 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. |

## Inproceedings |

Maiz, Cristina S; Miguez, Joaquin On the Optimization of Transportation Routes with Multiple Destinations in Random Networks Inproceedings 2011 IEEE Statistical Signal Processing Workshop (SSP), pp. 349–352, IEEE, Nice, 2011, ISBN: 978-1-4577-0569-4. Abstract | Links | BibTeX | Tags: Approximation algorithms, communication networks, Estimation, graph theory, Histograms, intelligent transportation, Monte Carlo algorithm, Monte Carlo methods, multiple destinations, optimisation, Optimization, random networks, route optimization, routing, Sequential Monte Carlo, Signal processing algorithms, stochastic graph, Stochastic processes, telecommunication network routing, time-varying graph, transportation routes @inproceedings{Maiz2011, title = {On the Optimization of Transportation Routes with Multiple Destinations in Random Networks}, author = {Cristina S Maiz and Joaquin Miguez}, url = {http://ieeexplore.ieee.org/lpdocs/epic03/wrapper.htm?arnumber=5967701}, isbn = {978-1-4577-0569-4}, year = {2011}, date = {2011-01-01}, booktitle = {2011 IEEE Statistical Signal Processing Workshop (SSP)}, pages = {349--352}, publisher = {IEEE}, address = {Nice}, abstract = {Various practical problems in transportation research and routing in communication networks can be reduced to the computation of the best path that traverses a certain graph and visits a set of D specified destination nodes. Simple versions of this problem have received attention in the literature. Optimal solutions exist for the cases in which (a) D >; 1 and the graph is deterministic or (b) D = 1 and the graph is stochastic (and possibly time-dependent). Here, we address the general problem in which both D >; 1 and the costs of the edges in the graph are stochastic and time-varying. We tackle this complex global optimization problem by first converting it into an equivalent estimation problem and then computing a numerical solution using a sequential Monte Carlo algorithm. The advantage of the proposed technique over some standard methods (devised for graphs with time-invariant statistics) is illustrated by way of computer simulations.}, keywords = {Approximation algorithms, communication networks, Estimation, graph theory, Histograms, intelligent transportation, Monte Carlo algorithm, Monte Carlo methods, multiple destinations, optimisation, Optimization, random networks, route optimization, routing, Sequential Monte Carlo, Signal processing algorithms, stochastic graph, Stochastic processes, telecommunication network routing, time-varying graph, transportation routes}, pubstate = {published}, tppubtype = {inproceedings} } Various practical problems in transportation research and routing in communication networks can be reduced to the computation of the best path that traverses a certain graph and visits a set of D specified destination nodes. Simple versions of this problem have received attention in the literature. Optimal solutions exist for the cases in which (a) D >; 1 and the graph is deterministic or (b) D = 1 and the graph is stochastic (and possibly time-dependent). Here, we address the general problem in which both D >; 1 and the costs of the edges in the graph are stochastic and time-varying. We tackle this complex global optimization problem by first converting it into an equivalent estimation problem and then computing a numerical solution using a sequential Monte Carlo algorithm. The advantage of the proposed technique over some standard methods (devised for graphs with time-invariant statistics) is illustrated by way of computer simulations. |

## 2010 |

## Inproceedings |

Vazquez, Manuel A; Miguez, Joaquin Adaptive MLSD for MIMO Transmission Systems with Unknown Subchannel Orders Inproceedings 2010 7th International Symposium on Wireless Communication Systems, pp. 451–455, IEEE, York, 2010, ISSN: 2154-0217. Abstract | Links | BibTeX | Tags: Bit error rate, Channel estimation, channel impulse response, computational complexity, Estimation, frequency-selective multiple-input multiple-output, maximum likelihood sequence detection, maximum likelihood sequence estimation, MIMO, MIMO communication, MIMO transmission systems, multiple subchannels, per survivor processing methodology, pilot data, Receivers, Signal to noise ratio, Time frequency analysis, time selective MIMO channel @inproceedings{Vazquez2010, title = {Adaptive MLSD for MIMO Transmission Systems with Unknown Subchannel Orders}, author = {Manuel A Vazquez and Joaquin Miguez}, url = {http://ieeexplore.ieee.org/lpdocs/epic03/wrapper.htm?arnumber=5624335}, issn = {2154-0217}, year = {2010}, date = {2010-01-01}, booktitle = {2010 7th International Symposium on Wireless Communication Systems}, pages = {451--455}, publisher = {IEEE}, address = {York}, abstract = {In the equalization of frequency-selective multiple-input multiple-output (MIMO) channels it is usually assumed that the length of the channel impulse response (CIR), also referred to as the channel order, is known. However, this is not true in most practical situations and, in order to avoid the serious performance degradation that occurs when the CIR length is underestimated, a channel with "more than enough" taps is usually considered. This very frequently leads to overestimating the channel order, which increases the computational complexity of any maximum likelihood sequence detection (MLSD) algorithm, while degrading its performance at the same time. The problem of estimating a single channel order for a time and frequency selective MIMO channel has recently been tackled. However, this is an idealized approach, since a MIMO channel comprises multiple subchannels (as many as the number of inputs times that of the outputs), each of them possibly with its own order. In this paper, we introduce an algorithm for MLSD that incorporates the full estimation of the MIMO CIR parameters, including one channel order per output. The proposed technique is based on the per survivor processing (PSP) methodology, it admits both blind and semiblind implementations, depending on the availability of pilot data, and it is designed to work with time-selective channels. Besides the analytical derivation of the algorithm, we provide computer simulation results that illustrate the effectiveness of the resulting receiver.}, keywords = {Bit error rate, Channel estimation, channel impulse response, computational complexity, Estimation, frequency-selective multiple-input multiple-output, maximum likelihood sequence detection, maximum likelihood sequence estimation, MIMO, MIMO communication, MIMO transmission systems, multiple subchannels, per survivor processing methodology, pilot data, Receivers, Signal to noise ratio, Time frequency analysis, time selective MIMO channel}, pubstate = {published}, tppubtype = {inproceedings} } In the equalization of frequency-selective multiple-input multiple-output (MIMO) channels it is usually assumed that the length of the channel impulse response (CIR), also referred to as the channel order, is known. However, this is not true in most practical situations and, in order to avoid the serious performance degradation that occurs when the CIR length is underestimated, a channel with "more than enough" taps is usually considered. This very frequently leads to overestimating the channel order, which increases the computational complexity of any maximum likelihood sequence detection (MLSD) algorithm, while degrading its performance at the same time. The problem of estimating a single channel order for a time and frequency selective MIMO channel has recently been tackled. However, this is an idealized approach, since a MIMO channel comprises multiple subchannels (as many as the number of inputs times that of the outputs), each of them possibly with its own order. In this paper, we introduce an algorithm for MLSD that incorporates the full estimation of the MIMO CIR parameters, including one channel order per output. The proposed technique is based on the per survivor processing (PSP) methodology, it admits both blind and semiblind implementations, depending on the availability of pilot data, and it is designed to work with time-selective channels. Besides the analytical derivation of the algorithm, we provide computer simulation results that illustrate the effectiveness of the resulting receiver. |